step 1: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"pytest -q 2>&1","timeoutMs":60000}
tool shell failed: denied: "pytest -q 2>&1" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:b282c48db6c9d065533e8fd9b499bb2ef71f1cb74d2d83a60749b25030f89b4c kind tool-call:shell]
step 2: calling local:qwen3.6:35b-a3b
tool list <- {"path":""}
tool list ok: .campaign/
.git/
.github/
.gitignore
.pytest_cache/
CODE_OF_CONDUCT.md
CONTRIBUTING.md
LICENSE
MANIFEST.in
README.md
algorithms.egg-info/
algorithms/
docs/
pyproject.toml
tests/
[evidence record sha256:fe651ceb43dfcfb2cd90cd185cdc0194db1d23a58bddafb1f82075fe36f6ad25 kind tool-call:list]
step 3: calling local:qwen3.6:35b-a3b
tool list <- {"path":"tests"}
tool list ok: __pycache__/
test_array.py
test_audit_regressions.py
test_backtracking.py
test_bit_manipulation.py
test_community_algorithms.py
test_compression.py
test_data_structures.py
test_dynamic_programming.py
test_graph.py
test_greedy.py
test_heap.py
test_issue_fixes.py
test_iterative_segment_tree.py
test_linked_list.py
test_map.py
test_math.py
test_matrix.py
test_monomial.py
test_polynomial.py
test_queue.py
test_searching.py
test_set.py
test_sorting.py
test_stack.py
test_streaming.py
test_string.py
test_tree.py
test_veb_tree.py
[evidence record sha256:49944976a187e3ab3540c0a5c30558a76b7818ae4fbe0a25d299781a7209ef6b kind tool-call:list]
tool list <- {"path":"algorithms"}
tool list ok: __init__.py
__pycache__/
array/
backtracking/
bit_manipulation/
common/
compression/
data_structures/
dynamic_programming/
graph/
greedy/
heap/
linked_list/
map/
math/
matrix/
py.typed
queue/
searching/
set/
sorting/
stack/
streaming/
string/
tree/
[evidence record sha256:22e01082efcc78ebde35a053751d4c6cd91c0f8487c7ee60cad614434f140bde kind tool-call:list]
step 4: calling local:qwen3.6:35b-a3b
tool read <- {"path":"pyproject.toml"}
tool read ok: [build-system]
requires = ["setuptools>=68.0"]
build-backend = "setuptools.build_meta"

[project]
name = "algorithms"
version = "1.0.1"
description = "Pythonic Data Structures and Algorithms"
readme = "README.md"
license = "MIT"
requires-python = ">=3.10"
authors = [
    { name = "Algorithms Team & Contributors", email = "kwk236@gmail.com" },
]
classifiers = [
    "Programming Language :: Python :: 3",
    "Programming Language :: Python :: 3.10",
    "Programming Language :: Python :: 3.11",
    "Programming Language :: Python :: 3.12",
    "Programming Language :: Python :: 3.13",
    "Topic :: Software Development :: Libraries :: Python Modules",
    "Topic :: Education",
]

[project.urls]
Homepage = "https://github.com/keon/algorithms"
Repository = "https://github.com/keon/algorithms"

[project.optional-dependencies]
dev = [
    "pytest",
    "ruff",
    "mypy",
    "black",
]

[tool.setuptools.packages.find]
exclude = ["tests", "tests.*", "tools", "tools.*", "docs", "docs.*"]

[tool.pytest.ini_options]
testpaths = ["tests"]
addopts = ["-v", "--tb=short"]

[tool.ruff]
line-length = 88
target-version = "py310"

[tool.ruff.lint]
select = ["E", "W", "F", "I", "N", "UP", "B", "SIM"]

[tool.ruff.lint.isort]
known-first-party = ["algorithms"]

[tool.mypy]
python_version = "3.10"
warn_return_any = true
check_untyped_defs = true
disallow_untyped_defs = false

[tool.black]
line-length = 88
target-version = ["py310"]

[evidence record sha256:533f690bc9d0dfd6ec6af198a5898b4e73755e6d8034a041501d28cdbcd76008 kind tool-call:read]
step 5: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"which pytest && pytest -q --no-header 2>&1 || python -m pytest -q --no-header 2>&1","timeoutMs":120000}
tool shell failed: denied: "which pytest && pytest -q --no-header 2>&1 || python -m pytest -q --no-header 2>&1" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:7a706f9f3d64b0ac246df327eafd9bce1e22a7dc4e50f2b8707013a652d9748e kind tool-call:shell]
step 6: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"python3 -m pytest -q 2>&1","timeoutMs":120000}
tool shell failed: denied: "python3 -m pytest -q 2>&1" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:3f3fdaf058ae472aa90520e997a78dc8656dcd364043bd5c97501fbc75d046c4 kind tool-call:shell]
step 7: calling local:qwen3.6:35b-a3b
tool read <- {"path":"tests/test_array.py"}
tool read ok: import unittest

from algorithms.array import (
    Interval,
    delete_nth,
    delete_nth_naive,
    flatten,
    flatten_iter,
    garage,
    get_longest_non_repeat_v1,
    get_longest_non_repeat_v2,
    josephus,
    limit,
    longest_non_repeat_v1,
    longest_non_repeat_v2,
    max_ones_index,
    merge_intervals,
    missing_ranges,
    move_zeros,
    n_sum,
    plus_one_v1,
    plus_one_v2,
    plus_one_v3,
    remove_duplicates,
    rotate_v1,
    rotate_v2,
    rotate_v3,
    summarize_ranges,
    three_sum,
    top_1,
    trimmean,
    two_sum,
)


class TestJosephus(unittest.TestCase):
    def test_josephus(self):

        a = ["1", "2", "3", "4", "5", "6", "7", "8", "9"]
        josephus_generator = josephus(a, 3)
        self.assertEqual(next(josephus_generator), "3")
        self.assertEqual(next(josephus_generator), "6")
        self.assertEqual(next(josephus_generator), "9")
        self.assertEqual(next(josephus_generator), "4")
        self.assertEqual(next(josephus_generator), "8")
        self.assertEqual(next(josephus_generator), "5")
        self.assertEqual(next(josephus_generator), "2")
        self.assertEqual(next(josephus_generator), "7")
        self.assertEqual(next(josephus_generator), "1")
        self.assertRaises(StopIteration, next, josephus_generator)


class TestDeleteNth(unittest.TestCase):
    def test_delete_nth_naive(self):

        self.assertListEqual(
            delete_nth_naive([20, 37, 20, 21, 37, 21, 21], n=1), [20, 37, 21]
        )
        self.assertListEqual(
            delete_nth_naive([1, 1, 3, 3, 7, 2, 2, 2, 2], n=3), [1, 1, 3, 3, 7, 2, 2, 2]
        )
        self.assertListEqual(
            delete_nth_naive([1, 2, 3, 1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 3, 1], n=3),
            [1, 2, 3, 1, 1, 2, 2, 3, 3, 4, 5],
        )
        self.assertListEqual(delete_nth_naive([], n=5), [])
        self.assertListEqual(
            delete_nth_naive([1, 2, 3, 1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 3, 1], n=0), []
        )

    def test_delete_nth(self):

        self.assertListEqual(
            delete_nth([20, 37, 20, 21, 37, 21, 21], n=1), [20, 37, 21]
        )
        self.assertListEqual(
            delete_nth([1, 1, 3, 3, 7, 2, 2, 2, 2], n=3), [1, 1, 3, 3, 7, 2, 2, 2]
        )
        self.assertListEqual(
            delete_nth([1, 2, 3, 1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 3, 1], n=3),
            [1, 2, 3, 1, 1, 2, 2, 3, 3, 4, 5],
        )
        self.assertListEqual(delete_nth([], n=5), [])
        self.assertListEqual(
            delete_nth([1, 2, 3, 1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 3, 1], n=0), []
        )


class TestFlatten(unittest.TestCase):
    def test_flatten(self):

        nested_list = [2, 1, [3, [4, 5], 6], 7, [8]]
        flattened = flatten(nested_list)
        self.assertEqual(flattened, [2, 1, 3, 4, 5, 6, 7, 8])

        nested_list = [[3, [4, 5], 6], 7, [8]]
        flattened = flatten(nested_list)
        self.assertEqual(flattened, [3, 4, 5, 6, 7, 8])

        nested_list = [[], [8]]
        flattened = flatten(nested_list)
        self.assertEqual(flattened, [8])

    def test_flatten_iter(self):

        nested_list = [2, 1, [3, [4, 5], 6], 7, [8]]
        flattened = flatten_iter(nested_list)
        self.assertEqual(next(flattened), 2)
        self.assertEqual(next(flattened), 1)
        self.assertEqual(next(flattened), 3)
        self.assertEqual(next(flattened), 4)
        self.assertEqual(next(flattened), 5)
        self.assertEqual(next(flattened), 6)
        self.assertEqual(next(flattened), 7)
        self.assertEqual(next(flattened), 8)
        self.assertRaises(StopIteration, next, flattened)

        nested_list = [[3, [4, 5], 6], 7, [8]]
        flattened = flatten_iter(nested_list)
        self.assertEqual(next(flattened), 3)
        self.assertEqual(next(flattened), 4)
        self.assertEqual(next(flattened), 5)
        self.assertEqual(next(flattened), 6)
        self.assertEqual(next(flattened), 7)
        self.assertEqual(next(flattened), 8)
        self.assertRaises(StopIteration, next, flattened)

        nested_list = [[], [8]]
        flattened = flatten_iter(nested_list)
        self.assertEqual(next(flattened), 8)
        self.assertRaises(StopIteration, next, flattened)


class TestGarage(unittest.TestCase):
    def test_garage(self):

        initial = [1, 2, 3, 0, 4]
        final = [0, 3, 2, 1, 4]
        steps, seq = garage(initial, final)

        self.assertEqual(steps, 4)
        self.assertListEqual(
            seq, [[0, 2, 3, 1, 4], [2, 0, 3, 1, 4], [2, 3, 0, 1, 4], [0, 3, 2, 1, 4]]
        )


class TestLongestNonRepeat(unittest.TestCase):
    def test_longest_non_repeat_v1(self):

        string = "abcabcbb"
        self.assertEqual(longest_non_repeat_v1(string), 3)

        string = "bbbbb"
        self.assertEqual(longest_non_repeat_v1(string), 1)

        string = "pwwkew"
        self.assertEqual(longest_non_repeat_v1(string), 3)

        string = "dvdf"
        self.assertEqual(longest_non_repeat_v1(string), 3)

        string = "asjrgapa"
        self.assertEqual(longest_non_repeat_v1(string), 6)

    def test_longest_non_repeat_v2(self):

        string = "abcabcbb"
        self.assertEqual(longest_non_repeat_v2(string), 3)

        string = "bbbbb"
        self.assertEqual(longest_non_repeat_v2(string), 1)

        string = "pwwkew"
        self.assertEqual(longest_non_repeat_v2(string), 3)

        string = "dvdf"
        self.assertEqual(longest_non_repeat_v2(string), 3)

        string = "asjrgapa"
        self.assertEqual(longest_non_repeat_v2(string), 6)

    def test_get_longest_non_repeat_v1(self):
        string = "abcabcbb"
        self.assertEqual(get_longest_non_repeat_v1(string), (3, "abc"))

        string = "bbbbb"
        self.assertEqual(get_longest_non_repeat_v1(string), (1, "b"))

        string = "pwwkew"
        self.assertEqual(get_longest_non_repeat_v1(string), (3, "wke"))

        string = "dvdf"
        self.assertEqual(get_longest_non_repeat_v1(string), (3, "vdf"))

        string = "asjrgapa"
        self.assertEqual(get_longest_non_repeat_v1(string), (6, "sjrgap"))

    def test_get_longest_non_repeat_v2(self):
        string = "abcabcbb"
        self.assertEqual(get_longest_non_repeat_v2(string), (3, "abc"))

        string = "bbbbb"
        self.assertEqual(get_longest_non_repeat_v2(string), (1, "b"))

        string = "pwwkew"
        self.assertEqual(get_longest_non_repeat_v2(string), (3, "wke"))

        string = "dvdf"
        self.assertEqual(get_longest_non_repeat_v2(string), (3, "vdf"))

        string = "asjrgapa"
        self.assertEqual(get_longest_non_repeat_v2(string), (6, "sjrgap"))


class TestMaxOnesIndex(unittest.TestCase):
    def test_max_ones_index(self):

        self.assertEqual(9, max_ones_index([1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]))
        self.assertEqual(3, max_ones_index([1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]))
        self.assertEqual(-1, max_ones_index([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))


class TestMergeInterval(unittest.TestCase):
    def test_merge(self):
        interval_list = [[1, 3], [2, 6], [8, 10], [15, 18]]
        intervals = [Interval(i[0], i[1]) for i in interval_list]
        merged_intervals = Interval.merge(intervals)
        self.assertEqual(
            merged_intervals, [Interval(1, 6), Interval(8, 10), Interval(15, 18)]
        )

    def test_merge_intervals(self):
        interval_list = [[1, 3], [2, 6], [8, 10], [15, 18]]
        merged_intervals = merge_intervals(interval_list)
        self.assertEqual(merged_intervals, [[1, 6], [8, 10], [15, 18]])


class TestMissingRanges(unittest.TestCase):
    def test_missing_ranges(self):

        arr = [3, 5, 10, 11, 12, 15, 19]

        self.assertListEqual(
            missing_ranges(arr, 0, 20),
            [(0, 2), (4, 4), (6, 9), (13, 14), (16, 18), (20, 20)],
        )

        self.assertListEqual(
            missing_ranges(arr, 6, 100), [(6, 9), (13, 14), (16, 18), (20, 100)]
        )


class TestMoveZeros(unittest.TestCase):
    def test_move_zeros(self):

        self.assertListEqual(
            move_zeros([False, 1, 0, 1, 2, 0, 1, 3, "a"]),
            [False, 1, 1, 2, 1, 3, "a", 0, 0],
        )

        self.assertListEqual(
            move_zeros([0, 34, "rahul", [], None, 0, True, 0]),
            [34, "rahul", [], None, True, 0, 0, 0],
        )


class TestPlusOne(unittest.TestCase):
    def test_plus_one_v1(self):

        self.assertListEqual(plus_one_v1([0]), [1])
        self.assertListEqual(plus_one_v1([9]), [1, 0])
        self.assertListEqual(plus_one_v1([1, 0, 9]), [1, 1, 0])
        self.assertListEqual(plus_one_v1([9, 9, 8, 0, 0, 9]), [9, 9, 8, 0, 1, 0])
        self.assertListEqual(plus_one_v1([9, 9, 9, 9]), [1, 0, 0, 0, 0])

    def test_plus_one_v2(self):

        self.assertListEqual(plus_one_v2([0]), [1])
        self.assertListEqual(plus_one_v2([9]), [1, 0])
        self.assertListEqual(plus_one_v2([1, 0, 9]), [1, 1, 0])
        self.assertListEqual(plus_one_v2([9, 9, 8, 0, 0, 9]), [9, 9, 8, 0, 1, 0])
        self.assertListEqual(plus_one_v2([9, 9, 9, 9]), [1, 0, 0, 0, 0])

    def test_plus_one_v3(self):

        self.assertListEqual(plus_one_v3([0]), [1])
        self.assertListEqual(plus_one_v3([9]), [1, 0])
        self.assertListEqual(plus_one_v3([1, 0, 9]), [1, 1, 0])
        self.assertListEqual(plus_one_v3([9, 9, 8, 0, 0, 9]), [9, 9, 8, 0, 1, 0])
        self.assertListEqual(plus_one_v3([9, 9, 9, 9]), [1, 0, 0, 0, 0])


class TestRemoveDuplicate(unittest.TestCase):
    def test_remove_duplicates(self):
        self.assertListEqual(
            remove_duplicates(
                [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 7, 7, 8, 8, 9, 10, 10]
            ),
            [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
        )
        self.assertListEqual(
            remove_duplicates(["hey", "hello", "hello", "car", "house", "house"]),
            ["hey", "hello", "car", "house"],
        )
        self.assertListEqual(
            remove_duplicates([True, True, False, True, False, None, None]),
            [True, False, None],
        )
        self.assertListEqual(
            remove_duplicates([1, 1, "hello", "hello", True, False, False]),
            [1, "hello", False],
        )
        self.assertListEqual(
            remove_duplicates([1, "hello", True, False]), [1, "hello", False]
        )


class TestRotateArray(unittest.TestCase):
    def test_rotate_v1(self):

        self.assertListEqual(
            rotate_v1([1, 2, 3, 4, 5, 6, 7], k=3), [5, 6, 7, 1, 2, 3, 4]
        )
        self.assertListEqual(
            rotate_v1([1, 2, 3, 4, 5, 6, 7], k=1), [7, 1, 2, 3, 4, 5, 6]
        )
        self.assertListEqual(
            rotate_v1([1, 2, 3, 4, 5, 6, 7], k=7), [1, 2, 3, 4, 5, 6, 7]
        )
        self.assertListEqual(rotate_v1([1, 2], k=111), [2, 1])

    def test_rotate_v2(self):

        self.assertListEqual(
            rotate_v2([1, 2, 3, 4, 5, 6, 7], k=3), [5, 6, 7, 1, 2, 3, 4]
        )
        self.assertListEqual(
            rotate_v2([1, 2, 3, 4, 5, 6, 7], k=1), [7, 1, 2, 3, 4, 5, 6]
        )
        self.assertListEqual(
            rotate_v2([1, 2, 3, 4, 5, 6, 7], k=7), [1, 2, 3, 4, 5, 6, 7]
        )
        self.assertListEqual(rotate_v2([1, 2], k=111), [2, 1])

    def test_rotate_v3(self):

        self.assertListEqual(
            rotate_v3([1, 2, 3, 4, 5, 6, 7], k=3), [5, 6, 7, 1, 2, 3, 4]
        )
        self.assertListEqual(
            rotate_v3([1, 2, 3, 4, 5, 6, 7], k=1), [7, 1, 2, 3, 4, 5, 6]
        )
        self.assertListEqual(
            rotate_v3([1, 2, 3, 4, 5, 6, 7], k=7), [1, 2, 3, 4, 5, 6, 7]
        )
        self.assertListEqual(rotate_v3([1, 2], k=111), [2, 1])


class TestSummaryRanges(unittest.TestCase):
    def test_summarize_ranges(self):

        self.assertListEqual(
            summarize_ranges([0, 1, 2, 4, 5, 7]), [(0, 2), (4, 5), (7, 7)]
        )
        self.assertListEqual(
            summarize_ranges([-5, -4, -3, 1, 2, 4, 5, 6]), [(-5, -3), (1, 2), (4, 6)]
        )
        self.assertListEqual(summarize_ranges([-2, -1, 0, 1, 2]), [(-2, 2)])


class TestThreeSum(unittest.TestCase):
    def test_three_sum(self):

        self.assertSetEqual(three_sum([-1, 0, 1, 2, -1, -4]), {(-1, 0, 1), (-1, -1, 2)})

        self.assertSetEqual(
            three_sum([-1, 3, 1, 2, -1, -4, -2]), {(-4, 1, 3), (-2, -1, 3), (-1, -1, 2)}
        )


class TestTwoSum(unittest.TestCase):
    def test_two_sum(self):

        self.assertTupleEqual((0, 2), two_sum([2, 11, 7, 9], target=9))
        self.assertTupleEqual((0, 3), two_sum([-3, 5, 2, 3, 8, -9], target=0))

        self.assertIsNone(two_sum([-3, 5, 2, 3, 8, -9], target=6))


class TestTrimmean(unittest.TestCase):
    def test_trimmean(self):

        self.assertEqual(trimmean([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 20), 5.5)
        self.assertEqual(trimmean([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 20), 6.0)


class TestTop1(unittest.TestCase):
    def test_top_1(self):
        self.assertListEqual(top_1([1, 1, 2, 2, 3]), [1, 2])
        self.assertListEqual(top_1([1, 2, 3, 324, 234, 23, 23, 1, 23, 23]), [23])


class TestLimit(unittest.TestCase):
    def test_limit(self):
        self.assertListEqual(limit([1, 2, 3, 4, 5]), [1, 2, 3, 4, 5])
        self.assertListEqual(limit([1, 2, 3, 4, 5], 2, 4), [2, 3, 4])
        self.assertListEqual(limit([1, 2, 3, 4, 5], 2), [2, 3, 4, 5])
        self.assertListEqual(limit([1, 2, 3, 4, 5], None, 4), [1, 2, 3, 4])


class TestNSum(unittest.TestCase):
    def test_n_sum(self):
        self.assertEqual(n_sum(2, [-3, 5, 2, 3, 8, -9], 6), [])  # noqa: E501
        self.assertEqual(
            n_sum(3, [-5, -4, -3, -2, -1, 0, 1, 2, 3], 0),
            sorted(
                [
                    [-5, 2, 3],
                    [-2, 0, 2],
                    [-4, 1, 3],
                    [-3, 1, 2],
                    [-1, 0, 1],
                    [-2, -1, 3],
                    [-3, 0, 3],
                ]
            ),
        )  # noqa: E501
        self.assertEqual(
            n_sum(3, [-1, 0, 1, 2, -1, -4], 0), sorted([[-1, -1, 2], [-1, 0, 1]])
        )  # noqa: E501
        self.assertEqual(
            n_sum(4, [1, 0, -1, 0, -2, 2], 0),
            sorted([[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]),
        )  # noqa: E501
        self.assertEqual(
            n_sum(
                4, [7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 4, -3, -2], 10
            ),
            sorted(
                [
                    [-6, 2, 7, 7],
                    [-6, 3, 6, 7],
                    [-6, 4, 5, 7],
                    [-6, 4, 6, 6],
                    [-5, 1, 7, 7],
                    [-5, 2, 6, 7],
                    [-5, 3, 5, 7],
                    [-5, 3, 6, 6],
                    [-5, 4, 4, 7],
                    [-5, 4, 5, 6],
                    [-4, 0, 7, 7],
                    [-4, 1, 6, 7],
                    [-4, 2, 5, 7],
                    [-4, 2, 6, 6],
                    [-4, 3, 4, 7],
                    [-4, 3, 5, 6],
                    [-4, 4, 4, 6],
                    [-3, -1, 7, 7],
                    [-3, 0, 6, 7],
                    [-3, 1, 5, 7],
                    [-3, 1, 6, 6],
                    [-3, 2, 4, 7],
                    [-3, 2, 5, 6],
                    [-3, 3, 4, 6],
                    [-3, 4, 4, 5],
                    [-2, -2, 7, 7],
                    [-2, -1, 6, 7],
                    [-2, 0, 5, 7],
                    [-2, 0, 6, 6],
                    [-2, 1, 4, 7],
                    [-2, 1, 5, 6],
                    [-2, 2, 3, 7],
                    [-2, 2, 4, 6],
                    [-2, 3, 4, 5],
                    [-1, 0, 4, 7],
                    [-1, 0, 5, 6],
                    [-1, 1, 3, 7],
                    [-1, 1, 4, 6],
                    [-1, 2, 3, 6],
                    [-1, 2, 4, 5],
                    [-1, 3, 4, 4],
                    [0, 1, 2, 7],
                    [0, 1, 3, 6],
                    [0, 1, 4, 5],
                    [0, 2, 3, 5],
                    [0, 2, 4, 4],
                    [1, 2, 3, 4],
                ]
            ),
        )  # noqa: E501

        self.assertEqual(
            n_sum(
                2,
                [[-3, 0], [-2, 1], [2, 2], [3, 3], [8, 4], [-9, 5]],
                0,  # noqa: E501
                sum_closure=lambda a, b: a[0] + b[0],
            ),  # noqa: E501
            [[[-3, 0], [3, 3]], [[-2, 1], [2, 2]]],
        )  # noqa: E501
        self.assertEqual(
            n_sum(
                2,
                [[-3, 0], [-2, 1], [2, 2], [3, 3], [8, 4], [-9, 5]],
                [0, 3],  # noqa: E501
                sum_closure=lambda a, b: [a[0] + b[0], a[1] + b[1]],  # noqa: E501
                same_closure=lambda a, b: a[0] == b[0] and a[1] == b[1],
            ),  # noqa: E501
            [[[-3, 0], [3, 3]], [[-2, 1], [2, 2]]],
        )  # noqa: E501
        self.assertEqual(
            n_sum(
                2,
                [[-3, 0], [-2, 1], [2, 2], [3, 3], [8, 4], [-9, 5]],
                -5,  # noqa: E501
                sum_closure=lambda a, b: [a[0] + b[1], a[1] + b[0]],  # noqa: E501
                compare_closure=lambda a, b: -1 if a[0] < b else 1 if a[0] > b else 0,
            ),  # noqa: E501
            [[[-9, 5], [8, 4]]],
        )  # noqa: E501


if __name__ == "__main__":
    unittest.main()

[evidence record sha256:c9ecc9330075f1b136d474da07ae5f468c1591dec464a69aae72a8c88294f500 kind tool-call:read]
tool read <- {"path":"tests/test_dynamic_programming.py"}
tool read ok: import unittest

from algorithms.dynamic_programming import (
    Item,
    Job,
    climb_stairs,
    climb_stairs_optimized,
    combination_sum_bottom_up,
    combination_sum_topdown,
    count,
    edit_distance,
    egg_drop,
    fib_iter,
    fib_list,
    fib_recursive,
    find_k_factor,
    get_maximum_value,
    hosoya_testing,
    house_robber,
    int_divide,
    longest_increasing_subsequence,
    max_profit_naive,
    max_profit_optimized,
    planting_trees,
    regex_matching,
    schedule,
)


class TestBuySellStock(unittest.TestCase):
    def test_max_profit_naive(self):
        self.assertEqual(max_profit_naive([7, 1, 5, 3, 6, 4]), 5)
        self.assertEqual(max_profit_naive([7, 6, 4, 3, 1]), 0)

    def test_max_profit_optimized(self):
        self.assertEqual(max_profit_optimized([7, 1, 5, 3, 6, 4]), 5)
        self.assertEqual(max_profit_optimized([7, 6, 4, 3, 1]), 0)


class TestClimbingStairs(unittest.TestCase):
    def test_climb_stairs(self):
        self.assertEqual(climb_stairs(2), 2)
        self.assertEqual(climb_stairs(10), 89)

    def test_climb_stairs_optimized(self):
        self.assertEqual(climb_stairs_optimized(2), 2)
        self.assertEqual(climb_stairs_optimized(10), 89)


class TestCoinChange(unittest.TestCase):
    def test_count(self):
        self.assertEqual(count([1, 2, 3], 4), 4)
        self.assertEqual(count([2, 5, 3, 6], 10), 5)


class TestCombinationSum(unittest.TestCase):
    def test_combination_sum_topdown(self):
        self.assertEqual(combination_sum_topdown([1, 2, 3], 4), 7)

    def test_combination_sum_bottom_up(self):
        self.assertEqual(combination_sum_bottom_up([1, 2, 3], 4), 7)


class TestEditDistance(unittest.TestCase):
    def test_edit_distance(self):
        self.assertEqual(edit_distance("food", "money"), 4)
        self.assertEqual(edit_distance("horse", "ros"), 3)


class TestEggDrop(unittest.TestCase):
    def test_egg_drop(self):
        self.assertEqual(egg_drop(1, 2), 2)
        self.assertEqual(egg_drop(2, 6), 3)
        self.assertEqual(egg_drop(3, 14), 4)


class TestFib(unittest.TestCase):
    def test_fib_recursive(self):
        self.assertEqual(fib_recursive(10), 55)
        self.assertEqual(fib_recursive(30), 832040)

    def test_fib_list(self):
        self.assertEqual(fib_list(10), 55)
        self.assertEqual(fib_list(30), 832040)

    def test_fib_iter(self):
        self.assertEqual(fib_iter(10), 55)
        self.assertEqual(fib_iter(30), 832040)


class TestHosoyaTriangle(unittest.TestCase):
    """[summary]
    Test for the file hosoya_triangle

    Arguments:
        unittest {[type]} -- [description]
    """

    def test_hosoya(self):
        self.assertEqual([1], hosoya_testing(1))
        self.assertEqual(
            [1, 1, 1, 2, 1, 2, 3, 2, 2, 3, 5, 3, 4, 3, 5, 8, 5, 6, 6, 5, 8],
            hosoya_testing(6),
        )
        self.assertEqual(
            [
                1,
                1,
                1,
                2,
                1,
                2,
                3,
                2,
                2,
                3,
                5,
                3,
                4,
                3,
                5,
                8,
                5,
                6,
                6,
                5,
                8,
                13,
                8,
                10,
                9,
                10,
                8,
                13,
                21,
                13,
                16,
                15,
                15,
                16,
                13,
                21,
                34,
                21,
                26,
                24,
                25,
                24,
                26,
                21,
                34,
                55,
                34,
                42,
                39,
                40,
                40,
                39,
                42,
                34,
                55,
            ],
            hosoya_testing(10),
        )


class TestHouseRobber(unittest.TestCase):
    def test_house_robber(self):
        self.assertEqual(44, house_robber([1, 2, 16, 3, 15, 3, 12, 1]))


class TestJobScheduling(unittest.TestCase):
    def test_job_scheduling(self):
        job1, job2 = Job(1, 3, 2), Job(2, 3, 4)
        self.assertEqual(4, schedule([job1, job2]))


class TestKnapsack(unittest.TestCase):
    def test_get_maximum_value(self):
        item1, item2, item3 = Item(60, 10), Item(100, 20), Item(120, 30)
        self.assertEqual(220, get_maximum_value([item1, item2, item3], 50))

        item1, item2, item3, item4 = Item(60, 5), Item(50, 3), Item(70, 4), Item(30, 2)
        self.assertEqual(80, get_maximum_value([item1, item2, item3, item4], 5))


class TestLongestIncreasingSubsequence(unittest.TestCase):
    def test_longest_increasing_subsequence(self):
        sequence = [1, 101, 10, 2, 3, 100, 4, 6, 2]
        self.assertEqual(5, longest_increasing_subsequence(sequence))


class TestLongestIncreasingSubsequenceOptimized(unittest.TestCase):
    def test_longest_increasing_subsequence_optimized(self):
        sequence = [1, 101, 10, 2, 3, 100, 4, 6, 2]
        self.assertEqual(5, longest_increasing_subsequence(sequence))


class TestLongestIncreasingSubsequenceOptimized2(unittest.TestCase):
    def test_longest_increasing_subsequence_optimized2(self):
        sequence = [1, 101, 10, 2, 3, 100, 4, 6, 2]
        self.assertEqual(5, longest_increasing_subsequence(sequence))


class TestIntDivide(unittest.TestCase):
    def test_int_divide(self):
        self.assertEqual(5, int_divide(4))
        self.assertEqual(42, int_divide(10))
        self.assertEqual(204226, int_divide(50))


class TestDpKFactor(unittest.TestCase):
    def test_kfactor(self):
        # Test 1
        n1 = 4
        k1 = 1
        self.assertEqual(find_k_factor(n1, k1), 1)

        # Test 2
        n2 = 7
        k2 = 1
        self.assertEqual(find_k_factor(n2, k2), 70302)

        # Test 3
        n3 = 10
        k3 = 2
        self.assertEqual(find_k_factor(n3, k3), 74357)

        # Test 4
        n4 = 8
        k4 = 2
        self.assertEqual(find_k_factor(n4, k4), 53)

        # Test 5
        n5 = 9
        k5 = 1
        self.assertEqual(find_k_factor(n5, k5), 71284044)


class TestPlantingTrees(unittest.TestCase):
    def test_simple(self):
        # arrange
        trees = [0, 1, 10, 10]
        length = 10
        width = 1

        # act
        res = planting_trees(trees, length, width)

        # assert
        self.assertEqual(res, 2.414213562373095)

    def test_simple2(self):
        # arrange
        trees = [0, 3, 5, 5, 6, 9]
        length = 10
        width = 1

        # act
        res = planting_trees(trees, length, width)

        # assert
        self.assertEqual(res, 9.28538328578604)


class TestRegexMatching(unittest.TestCase):
    def test_none_0(self):
        s = ""
        p = ""
        self.assertTrue(regex_matching.is_match(s, p))

    def test_none_1(self):
        s = ""
        p = "a"
        self.assertFalse(regex_matching.is_match(s, p))

    def test_no_symbol_equal(self):
        s = "abcd"
        p = "abcd"
        self.assertTrue(regex_matching.is_match(s, p))

    def test_no_symbol_not_equal_0(self):
        s = "abcd"
        p = "efgh"
        self.assertFalse(regex_matching.is_match(s, p))

    def test_no_symbol_not_equal_1(self):
        s = "ab"
        p = "abb"
        self.assertFalse(regex_matching.is_match(s, p))

    def test_symbol_0(self):
        s = ""
        p = "a*"
        self.assertTrue(regex_matching.is_match(s, p))

    def test_symbol_1(self):
        s = "a"
        p = "ab*"
        self.assertTrue(regex_matching.is_match(s, p))

    def test_symbol_2(self):
        # E.g.
        #   s a b b
        # p 1 0 0 0
        # a 0 1 0 0
        # b 0 0 1 0
        # * 0 1 1 1
        s = "abb"
        p = "ab*"
        self.assertTrue(regex_matching.is_match(s, p))


if __name__ == "__main__":
    unittest.main()

[evidence record sha256:dcc47d12a5440e80d94e315aac15dd6a37b4fb94c87bbef7625cc44f95ae8c53 kind tool-call:read]
tool read <- {"path":"tests/test_bit_manipulation.py"}
tool read ok: import random
import unittest

from algorithms.bit_manipulation import (
    add_bitwise_operator,
    binary_gap,
    bytes_big_endian_to_int,
    bytes_little_endian_to_int,
    clear_bit,
    count_flips_to_convert,
    count_ones_iter,
    count_ones_recur,
    find_difference,
    find_missing_number,
    find_missing_number2,
    flip_bit_longest_seq,
    get_bit,
    has_alternative_bit,
    has_alternative_bit_fast,
    insert_mult_bits,
    insert_one_bit,
    int_to_bytes_big_endian,
    int_to_bytes_little_endian,
    is_power_of_two,
    remove_bit,
    reverse_bits,
    set_bit,
    single_number,
    single_number2,
    single_number3,
    subsets,
    swap_pair,
    update_bit,
)


class TestSuite(unittest.TestCase):
    def setUp(self):
        """Initialize seed."""
        random.seed("test")

    def test_add_bitwise_operator(self):
        self.assertEqual(5432 + 97823, add_bitwise_operator(5432, 97823))
        self.assertEqual(0, add_bitwise_operator(0, 0))
        self.assertEqual(10, add_bitwise_operator(10, 0))
        self.assertEqual(10, add_bitwise_operator(0, 10))

    def test_count_ones_recur(self):

        # 8 -> 1000
        self.assertEqual(1, count_ones_recur(8))

        # 109 -> 1101101
        self.assertEqual(5, count_ones_recur(109))

        # 63 -> 111111
        self.assertEqual(6, count_ones_recur(63))

        # 0 -> 0
        self.assertEqual(0, count_ones_recur(0))

    def test_count_ones_iter(self):

        # 8 -> 1000
        self.assertEqual(1, count_ones_iter(8))

        # 109 -> 1101101
        self.assertEqual(5, count_ones_iter(109))

        # 63 -> 111111
        self.assertEqual(6, count_ones_iter(63))

        # 0 -> 0
        self.assertEqual(0, count_ones_iter(0))

    def test_count_flips_to_convert(self):
        # 29: 11101 and 15: 01111
        self.assertEqual(2, count_flips_to_convert(29, 15))
        # 45: 0000101101 and 987: 1111011011
        self.assertEqual(8, count_flips_to_convert(45, 987))
        # 34: 100010
        self.assertEqual(0, count_flips_to_convert(34, 34))
        # 34: 100010 and 53: 110101
        self.assertEqual(4, count_flips_to_convert(34, 53))

    def test_find_missing_number(self):

        self.assertEqual(7, find_missing_number([4, 1, 3, 0, 6, 5, 2]))
        self.assertEqual(0, find_missing_number([1]))
        self.assertEqual(1, find_missing_number([0]))

        nums = [i for i in range(100000) if i != 12345]
        random.shuffle(nums)
        self.assertEqual(12345, find_missing_number(nums))

    def test_find_missing_number2(self):

        self.assertEqual(7, find_missing_number2([4, 1, 3, 0, 6, 5, 2]))
        self.assertEqual(0, find_missing_number2([1]))
        self.assertEqual(1, find_missing_number2([0]))

        nums = [i for i in range(100000) if i != 12345]
        random.shuffle(nums)
        self.assertEqual(12345, find_missing_number2(nums))

    def test_flip_bit_longest_seq(self):
        # 1775: 11011101111
        self.assertEqual(8, flip_bit_longest_seq(1775))
        # 5: 101
        self.assertEqual(3, flip_bit_longest_seq(5))
        # 71: 1000111
        self.assertEqual(4, flip_bit_longest_seq(71))
        # 0: 0
        self.assertEqual(1, flip_bit_longest_seq(0))

    def test_is_power_of_two(self):

        self.assertTrue(is_power_of_two(64))
        self.assertFalse(is_power_of_two(91))
        self.assertTrue(is_power_of_two(2**1001))
        self.assertTrue(is_power_of_two(1))
        self.assertFalse(is_power_of_two(0))

    def test_reverse_bits(self):

        self.assertEqual(43261596, reverse_bits(964176192))
        self.assertEqual(964176192, reverse_bits(43261596))
        self.assertEqual(1, reverse_bits(2147483648))

        # bin(0) => 00000000000000000000000000000000
        self.assertEqual(0, reverse_bits(0))

        # bin(2**32 - 1) => 11111111111111111111111111111111
        self.assertEqual(2**32 - 1, reverse_bits(2**32 - 1))

    def test_single_number(self):

        random.seed("test")

        self.assertEqual(0, single_number([1, 0, 2, 1, 2, 3, 3]))
        self.assertEqual(101, single_number([101]))

        single = random.randint(1, 100000)
        nums = [random.randint(1, 100000) for _ in range(1000)]
        nums *= 2  # nums contains pairs of random integers
        nums.append(single)
        random.shuffle(nums)

        self.assertEqual(single, single_number(nums))

    def test_single_number2(self):

        self.assertEqual(3, single_number2([4, 2, 3, 2, 1, 1, 4, 2, 4, 1]))
        single = random.randint(1, 100000)
        nums = [random.randint(1, 100000) for _ in range(1000)]
        nums *= 3  # nums contains triplets of random integers
        nums.append(single)
        random.shuffle(nums)
        self.assertEqual(single, single_number2(nums))

    def test_single_number3(self):
        self.assertEqual(sorted([2, 5]), sorted(single_number3([2, 1, 5, 6, 6, 1])))
        self.assertEqual(sorted([4, 3]), sorted(single_number3([9, 9, 4, 3])))

    def test_subsets(self):

        self.assertSetEqual(
            subsets([1, 2, 3]),
            {(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)},
        )

        self.assertSetEqual(
            subsets([10, 20, 30, 40]),
            {
                (10, 40),
                (10, 20, 40),
                (10, 30),
                (10, 20, 30, 40),
                (40,),
                (10, 30, 40),
                (30,),
                (20, 30),
                (30, 40),
                (10,),
                (),
                (10, 20),
                (20, 40),
                (20, 30, 40),
                (10, 20, 30),
                (20,),
            },
        )

    def test_get_bit(self):
        # 22 = 10110
        self.assertEqual(1, get_bit(22, 2))
        self.assertEqual(0, get_bit(22, 3))

    def test_set_bit(self):
        # 22 = 10110  --> after set bit at 3th position: 30 = 11110
        self.assertEqual(30, set_bit(22, 3))

    def test_clear_bit(self):
        # 22 = 10110 --> after clear bit at 2nd position: 20 = 10010
        self.assertEqual(18, clear_bit(22, 2))

    def test_update_bit(self):
        # 22 = 10110 --> after update bit at 3th position with
        # value 1: 30 = 11110
        self.assertEqual(30, update_bit(22, 3, 1))
        # 22 = 10110 --> after update bit at 2nd position with
        # value 0: 20 = 10010
        self.assertEqual(18, update_bit(22, 2, 0))

    def test_int_to_bytes_big_endian(self):
        self.assertEqual(b"\x11", int_to_bytes_big_endian(17))

    def test_int_to_bytes_little_endian(self):
        self.assertEqual(b"\x11", int_to_bytes_little_endian(17))

    def test_bytes_big_endian_to_int(self):
        self.assertEqual(17, bytes_big_endian_to_int(b"\x11"))

    def test_bytes_little_endian_to_int(self):
        self.assertEqual(17, bytes_little_endian_to_int(b"\x11"))

    def test_swap_pair(self):
        # 22: 10110  --> 41: 101001
        self.assertEqual(41, swap_pair(22))
        # 10: 1010   --> 5 : 0101
        self.assertEqual(5, swap_pair(10))

    def test_find_difference(self):
        self.assertEqual("e", find_difference("abcd", "abecd"))

    def test_has_alternative_bit(self):
        self.assertTrue(has_alternative_bit(5))
        self.assertFalse(has_alternative_bit(7))
        self.assertFalse(has_alternative_bit(11))
        self.assertTrue(has_alternative_bit(10))

    def test_has_alternative_bit_fast(self):
        self.assertTrue(has_alternative_bit_fast(5))
        self.assertFalse(has_alternative_bit_fast(7))
        self.assertFalse(has_alternative_bit_fast(11))
        self.assertTrue(has_alternative_bit_fast(10))

    def test_insert_one_bit(self):
        """
        Input: num = 10101 (21)
        insert_one_bit(num, 1, 2): 101101 (45)
        insert_one_bit(num, 0 ,2): 101001 (41)
        insert_one_bit(num, 1, 5): 110101 (53)
        insert_one_bit(num, 1, 0): 101010 (42)
        """
        self.assertEqual(45, insert_one_bit(21, 1, 2))
        self.assertEqual(41, insert_one_bit(21, 0, 2))
        self.assertEqual(53, insert_one_bit(21, 1, 5))
        self.assertEqual(43, insert_one_bit(21, 1, 0))

    def test_insert_mult_bits(self):
        """
        Input: num = 101 (5)
        insert_mult_bits(num, 7, 3, 1): 101111 (47)
        insert_mult_bits(num, 7, 3, 0): 101111 (47)
        insert_mult_bits(num, 7, 3, 3): 111101 (61)
        """
        self.assertEqual(47, insert_mult_bits(5, 7, 3, 1))
        self.assertEqual(47, insert_mult_bits(5, 7, 3, 0))
        self.assertEqual(61, insert_mult_bits(5, 7, 3, 3))

    def test_remove_bit(self):
        """
        Input: num = 10101 (21)
        remove_bit(num, 2): output = 1001 (9)
        remove_bit(num, 4): output = 101 (5)
        remove_bit(num, 0): output = 1010 (10)
        """
        self.assertEqual(9, remove_bit(21, 2))
        self.assertEqual(5, remove_bit(21, 4))
        self.assertEqual(10, remove_bit(21, 0))

    def test_binary_gap(self):
        # 22 = 10110
        self.assertEqual(2, binary_gap(22))
        # 6 = 110
        self.assertEqual(1, binary_gap(6))
        # 8 = 1000
        self.assertEqual(0, binary_gap(8))
        # 145 = 10010001
        self.assertEqual(4, binary_gap(145))


if __name__ == "__main__":
    unittest.main()

[evidence record sha256:b0b3f01a7597791faecdf3ed11357ad662e389aacbe82017dcfb059dde399b3a kind tool-call:read]
step 8: calling local:qwen3.6:35b-a3b
tool list <- {"path":".campaign"}
tool list ok: venv/
[evidence record sha256:0fd9bd35153b6c5d9c1755f9f00f95b5d27755946c7aba55196d169cd096e926 kind tool-call:list]
tool shell <- {"command":"ls -la .github/ 2>/dev/null; cat .github/workflows/*.yml 2>/dev/null || echo \"no workflows\""}
tool shell failed: denied: /dev/null resolves outside the workspace /work
[evidence record sha256:35818657c44f199178ede136439fa6c3adc0c283b0c2a1339ef6124efb5b46bb kind tool-call:shell]
step 9: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"python3 -m pytest tests/ -q 2>&1 | head -100","timeoutMs":180000}
tool shell failed: denied: "python3 -m pytest tests/ -q 2>&1 | head -100" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:73f7961546e3b5bd56c50352eef1ed13c02e29a332994c83356a987088be4399 kind tool-call:shell]
step 10: calling local:qwen3.6:35b-a3b
tool list <- {"path":".campaign/venv"}
tool list ok: bin/
include/
lib/
lib64
pyvenv.cfg
[evidence record sha256:2c3765dc01839b88a940d34f23e22ebac1e33309d3a60a6723db44c21ac344a8 kind tool-call:list]
tool read <- {"path":".github/workflows/1.yml"}
tool read failed: failed: ENOENT: no such file or directory, open '/work/.github/workflows/1.yml', caused by ENOENT
[evidence record sha256:585380f9c2629137ff17d6ed681bd13f18fedeb6501c885de06b38f86b42358e kind tool-call:read]
step 11: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"echo hello","timeoutMs":10000}
tool shell failed: denied: "echo hello" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:6233d92cb8b25b40aaca46753f299a95f5da6f59b92996f9d2425abb0fc1cf15 kind tool-call:shell]
step 12: calling local:qwen3.6:35b-a3b
tool list <- {"path":".campaign/venv/bin"}
tool list ok: Activate.ps1
activate
activate.csh
activate.fish
black
blackd
dmypy
mypy
mypyc
pip
pip3
pip3.12
py.test
pygmentize
pytest
python
python3
python3.12
ruff
stubgen
stubtest
[evidence record sha256:c886611a4775bb5aee2e3cc2037fd25af6f63f34cf21448ab8728c5c8f5d251d kind tool-call:list]
step 13: calling local:qwen3.6:35b-a3b
tool list <- {"path":"algorithms/array"}
tool list ok: __init__.py
__pycache__/
delete_nth.py
flatten.py
garage.py
josephus.py
limit.py
longest_non_repeat.py
max_ones_index.py
merge_intervals.py
missing_ranges.py
move_zeros.py
n_sum.py
plus_one.py
remove_duplicates.py
rotate.py
summarize_ranges.py
three_sum.py
top_1.py
trimmean.py
two_sum.py
[evidence record sha256:37acf1c79cfa8dbf46f66b3c7b4c34017a2e39e7bbf0b32879fcb5a94f1716ae kind tool-call:list]
tool list <- {"path":"algorithms/dynamic_programming"}
tool list ok: __init__.py
__pycache__/
bitmask.py
buy_sell_stock.py
climbing_stairs.py
coin_change.py
combination_sum.py
count_paths_dp.py
edit_distance.py
egg_drop.py
fib.py
hosoya_triangle.py
house_robber.py
int_divide.py
job_scheduling.py
k_factor.py
knapsack.py
longest_common_subsequence.py
longest_increasing.py
matrix_chain_order.py
max_product_subarray.py
max_subarray.py
min_cost_path.py
num_decodings.py
planting_trees.py
regex_matching.py
rod_cut.py
word_break.py
[evidence record sha256:0396df7f97fa3f47016a813b90bb36e2aa7fd80f990df614d50fba196a096fca kind tool-call:list]
tool list <- {"path":"algorithms/bit_manipulation"}
tool list ok: __init__.py
__pycache__/
add_bitwise_operator.py
binary_gap.py
bit_operation.py
bytes_int_conversion.py
count_flips_to_convert.py
count_ones.py
find_difference.py
find_missing_number.py
flip_bit_longest_sequence.py
gray_code.py
has_alternative_bit.py
insert_bit.py
power_of_two.py
remove_bit.py
reverse_bits.py
single_number.py
single_number2.py
single_number3.py
subsets.py
swap_pair.py
[evidence record sha256:2d33bb40a75dcfa5f8ef6e7d99592c16e42f7cada7fe185292e51b9a54018e73 kind tool-call:list]
step 14: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"git log --oneline -20"}
tool shell ok: exit code: 0
stdout:
0b64801 campaign: seeded defect
7f71a91 Merge pull request #2770 from intagliated/add_dag_longest_path
[evidence record sha256:160362cf8a4654d8dc078652ae68cbf6fc2e5a5ec34292cf427a40718a053b04 kind tool-call:shell]
step 15: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"git show --stat 0b64801"}
tool shell ok: exit code: 0
stdout:
commit 0b64801ff97fb532d2c01dc3fa48d6727b52ec84
Author: campaign <campaign@example.invalid>
Date:   Thu Sep 3 20:00:09 2026 -0600

    campaign: seeded defect

 algorithms/array/delete_nth.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)
[evidence record sha256:10efb23585f31fee7cbb3b17a72fe7321ccb1cee6c0d75ad3a5a13b32a5f211f kind tool-call:shell]
step 16: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/array/delete_nth.py"}
tool read ok: """
Delete Nth Occurrence

Given a list and a number N, create a new list that contains each element
of the original list at most N times, without reordering.

Reference: https://www.geeksforgeeks.org/remove-duplicates-from-an-array/

Complexity:
    delete_nth_naive:
        Time:  O(n^2) due to list.count()
        Space: O(n)
    delete_nth:
        Time:  O(n)
        Space: O(n)
"""

from __future__ import annotations

import collections


def delete_nth_naive(array: list[int], n: int) -> list[int]:
    """Keep at most n copies of each element using naive counting.

    Args:
        array: Source list of integers.
        n: Maximum number of allowed occurrences per element.

    Returns:
        New list with each element appearing at most n times.

    Examples:
        >>> delete_nth_naive([1, 2, 3, 1, 2, 1, 2, 3], 2)
        [1, 2, 3, 1, 2, 3]
    """
    result = []
    for num in array:
        if result.count(num) <= n:
            result.append(num)
    return result


def delete_nth(array: list[int], n: int) -> list[int]:
    """Keep at most n copies of each element using a hash table.

    Args:
        array: Source list of integers.
        n: Maximum number of allowed occurrences per element.

    Returns:
        New list with each element appearing at most n times.

    Examples:
        >>> delete_nth([1, 2, 3, 1, 2, 1, 2, 3], 2)
        [1, 2, 3, 1, 2, 3]
    """
    result = []
    counts = collections.defaultdict(int)

    for element in array:
        if counts[element] < n:
            result.append(element)
            counts[element] += 1

    return result

[evidence record sha256:bf651ffc40b944790d4a91b7bb16caf11b226e37b5491a0767a5c18b16c18f00 kind tool-call:read]
step 17: calling local:qwen3.6:35b-a3b
tool edit <- {"path":"algorithms/array/delete_nth.py","find":"        if result.count(num) <= n:","replace":"        if result.count(num) < n:"}
tool edit ok: replaced 1 occurrence(s) in algorithms/array/delete_nth.py
[evidence record sha256:65e23842745aea1837a7c03837bfe40dafc47483a52864a7c205e5a583dce0cd kind tool-call:edit]
step 18: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/array/delete_nth.py"}
tool read ok: """
Delete Nth Occurrence

Given a list and a number N, create a new list that contains each element
of the original list at most N times, without reordering.

Reference: https://www.geeksforgeeks.org/remove-duplicates-from-an-array/

Complexity:
    delete_nth_naive:
        Time:  O(n^2) due to list.count()
        Space: O(n)
    delete_nth:
        Time:  O(n)
        Space: O(n)
"""

from __future__ import annotations

import collections


def delete_nth_naive(array: list[int], n: int) -> list[int]:
    """Keep at most n copies of each element using naive counting.

    Args:
        array: Source list of integers.
        n: Maximum number of allowed occurrences per element.

    Returns:
        New list with each element appearing at most n times.

    Examples:
        >>> delete_nth_naive([1, 2, 3, 1, 2, 1, 2, 3], 2)
        [1, 2, 3, 1, 2, 3]
    """
    result = []
    for num in array:
        if result.count(num) < n:
            result.append(num)
    return result


def delete_nth(array: list[int], n: int) -> list[int]:
    """Keep at most n copies of each element using a hash table.

    Args:
        array: Source list of integers.
        n: Maximum number of allowed occurrences per element.

    Returns:
        New list with each element appearing at most n times.

    Examples:
        >>> delete_nth([1, 2, 3, 1, 2, 1, 2, 3], 2)
        [1, 2, 3, 1, 2, 3]
    """
    result = []
    counts = collections.defaultdict(int)

    for element in array:
        if counts[element] < n:
            result.append(element)
            counts[element] += 1

    return result

[evidence record sha256:415d0f17f4c7fff8b46cfb4ac40428984a25edea2cca71c305117a30a8846d0a kind tool-call:read]
step 19: calling local:qwen3.6:35b-a3b
tool shell <- {"command":".gampaign/venv/bin/pytest tests/test_array.py -q 2>&1"}
tool shell failed: denied: ".gampaign/venv/bin/pytest tests/test_array.py -q 2>&1" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:e6928d1ca6885f23f49f0ed85e70e553a4172d2cb24106ffc80bed6bea186639 kind tool-call:shell]
step 20: calling local:qwen3.6:35b-a3b
tool read <- {"path":"tests/test_array.py","maxBytes":300}
tool read ok: import unittest

from algorithms.array import (
    Interval,
    delete_nth,
    delete_nth_naive,
    flatten,
    flatten_iter,
    garage,
    get_longest_non_repeat_v1,
    get_longest_non_repeat_v2,
    josephus,
    limit,
    longest_non_repeat_v1,
    longest_non_repeat_v2,
    max_ones_ind
[truncated at 300 of 17433 bytes]
[evidence record sha256:13a095846cf9b875c0f181a5ae55d068bffa8a660ffd526183c835e84f6148e5 kind tool-call:read]
step 21: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/array/delete_nth.py"}
tool read ok: """
Delete Nth Occurrence

Given a list and a number N, create a new list that contains each element
of the original list at most N times, without reordering.

Reference: https://www.geeksforgeeks.org/remove-duplicates-from-an-array/

Complexity:
    delete_nth_naive:
        Time:  O(n^2) due to list.count()
        Space: O(n)
    delete_nth:
        Time:  O(n)
        Space: O(n)
"""

from __future__ import annotations

import collections


def delete_nth_naive(array: list[int], n: int) -> list[int]:
    """Keep at most n copies of each element using naive counting.

    Args:
        array: Source list of integers.
        n: Maximum number of allowed occurrences per element.

    Returns:
        New list with each element appearing at most n times.

    Examples:
        >>> delete_nth_naive([1, 2, 3, 1, 2, 1, 2, 3], 2)
        [1, 2, 3, 1, 2, 3]
    """
    result = []
    for num in array:
        if result.count(num) < n:
            result.append(num)
    return result


def delete_nth(array: list[int], n: int) -> list[int]:
    """Keep at most n copies of each element using a hash table.

    Args:
        array: Source list of integers.
        n: Maximum number of allowed occurrences per element.

    Returns:
        New list with each element appearing at most n times.

    Examples:
        >>> delete_nth([1, 2, 3, 1, 2, 1, 2, 3], 2)
        [1, 2, 3, 1, 2, 3]
    """
    result = []
    counts = collections.defaultdict(int)

    for element in array:
        if counts[element] < n:
            result.append(element)
            counts[element] += 1

    return result

[evidence record sha256:f6ab5a6e2475072ae759ce3e392e650b3f5a82e69b94174df4045080840f4101 kind tool-call:read]
step 22: calling local:qwen3.6:35b-a3b
tool claim <- {"predicate":"facts.exitCode == 0 && facts.textBytes > 0","record":"415d0f17f4c7fff8b46cfb4ac40428984a25edea2cca71c305117a30a8846d0a","recordKind":"tool-call:read","narrative":"Confirmed the fixed file has the correct condition < n instead of <= n in delete_nth_naive."}
tool claim failed: denied: input rejected: [
  {
    "origin": "string",
    "code": "invalid_format",
    "format": "regex",
    "pattern": "/^sha256:[0-9a-f]{64}$/",
    "path": [
      "record"
    ],
    "message": "Invalid string: must match pattern /^sha256:[0-9a-f]{64}$/"
  }
]
[evidence record sha256:0a108d0f7582290f0744928740e2ca7044713b0c06438ac77ab0809d0541ce6e kind tool-call:claim]
step 23: calling local:qwen3.6:35b-a3b
claim (unverified): **Summary:**

I found and fixed the seeded defect in this repository. 

**Root cause:** In `algorithms/array/delete_nth.py`, the `delete_nth_naive` function had an off-by-one error: it used `<= n` instead of `< n` when checking if an element could be added to the result. This caused elements to appear up to **n+1 times** instead of at most **n times**.

**Fix applied:** Changed line 38 from:
```python
if result.count(num) <= n:
```
to:
```python
if result.count(num) < n:
```

This is a minimal, targeted fix that aligns the behavior with the function's documented contract ("keep at most n copies of each element") and makes it consistent with `delete_nth` which already uses `< n`. The change was seeded in the commit "campaign: seeded defect" which only touched this one file.
stopped: completed after 23 steps, 329868 tokens
gate typecheck failed: the command exited 1 [evidence record sha256:0044c433a87f24e6d27ec0b25273df4669db622571c3d7cef22d0d73c0cb4e4f]
gate lint passed: the command exited 0 [evidence record sha256:e90bffeb39efc5b7d4e07b0c3ad7422b9924dd8f4520ed7ffcf2ad0e0d97217e]
gate format failed: the command exited 1 [evidence record sha256:bbc98585bfc3ae769e3e1203b305996d08f94c6a1b9618e15f389e15dda7a54b]
gate tests passed: the command exited 0 [evidence record sha256:50a8316738a1eff5e2d696810ab4fe9ee749c03d260a96bd97ecf4f581c70cec]
gate file-set failed: 1 file(s) changed but no file set was declared before editing. Declare the intended set first; the check is set membership, not judgement. [evidence record sha256:952bdbff3c7121c9daa12b53b5b383f2ffc3ee06c2f9044c1928ee70fc4dd1a3]
gate placeholder passed: no placeholder marker was introduced by this change [evidence record sha256:04cbfbf05767e77d5767fb5772e9a7e62cec4ae74d421e013fe257c5eccb892c]
gate secret-scan passed: no known credential pattern appears in the added lines [evidence record sha256:1205c218e3298f2b2a033cfedf23b7ee3ea0c6b62794e4df970e745e5f7a0cb4]
gate behaviour-probe passed: 0 changed function(s) still answer to their inputs. [evidence record sha256:6c58dc822ecce8f4da2f5c78e5027adb86eef9574d10c896a93cc27d285aa5df]
gate diff-budget passed (advisory): within budget: 1 file(s) and 1 added line(s) [evidence record sha256:ede4b1a546ba6f4583c33140cd1c857444d0095fb5d2eff66db7030505370e36]
auto-resolve attempt 1 of 2
step 1: calling local:qwen3.6:35b-a3b
plan: I'll analyze this systematically. The quality gates are failing due to mypy type errors, format issues, and a file-set gate issue. Let me first explore the project structure and understand the codebase.
tool list <- {"path":"."}
tool list ok: .campaign/
.git/
.github/
.gitignore
.mypy_cache/
.pytest_cache/
.ruff_cache/
CODE_OF_CONDUCT.md
CONTRIBUTING.md
LICENSE
MANIFEST.in
README.md
algorithms.egg-info/
algorithms/
docs/
pyproject.toml
tests/
[evidence record sha256:bd3c072804366252dde64d1ee3ffe655e38022cdf66c0a58cf96b0251dc713f2 kind tool-call:list]
step 2: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"cd /home/user/repos/algorithms-python && python -m pytest -q 2>&1 | tail -80","timeoutMs":120000}
tool shell failed: denied: /home/user/repos/algorithms-python resolves outside the workspace /work
[evidence record sha256:7b54918e217dfb7207d1d87eea8619c78baa2a4c9b2fc31024d87e2a41c275aa kind tool-call:shell]
step 3: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"pwd && ls"}
tool shell ok: exit code: 0
stdout:
/work
CODE_OF_CONDUCT.md
CONTRIBUTING.md
LICENSE
MANIFEST.in
README.md
algorithms
algorithms.egg-info
docs
pyproject.toml
tests
[evidence record sha256:ee16f5379530fa876acf04644ee520ad6e8ecd67814f6e7932b7d1fe99371549 kind tool-call:shell]
step 4: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"pwd && head -5 pyproject.toml"}
tool shell ok: exit code: 0
stdout:
/work
[build-system]
requires = ["setuptools>=68.0"]
build-backend = "setuptools.build_meta"

[project]
[evidence record sha256:21809c1b611425336c56ba6e130bbd6771fcc5871f2456ae2ce3e8260693b195 kind tool-call:shell]
step 5: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"python -m pytest -q 2>&1 | tail -80","timeoutMs":300000}
tool shell failed: denied: "python -m pytest -q 2>&1 | tail -80" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:243dddd11d5c99cf7ab179c0c0916004ad166fe3f245b2dd78a37c39c7a143dc kind tool-call:shell]
step 6: calling local:qwen3.6:35b-a3b
stopped: empty-response after 6 steps, 136372 tokens
gate typecheck failed: the command exited 1 [evidence record sha256:3707867429783716ba6abfe6b2034c18b786d9bc17b28d68ef1b4cadac43cb42]
gate lint passed: the command exited 0 [evidence record sha256:94a4495fb87fdc2f40ce3e52709dda0145ce8d2829cdf4e527841f7a64f8be02]
gate format failed: the command exited 1 [evidence record sha256:356bb1afa244bab88d0bff280e5ec42b63e5a73db3c2d0659f4411657cc0a353]
gate tests passed: the command exited 0 [evidence record sha256:7d7b7c16c37ea7d5b467bce872f52d2619f0cf5089d5b8030e9ec7d522f159ef]
gate file-set failed: 1 file(s) changed but no file set was declared before editing. Declare the intended set first; the check is set membership, not judgement. [evidence record sha256:a19dac5a6fcab0dc5413855574c0cd85632a92f7b50c2bfd21af23fd8f76ce5f]
gate placeholder passed: no placeholder marker was introduced by this change [evidence record sha256:6ab4a60c77fbee0a6e8337589bb53775332ffb0cc3347a678c83b90c1c1257c8]
gate secret-scan passed: no known credential pattern appears in the added lines [evidence record sha256:0d1bddaaa0335ae01c8ded7b8c8df77a28e4d5968164123819f75b8963b3a344]
gate behaviour-probe passed: 0 changed function(s) still answer to their inputs. [evidence record sha256:e4544917a11298f6a754745d2738fe0f6523c4e67aad3f27582878f46f5e3ebd]
gate diff-budget passed (advisory): within budget: 1 file(s) and 1 added line(s) [evidence record sha256:7ff4b1f10fd971599241eba5c7b92342e09bc8c3fe67b6d0f096db24aa42773c]
ratchet accepted attempt 1: the ratchet accepted the attempt: no measure moved the wrong way (not compared: testsCollected, changedLineCoverage) [evidence record sha256:db5ae403987de35885f52e6dbf4fae8f584564c3b1be637486415a7f7d5597e5]
auto-resolve attempt 2 of 2
step 1: calling local:qwen3.6:35b-a3b
plan: I'll start by understanding the current state of the project and then fix the issues systematically. Let me first check what files exist and run the tests to see the failures.
tool list <- {"path":"."}
tool list ok: .campaign/
.git/
.github/
.gitignore
.mypy_cache/
.pytest_cache/
.ruff_cache/
CODE_OF_CONDUCT.md
CONTRIBUTING.md
LICENSE
MANIFEST.in
README.md
algorithms.egg-info/
algorithms/
docs/
pyproject.toml
tests/
[evidence record sha256:8de6372f7d329580fcb49f86084ff3d4b134e8d59a231d1d6644f79d628b29e8 kind tool-call:list]
step 2: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"pytest -q 2>&1 | head -100","timeoutMs":120000}
tool shell failed: denied: "pytest -q 2>&1 | head -100" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:549b080d7911d0a76d86f7e837e4ac7693912ae92c797864d9a70e6be2869fdd kind tool-call:shell]
step 3: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"python -m pytest -q 2>&1 | head -100","timeoutMs":120000}
tool shell failed: denied: "python -m pytest -q 2>&1 | head -100" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:65bc3e3127f7560048f8c373520a58720f924545f019c6cbe7a59c17203a9a65 kind tool-call:shell]
step 4: calling local:qwen3.6:35b-a3b
tool read <- {"path":"pyproject.toml"}
tool read ok: [build-system]
requires = ["setuptools>=68.0"]
build-backend = "setuptools.build_meta"

[project]
name = "algorithms"
version = "1.0.1"
description = "Pythonic Data Structures and Algorithms"
readme = "README.md"
license = "MIT"
requires-python = ">=3.10"
authors = [
    { name = "Algorithms Team & Contributors", email = "kwk236@gmail.com" },
]
classifiers = [
    "Programming Language :: Python :: 3",
    "Programming Language :: Python :: 3.10",
    "Programming Language :: Python :: 3.11",
    "Programming Language :: Python :: 3.12",
    "Programming Language :: Python :: 3.13",
    "Topic :: Software Development :: Libraries :: Python Modules",
    "Topic :: Education",
]

[project.urls]
Homepage = "https://github.com/keon/algorithms"
Repository = "https://github.com/keon/algorithms"

[project.optional-dependencies]
dev = [
    "pytest",
    "ruff",
    "mypy",
    "black",
]

[tool.setuptools.packages.find]
exclude = ["tests", "tests.*", "tools", "tools.*", "docs", "docs.*"]

[tool.pytest.ini_options]
testpaths = ["tests"]
addopts = ["-v", "--tb=short"]

[tool.ruff]
line-length = 88
target-version = "py310"

[tool.ruff.lint]
select = ["E", "W", "F", "I", "N", "UP", "B", "SIM"]

[tool.ruff.lint.isort]
known-first-party = ["algorithms"]

[tool.mypy]
python_version = "3.10"
warn_return_any = true
check_untyped_defs = true
disallow_untyped_defs = false

[tool.black]
line-length = 88
target-version = ["py310"]

[evidence record sha256:49f6893f7b092d286ecfed85f7a5572031ee48bdbfce944008495a34dcaa1caf kind tool-call:read]
step 5: calling local:qwen3.6:35b-a3b
tool list <- {"path":"algorithms"}
tool list ok: __init__.py
__pycache__/
array/
backtracking/
bit_manipulation/
common/
compression/
data_structures/
dynamic_programming/
graph/
greedy/
heap/
linked_list/
map/
math/
matrix/
py.typed
queue/
searching/
set/
sorting/
stack/
streaming/
string/
tree/
[evidence record sha256:7f9723243835346a69cb5bf5cd0c79598c58ab4c8973dfd33aa0ea4f71ecc095 kind tool-call:list]
step 6: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"git diff --name-only 2>/dev/null || echo \"no git changes\""}
tool shell failed: denied: /dev/null resolves outside the workspace /work
[evidence record sha256:7c03de3519e773f568503e7308b20d5e80f6a0a0b92314f9b8720ff1d8ae0730 kind tool-call:shell]
step 7: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/math/polynomial.py"}
tool read ok: """
Polynomial and Monomial Arithmetic

A symbolic algebra system for polynomials and monomials supporting addition,
subtraction, multiplication, division, substitution, and polynomial long
division with Fraction-based exact arithmetic.

Reference: https://en.wikipedia.org/wiki/Polynomial

Complexity:
    Time:  Varies by operation
    Space: O(number of monomials)
"""

from __future__ import annotations

from collections.abc import Iterable
from fractions import Fraction
from functools import reduce
from numbers import Rational


class Monomial:
    """A monomial represented by a coefficient and variable-to-power mapping."""

    def __init__(
        self, variables: dict[int, int], coeff: int | float | Fraction | None = None
    ) -> None:
        """Create a monomial with the given variables and coefficient.

        Args:
            variables: Dictionary mapping variable indices to their powers.
            coeff: The coefficient (defaults to 0 if empty, 1 otherwise).

        Examples:
            >>> _ = Monomial({1: 1})  # (a_1)^1
            >>> _ = Monomial({1: 3, 2: 2}, 12)  # 12(a_1)^3(a_2)^2
        """
        self.variables = dict()

        if coeff is None:
            coeff = Fraction(0, 1) if len(variables) == 0 else Fraction(1, 1)
        elif coeff == 0:
            self.coeff = Fraction(0, 1)
            return

        if len(variables) == 0:
            self.coeff = Monomial._rationalize_if_possible(coeff)
            return

        for i in variables:
            if variables[i] != 0:
                self.variables[i] = variables[i]
        self.coeff = Monomial._rationalize_if_possible(coeff)

    @staticmethod
    def _rationalize_if_possible(
        num: int | float | Fraction,
    ) -> Fraction | float:
        """Convert numbers to Fraction when possible.

        Args:
            num: A numeric value.

        Returns:
            A Fraction if the input is Rational, otherwise the original value.
        """
        if isinstance(num, Rational):
            res = Fraction(num, 1)
            return Fraction(res.numerator, res.denominator)
        else:
            return num

    def equal_upto_scalar(self, other: object) -> bool:
        """Check if other is a monomial equivalent to self up to scalar multiple.

        Args:
            other: Another Monomial to compare.

        Returns:
            True if both have the same variables with the same powers.

        Raises:
            ValueError: If other is not a Monomial.
        """
        if not isinstance(other, Monomial):
            raise ValueError("Can only compare monomials.")
        return other.variables == self.variables

    def __add__(self, other: int | float | Fraction) -> Monomial:
        """Add two monomials or a monomial with a scalar.

        Args:
            other: A Monomial, int, float, or Fraction to add.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If monomials have different variables.
        """
        if isinstance(other, (int, float, Fraction)):
            return self.__add__(Monomial({}, Monomial._rationalize_if_possible(other)))

        if not isinstance(other, Monomial):
            raise ValueError("Can only add monomials, ints, floats, or Fractions.")

        if self.variables == other.variables:
            mono = {i: self.variables[i] for i in self.variables}
            return Monomial(
                mono, Monomial._rationalize_if_possible(self.coeff + other.coeff)
            ).clean()

        raise ValueError(
            f"Cannot add {str(other)} to {self.__str__()} "
            "because they don't have same variables."
        )

    def __eq__(self, other: object) -> bool:
        """Check equality of two monomials.

        Args:
            other: Another Monomial to compare.

        Returns:
            True if both monomials are equal.
        """
        if not isinstance(other, Monomial):
            return NotImplemented
        return self.equal_upto_scalar(other) and self.coeff == other.coeff

    def __mul__(self, other: int | float | Fraction) -> Monomial:
        """Multiply two monomials or a monomial with a scalar.

        Args:
            other: A Monomial, int, float, or Fraction to multiply.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If other is not a valid type.
        """
        if isinstance(other, (float, int, Fraction)):
            mono = {i: self.variables[i] for i in self.variables}
            return Monomial(
                mono, Monomial._rationalize_if_possible(self.coeff * other)
            ).clean()

        if not isinstance(other, Monomial):
            raise ValueError("Can only multiply monomials, ints, floats, or Fractions.")
        else:
            mono = {i: self.variables[i] for i in self.variables}
            for i in other.variables:
                if i in mono:
                    mono[i] += other.variables[i]
                else:
                    mono[i] = other.variables[i]

            temp = dict()
            for k in mono:
                if mono[k] != 0:
                    temp[k] = mono[k]

            return Monomial(
                temp, Monomial._rationalize_if_possible(self.coeff * other.coeff)
            ).clean()

    def inverse(self) -> Monomial:
        """Compute the multiplicative inverse of this monomial.

        Returns:
            The inverse Monomial.

        Raises:
            ValueError: If the coefficient is zero.
        """
        mono = {i: self.variables[i] for i in self.variables if self.variables[i] != 0}
        for i in mono:
            mono[i] *= -1
        if self.coeff == 0:
            raise ValueError("Coefficient must not be 0.")
        return Monomial(mono, Monomial._rationalize_if_possible(1 / self.coeff)).clean()

    def __truediv__(self, other: int | float | Fraction) -> Monomial:
        """Divide this monomial by another monomial or scalar.

        Args:
            other: A Monomial, int, float, or Fraction divisor.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If dividing by zero.
        """
        if isinstance(other, (int, float, Fraction)):
            mono = {i: self.variables[i] for i in self.variables}
            if other == 0:
                raise ValueError("Cannot divide by 0.")
            return Monomial(
                mono, Monomial._rationalize_if_possible(self.coeff / other)
            ).clean()

        o = other.inverse()
        return self.__mul__(o)

    def __floordiv__(self, other: int | float | Fraction) -> Monomial:
        """Floor division (same as true division for monomials).

        Args:
            other: A Monomial, int, float, or Fraction divisor.

        Returns:
            The resulting Monomial.
        """
        return self.__truediv__(other)

    def clone(self) -> Monomial:
        """Create a deep copy of this monomial.

        Returns:
            A new Monomial with the same variables and coefficient.
        """
        temp_variables = {i: self.variables[i] for i in self.variables}
        return Monomial(
            temp_variables, Monomial._rationalize_if_possible(self.coeff)
        ).clean()

    def clean(self) -> Monomial:
        """Remove variables with zero power.

        Returns:
            A cleaned Monomial.
        """
        temp_variables = {
            i: self.variables[i] for i in self.variables if self.variables[i] != 0
        }
        return Monomial(temp_variables, Monomial._rationalize_if_possible(self.coeff))

    def __sub__(self, other: int | float | Fraction) -> Monomial:
        """Subtract a value from this monomial.

        Args:
            other: A Monomial, int, float, or Fraction to subtract.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If monomials have different variables.
        """
        if isinstance(other, (int, float, Fraction)):
            mono = {
                i: self.variables[i] for i in self.variables if self.variables[i] != 0
            }
            if len(mono) != 0:
                raise ValueError("Can only subtract like monomials.")
            other_term = Monomial(mono, Monomial._rationalize_if_possible(other))
            return self.__sub__(other_term)
        if not isinstance(other, Monomial):
            raise ValueError("Can only subtract monomials")
        return self.__add__(other.__mul__(Fraction(-1, 1)))

    def __hash__(self) -> int:
        """Hash based on the underlying variables.

        Returns:
            An integer hash value.
        """
        arr = []
        for i in sorted(self.variables):
            if self.variables[i] > 0:
                for _ in range(self.variables[i]):
                    arr.append(i)
        return hash(tuple(arr))

    def all_variables(self) -> set:
        """Get the set of all variable indices in this monomial.

        Returns:
            A set of variable indices.
        """
        return set(sorted(self.variables.keys()))

    def substitute(
        self,
        substitutions: int | float | Fraction | dict[int, int | float | Fraction],
    ) -> Fraction:
        """Evaluate the monomial by substituting values for variables.

        Args:
            substitutions: A single value applied to all variables, or a
                dict mapping variable indices to values.

        Returns:
            The evaluated result.

        Raises:
            ValueError: If some variables are not given values.
        """
        if isinstance(substitutions, (int, float, Fraction)):
            substitutions = {
                v: Monomial._rationalize_if_possible(substitutions)
                for v in self.all_variables()
            }
        else:
            if not self.all_variables().issubset(set(substitutions.keys())):
                raise ValueError("Some variables didn't receive their values.")
        if self.coeff == 0:
            return Fraction(0, 1)
        ans = Monomial._rationalize_if_possible(self.coeff)
        for k in self.variables:
            ans *= Monomial._rationalize_if_possible(
                substitutions[k] ** self.variables[k]
            )
        return Monomial._rationalize_if_possible(ans)

    def __str__(self) -> str:
        """Get a string representation of the monomial.

        Returns:
            A human-readable string.
        """
        if len(self.variables) == 0:
            return str(self.coeff)

        result = str(self.coeff)
        result += "("
        for i in self.variables:
            temp = f"a_{str(i)}"
            if self.variables[i] > 1:
                temp = "(" + temp + f")**{self.variables[i]}"
            elif self.variables[i] < 0:
                temp = "(" + temp + f")**(-{-self.variables[i]})"
            elif self.variables[i] == 0:
                continue
            else:
                temp = "(" + temp + ")"
            result += temp
        return result + ")"


class Polynomial:
    """A polynomial represented as a set of Monomial terms."""

    def __init__(
        self, monomials: Iterable[int | float | Fraction | Monomial]
    ) -> None:
        """Create a polynomial from an iterable of monomials or scalars.

        Args:
            monomials: An iterable of Monomial, int, float, or Fraction values.

        Raises:
            ValueError: If an element is not a valid type.
        """
        self.monomials: set = set()
        for m in monomials:
            if any(map(lambda x: isinstance(m, x), [int, float, Fraction])):
                self.monomials |= {Monomial({}, m)}
            elif isinstance(m, Monomial):
                self.monomials |= {m}
            else:
                raise ValueError(
                    "Iterable should have monomials, int, float, or Fraction."
                )
        self.monomials -= {Monomial({}, 0)}

    @staticmethod
    def _rationalize_if_possible(
        num: int | float | Fraction,
    ) -> Fraction | float:
        """Convert numbers to Fraction when possible.

        Args:
            num: A numeric value.

        Returns:
            A Fraction if the input is Rational, otherwise the original value.
        """
        if isinstance(num, Rational):
            res = Fraction(num, 1)
            return Fraction(res.numerator, res.denominator)
        else:
            return num

    def __add__(self, other: int | float | Fraction | Monomial) -> Polynomial:
        """Add a polynomial, monomial, or scalar to this polynomial.

        Args:
            other: Value to add.

        Returns:
            The resulting Polynomial.

        Raises:
            ValueError: If other is not a valid type.
        """
        if isinstance(other, (int, float, Fraction)):
            return self.__add__(
                Monomial({}, Polynomial._rationalize_if_possible(other))
            )
        elif isinstance(other, Monomial):
            monos = {m.clone() for m in self.monomials}

            for _own_monos in monos:
                if _own_monos.equal_upto_scalar(other):
                    scalar = _own_monos.coeff
                    monos -= {_own_monos}
                    temp_variables = {i: other.variables[i] for i in other.variables}
                    monos |= {
                        Monomial(
                            temp_variables,
                            Polynomial._rationalize_if_possible(scalar + other.coeff),
                        )
                    }
                    return Polynomial([z for z in monos])

            monos |= {other.clone()}
            return Polynomial([z for z in monos])
        elif isinstance(other, Polynomial):
            temp = list(z for z in {m.clone() for m in self.all_monomials()})

            p = Polynomial(temp)
            for o in other.all_monomials():
                p = p.__add__(o.clone())
            return p
        else:
            raise ValueError(
                "Can only add int, float, Fraction, Monomials, "
                "or Polynomials to Polynomials."
            )

    def __sub__(self, other: int | float | Fraction | Monomial) -> Polynomial:
        """Subtract a polynomial, monomial, or scalar from this polynomial.

        Args:
            other: Value to subtract.

        Returns:
            The resulting Polynomial.

        Raises:
            ValueError: If other is not a valid type.
        """
        if isinstance(other, (int, float, Fraction)):
            return self.__sub__(
                Monomial({}, Polynomial._rationalize_if_possible(other))
            )
        elif isinstance(other, Monomial):
            monos = {m.clone() for m in self.all_monomials()}
            for _own_monos in monos:
                if _own_monos.equal_upto_scalar(other):
                    scalar = _own_monos.coeff
                    monos -= {_own_monos}
                    temp_variables = {i: other.variables[i] for i in other.variables}
                    monos |= {
                        Monomial(
                            temp_variables,
                            Polynomial._rationalize_if_possible(scalar - other.coeff),
                        )
                    }
                    return Polynomial([z for z in monos])

            to_insert = other.clone()
            to_insert.coeff *= -1

            monos |= {to_insert}
            return Polynomial([z for z in monos])

        elif isinstance(other, Polynomial):
            p = Polynomial(list(z for z in {m.clone() for m in self.all_monomials()}))
            for o in other.all_monomials():
                p = p.__sub__(o.clone())
            return p

        else:
            raise ValueError(
                "Can only subtract int, float, Fraction, "
                "Monomials, or Polynomials from Polynomials."
            )

    def __mul__(self, other: int | float | Fraction | Monomial) -> Polynomial:
        """Multiply this polynomial by another polynomial, monomial, or scalar.

        Args:
            other: Value to multiply by.

        Returns:
            The resulting Polynomial.

        Raises:
            ValueError: If other is not a valid type.
        """
        if isinstance(other, (int, float, Fraction, Monomial)):
            result = Polynomial([])
            monos = {m.clone() for m in self.all_monomials()}
            for m in monos:
                result = result.__add__(m.clone() * other)
            return result
        elif isinstance(other, Polynomial):
            temp_self = {m.clone() for m in self.all_monomials()}
            temp_other = {m.clone() for m in other.all_monomials()}

            result = Polynomial([])

            for i in temp_self:
                for j in temp_other:
                    result = result.__add__(i * j)

            return result
        else:
            raise ValueError(
                "Can only multiple int, float, Fraction, "
                "Monomials, or Polynomials with Polynomials."
            )

    def __floordiv__(self, other: int | float | Fraction | Monomial) -> Polynomial:
        """Floor division (same as true division for polynomials).

        Args:
            other: Divisor value.

        Returns:
            The resulting Polynomial.
        """
        return self.__truediv__(other)

    def __truediv__(self, other: int | float | Fraction | Monomial) -> Polynomial:
        """Divide this polynomial by another value.

        Args:
            other: Divisor (int, float, Fraction, Monomial, or Polynomial).

        Returns:
            The quotient Polynomial.

        Raises:
            ValueError: If other is not a valid type.
        """
        if isinstance(other, (int, float, Fraction)):
            return self.__truediv__(Monomial({}, other))
        elif isinstance(other, Monomial):
            poly_temp = reduce(
                lambda acc, val: acc + val,
                map(lambda x: x / other, [z for z in self.all_monomials()]),
                Polynomial([Monomial({}, 0)]),
            )
            return poly_temp
        elif isinstance(other, Polynomial):
            quotient, remainder = self.poly_long_division(other)
            return quotient

        raise ValueError(
            "Can only divide a polynomial by an int, float, "
            "Fraction, Monomial, or Polynomial."
        )

    def clone(self) -> Polynomial:
        """Create a deep copy of this polynomial.

        Returns:
            A new Polynomial with cloned monomials.
        """
        return Polynomial(list({m.clone() for m in self.all_monomials()}))

    def variables(self) -> set:
        """Get all variable indices present in this polynomial.

        Returns:
            A set of variable indices.
        """
        res = set()
        for i in self.all_monomials():
            res |= {j for j in i.variables}
        res = list(res)
        return set(res)

    def all_monomials(self) -> Iterable[Monomial]:
        """Get all non-zero monomials in this polynomial.

        Returns:
            A set of Monomial terms.
        """
        return {m for m in self.monomials if m != Monomial({}, 0)}

    def __eq__(self, other: object) -> bool:
        """Check equality of two polynomials.

        Args:
            other: Another Polynomial, Monomial, or scalar.

        Returns:
            True if both represent the same polynomial.

        Raises:
            ValueError: If other is not a valid type.
        """
        if isinstance(other, (int, float, Fraction)):
            other_poly = Polynomial([Monomial({}, other)])
            return self.__eq__(other_poly)
        elif isinstance(other, Monomial):
            return self.__eq__(Polynomial([other]))
        elif isinstance(other, Polynomial):
            return self.all_monomials() == other.all_monomials()
        else:
            raise ValueError(
                "Can only compare a polynomial with an int, "
                "float, Fraction, Monomial, or another Polynomial."
            )

    def subs(
        self,
        substitutions: int | float | Fraction | dict[int, int | float | Fraction],
    ) -> int | float | Fraction:
        """Evaluate the polynomial by substituting values for variables.

        Args:
            substitutions: A single value applied to all variables, or a
                dict mapping variable indices to values.

        Returns:
            The evaluated result.

        Raises:
            ValueError: If some variables are not given values.
        """
        if isinstance(substitutions, (int, float, Fraction)):
            substitutions = {
                i: Polynomial._rationalize_if_possible(substitutions)
                for i in set(self.variables())
            }
            return self.subs(substitutions)
        elif not isinstance(substitutions, dict):
            raise ValueError("The substitutions should be a dictionary.")
        if not self.variables().issubset(set(substitutions.keys())):
            raise ValueError("Some variables didn't receive their values.")

        ans = 0
        for m in self.all_monomials():
            ans += Polynomial._rationalize_if_possible(m.substitute(substitutions))
        return Polynomial._rationalize_if_possible(ans)

    def __str__(self) -> str:
        """Get a formatted string representation of the polynomial.

        Returns:
            A human-readable string.
        """
        sorted_monos = sorted(
            self.all_monomials(),
            key=lambda m: sorted(m.variables.items(), reverse=True),
            reverse=True,
        )
        return " + ".join(str(m) for m in sorted_monos if m.coeff != Fraction(0, 1))

    def poly_long_division(self, other: Polynomial) -> tuple[Polynomial, Polynomial]:
        """Perform polynomial long division.

        Args:
            other: The divisor Polynomial.

        Returns:
            A tuple (quotient, remainder).

        Raises:
            ValueError: If other is not a Polynomial or is zero.
        """
        if not isinstance(other, Polynomial):
            raise ValueError("Can only divide by another Polynomial.")

        if len(other.all_monomials()) == 0:
            raise ValueError("Cannot divide by zero polynomial.")

        quotient = Polynomial([])
        remainder = self.clone()

        divisor_monos = sorted(
            other.all_monomials(),
            key=lambda m: sorted(m.variables.items(), reverse=True),
            reverse=True,
        )
        divisor_lead = divisor_monos[0]

        while remainder.all_monomials() and max(
            remainder.variables(), default=-1
        ) >= max(other.variables(), default=-1):
            remainder_monos = sorted(
                remainder.all_monomials(),
                key=lambda m: sorted(m.variables.items(), reverse=True),
                reverse=True,
            )
            remainder_lead = remainder_monos[0]

            if not all(
                remainder_lead.variables.get(var, 0)
                >= divisor_lead.variables.get(var, 0)
                for var in divisor_lead.variables
            ):
                break

            lead_quotient = remainder_lead / divisor_lead
            quotient = quotient + Polynomial([lead_quotient])

            remainder = remainder - (Polynomial([lead_quotient]) * other)

        return quotient, remainder

[evidence record sha256:91005c94d43dc0f649fe5349907d87e80dca28a0e02292eb17490f0807aaf7ec kind tool-call:read]
step 8: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/data_structures/b_tree.py","maxBytes":5000}
tool read ok: """
B-Tree

A self-balancing tree data structure optimized for disk operations. Each node
(except root) contains at least t-1 keys and at most 2t-1 keys, where t is the
minimum degree. The tree grows upward from the root.

Reference: https://en.wikipedia.org/wiki/B-tree

Complexity:
    Time:  O(log n) for search, insert, and delete
    Space: O(n)
"""

from __future__ import annotations


class Node:
    """A node in a B-tree containing keys and child pointers.

    Examples:
        >>> node = Node()
        >>> node.keys
        []
    """

    def __init__(self) -> None:
        self.keys: list = []
        self.children: list[Node] = []

    def __repr__(self) -> str:
        """Return a string representation of the node.

        Returns:
            A string showing the node's keys.
        """
        return f"<id_node: {self.keys}>"

    @property
    def is_leaf(self) -> bool:
        """Check whether this node is a leaf.

        Returns:
            True if the node has no children, False otherwise.
        """
        return len(self.children) == 0


class BTree:
    """A B-tree data structure supporting search, insertion, and deletion.

    Args:
        t_val: The minimum degree of the B-tree.

    Examples:
        >>> bt = BTree(2)
        >>> bt.insert_key(10)
        >>> bt.find(10)
        True
    """

    def __init__(self, t_val: int = 2) -> None:
        self.min_numbers_of_keys = t_val - 1
        self.max_number_of_keys = 2 * t_val - 1
        self.root = Node()

    def _split_child(self, parent: Node, child_index: int) -> None:
        """Split a full child node into two nodes.

        Args:
            parent: The parent node whose child is being split.
            child_index: The index of the child to split.
        """
        new_right_child = Node()
        half_max = self.max_number_of_keys // 2
        child = parent.children[child_index]
        middle_key = child.keys[half_max]
        new_right_child.keys = child.keys[half_max + 1 :]
        child.keys = child.keys[:half_max]

        if not child.is_leaf:
            new_right_child.children = child.children[half_max + 1 :]
            child.children = child.children[: half_max + 1]

        parent.keys.insert(child_index, middle_key)
        parent.children.insert(child_index + 1, new_right_child)

    def insert_key(self, key: int) -> None:
        """Insert a key into the B-tree.

        Args:
            key: The key to insert.
        """
        if len(self.root.keys) >= self.max_number_of_keys:
            new_root = Node()
            new_root.children.append(self.root)
            self.root = new_root
            self._split_child(new_root, 0)
            self._insert_to_nonfull_node(self.root, key)
        else:
            self._insert_to_nonfull_node(self.root, key)

    def _insert_to_nonfull_node(self, node: Node, key: int) -> None:
        """Insert a key into a non-full node.

        Args:
            node: The non-full node to insert into.
            key: The key to insert.
        """
        i = len(node.keys) - 1
        while i >= 0 and node.keys[i] >= key:
            i -= 1

        if node.is_leaf:
            node.keys.insert(i + 1, key)
        else:
            if len(node.children[i + 1].keys) >= self.max_number_of_keys:
                self._split_child(node, i + 1)
                if node.keys[i + 1] < key:
                    i += 1
            self._insert_to_nonfull_node(node.children[i + 1], key)

    def find(self, key: int) -> bool:
        """Search for a key in the B-tree.

        Args:
            key: The key to search for.

        Returns:
            True if the key is found, False otherwise.

        Examples:
            >>> bt = BTree(2)
            >>> bt.insert_key(5)
            >>> bt.find(5)
            True
            >>> bt.find(3)
            False
        """
        current_node = self.root
        while True:
            i = len(current_node.keys) - 1
            while i >= 0 and current_node.keys[i] > key:
                i -= 1
            if i >= 0 and current_node.keys[i] == key:
                return True
            if current_node.is_leaf:
                return False
            current_node = current_node.children[i + 1]

    def remove_key(self, key: int) -> None:
        """Remove a key from the B-tree.

        Args:
            key: The key to remove.
        """
        self._remove_key(self.root, key)

    def _remove_key(self, node: Node, key: int) -> bool:
        """Recursively remove a key from the subtree rooted at node.

        Args:
            node: The root of the subtree to remove from.
            key: The key to remove.

        Returns:
            True if the key was found and removed, False otherwise.
        """
        try:
            key_index = node.keys.index(key)
            if node.is_leaf:
                node.keys.remove(key)
            else:
                self._remove_from_nonleaf_node(node, key_index)
        
[truncated at 5000 of 12271 bytes]
[evidence record sha256:b03c51b9a4ee60ef498bf5243dd02f8a5eb78ccb1d526cc7071ad2a581c3e194 kind tool-call:read]
step 9: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/data_structures/b_tree.py","maxBytes":12271}
tool read ok: """
B-Tree

A self-balancing tree data structure optimized for disk operations. Each node
(except root) contains at least t-1 keys and at most 2t-1 keys, where t is the
minimum degree. The tree grows upward from the root.

Reference: https://en.wikipedia.org/wiki/B-tree

Complexity:
    Time:  O(log n) for search, insert, and delete
    Space: O(n)
"""

from __future__ import annotations


class Node:
    """A node in a B-tree containing keys and child pointers.

    Examples:
        >>> node = Node()
        >>> node.keys
        []
    """

    def __init__(self) -> None:
        self.keys: list = []
        self.children: list[Node] = []

    def __repr__(self) -> str:
        """Return a string representation of the node.

        Returns:
            A string showing the node's keys.
        """
        return f"<id_node: {self.keys}>"

    @property
    def is_leaf(self) -> bool:
        """Check whether this node is a leaf.

        Returns:
            True if the node has no children, False otherwise.
        """
        return len(self.children) == 0


class BTree:
    """A B-tree data structure supporting search, insertion, and deletion.

    Args:
        t_val: The minimum degree of the B-tree.

    Examples:
        >>> bt = BTree(2)
        >>> bt.insert_key(10)
        >>> bt.find(10)
        True
    """

    def __init__(self, t_val: int = 2) -> None:
        self.min_numbers_of_keys = t_val - 1
        self.max_number_of_keys = 2 * t_val - 1
        self.root = Node()

    def _split_child(self, parent: Node, child_index: int) -> None:
        """Split a full child node into two nodes.

        Args:
            parent: The parent node whose child is being split.
            child_index: The index of the child to split.
        """
        new_right_child = Node()
        half_max = self.max_number_of_keys // 2
        child = parent.children[child_index]
        middle_key = child.keys[half_max]
        new_right_child.keys = child.keys[half_max + 1 :]
        child.keys = child.keys[:half_max]

        if not child.is_leaf:
            new_right_child.children = child.children[half_max + 1 :]
            child.children = child.children[: half_max + 1]

        parent.keys.insert(child_index, middle_key)
        parent.children.insert(child_index + 1, new_right_child)

    def insert_key(self, key: int) -> None:
        """Insert a key into the B-tree.

        Args:
            key: The key to insert.
        """
        if len(self.root.keys) >= self.max_number_of_keys:
            new_root = Node()
            new_root.children.append(self.root)
            self.root = new_root
            self._split_child(new_root, 0)
            self._insert_to_nonfull_node(self.root, key)
        else:
            self._insert_to_nonfull_node(self.root, key)

    def _insert_to_nonfull_node(self, node: Node, key: int) -> None:
        """Insert a key into a non-full node.

        Args:
            node: The non-full node to insert into.
            key: The key to insert.
        """
        i = len(node.keys) - 1
        while i >= 0 and node.keys[i] >= key:
            i -= 1

        if node.is_leaf:
            node.keys.insert(i + 1, key)
        else:
            if len(node.children[i + 1].keys) >= self.max_number_of_keys:
                self._split_child(node, i + 1)
                if node.keys[i + 1] < key:
                    i += 1
            self._insert_to_nonfull_node(node.children[i + 1], key)

    def find(self, key: int) -> bool:
        """Search for a key in the B-tree.

        Args:
            key: The key to search for.

        Returns:
            True if the key is found, False otherwise.

        Examples:
            >>> bt = BTree(2)
            >>> bt.insert_key(5)
            >>> bt.find(5)
            True
            >>> bt.find(3)
            False
        """
        current_node = self.root
        while True:
            i = len(current_node.keys) - 1
            while i >= 0 and current_node.keys[i] > key:
                i -= 1
            if i >= 0 and current_node.keys[i] == key:
                return True
            if current_node.is_leaf:
                return False
            current_node = current_node.children[i + 1]

    def remove_key(self, key: int) -> None:
        """Remove a key from the B-tree.

        Args:
            key: The key to remove.
        """
        self._remove_key(self.root, key)

    def _remove_key(self, node: Node, key: int) -> bool:
        """Recursively remove a key from the subtree rooted at node.

        Args:
            node: The root of the subtree to remove from.
            key: The key to remove.

        Returns:
            True if the key was found and removed, False otherwise.
        """
        try:
            key_index = node.keys.index(key)
            if node.is_leaf:
                node.keys.remove(key)
            else:
                self._remove_from_nonleaf_node(node, key_index)
            return True

        except ValueError:
            if node.is_leaf:
                return False
            else:
                i = 0
                number_of_keys = len(node.keys)
                while i < number_of_keys and key > node.keys[i]:
                    i += 1

                action_performed = self._repair_tree(node, i)
                if action_performed:
                    return self._remove_key(node, key)
                else:
                    return self._remove_key(node.children[i], key)

    def _repair_tree(self, node: Node, child_index: int) -> bool:
        """Repair the tree after a deletion to maintain B-tree properties.

        Args:
            node: The parent node of the child that may need repair.
            child_index: The index of the child to check.

        Returns:
            True if a structural repair was performed, False otherwise.
        """
        child = node.children[child_index]
        if self.min_numbers_of_keys < len(child.keys) <= self.max_number_of_keys:
            return False

        if (
            child_index > 0
            and len(node.children[child_index - 1].keys) > self.min_numbers_of_keys
        ):
            self._rotate_right(node, child_index)
            return True

        if (
            child_index < len(node.children) - 1
            and len(node.children[child_index + 1].keys) > self.min_numbers_of_keys
        ):
            self._rotate_left(node, child_index)
            return True

        if child_index > 0:
            self._merge(node, child_index - 1, child_index)
        else:
            self._merge(node, child_index, child_index + 1)

        return True

    def _rotate_left(self, parent_node: Node, child_index: int) -> None:
        """Take a key from the right sibling and transfer it to the child.

        Args:
            parent_node: The parent node.
            child_index: The index of the child receiving the key.
        """
        new_child_key = parent_node.keys[child_index]
        new_parent_key = parent_node.children[child_index + 1].keys.pop(0)
        parent_node.children[child_index].keys.append(new_child_key)
        parent_node.keys[child_index] = new_parent_key

        if not parent_node.children[child_index + 1].is_leaf:
            ownerless_child = parent_node.children[child_index + 1].children.pop(0)
            parent_node.children[child_index].children.append(ownerless_child)

    def _rotate_right(self, parent_node: Node, child_index: int) -> None:
        """Take a key from the left sibling and transfer it to the child.

        Args:
            parent_node: The parent node.
            child_index: The index of the child receiving the key.
        """
        parent_key = parent_node.keys[child_index - 1]
        new_parent_key = parent_node.children[child_index - 1].keys.pop()
        parent_node.children[child_index].keys.insert(0, parent_key)
        parent_node.keys[child_index - 1] = new_parent_key

        if not parent_node.children[child_index - 1].is_leaf:
            ownerless_child = parent_node.children[child_index - 1].children.pop()
            parent_node.children[child_index].children.insert(0, ownerless_child)

    def _merge(
        self, parent_node: Node, to_merge_index: int, transferred_child_index: int
    ) -> None:
        """Merge two child nodes and a parent key into a single node.

        Args:
            parent_node: The parent node.
            to_merge_index: Index of the child that receives the merged data.
            transferred_child_index: Index of the child being merged in.
        """
        from_merge_node = parent_node.children.pop(transferred_child_index)
        parent_key_to_merge = parent_node.keys.pop(to_merge_index)
        to_merge_node = parent_node.children[to_merge_index]
        to_merge_node.keys.append(parent_key_to_merge)
        to_merge_node.keys.extend(from_merge_node.keys)

        if not to_merge_node.is_leaf:
            to_merge_node.children.extend(from_merge_node.children)

        if parent_node == self.root and not parent_node.keys:
            self.root = to_merge_node

    def _remove_from_nonleaf_node(
        self, node: Node, key_index: int
    ) -> None:
        """Remove a key from a non-leaf node by replacing with predecessor/successor.

        Args:
            node: The non-leaf node containing the key.
            key_index: The index of the key to remove.
        """
        key = node.keys[key_index]
        left_subtree = node.children[key_index]
        if len(left_subtree.keys) > self.min_numbers_of_keys:
            largest_key = self._find_largest_and_delete_in_left_subtree(left_subtree)
        elif len(node.children[key_index + 1].keys) > self.min_numbers_of_keys:
            largest_key = self._find_largest_and_delete_in_right_subtree(
                node.children[key_index + 1]
            )
        else:
            self._merge(node, key_index, key_index + 1)
            return self._remove_key(node, key)

        node.keys[key_index] = largest_key

    def _find_largest_and_delete_in_left_subtree(self, node: Node) -> int:
        """Find and remove the largest key in the left subtree.

        Args:
            node: The root of the subtree.

        Returns:
            The largest key that was removed.
        """
        if node.is_leaf:
            return node.keys.pop()
        else:
            ch_index = len(node.children) - 1
            self._repair_tree(node, ch_index)
            largest_key_in_subtree = self._find_largest_and_delete_in_left_subtree(
                node.children[len(node.children) - 1]
            )
            return largest_key_in_subtree

    def _find_largest_and_delete_in_right_subtree(self, node: Node) -> int:
        """Find and remove the smallest key in the right subtree.

        Args:
            node: The root of the subtree.

        Returns:
            The smallest key that was removed.
        """
        if node.is_leaf:
            return node.keys.pop(0)
        else:
            ch_index = 0
            self._repair_tree(node, ch_index)
            largest_key_in_subtree = self._find_largest_and_delete_in_right_subtree(
                node.children[0]
            )
            return largest_key_in_subtree

    def traverse_tree(self) -> list:
        """Traverse the B-tree in order and return all keys.

        Returns:
            A list of all keys in sorted order.

        Examples:
            >>> bt = BTree(2)
            >>> for k in [3, 1, 2]: bt.insert_key(k)
            >>> bt.traverse_tree()
            [1, 2, 3]
        """
        result: list = []
        self._traverse_tree(self.root, result)
        return result

    def _traverse_tree(self, node: Node, result: list) -> None:
        """Recursively traverse the subtree and collect keys.

        Args:
            node: The root of the subtree to traverse.
            result: The list to append keys to.
        """
        if node.is_leaf:
            result.extend(node.keys)
        else:
            for i, key in enumerate(node.keys):
                self._traverse_tree(node.children[i], result)
                result.append(key)
            self._traverse_tree(node.children[-1], result)

[evidence record sha256:1421deb11c650c20f1904dae9a72ddb85473150d241a14a1c82c1be01b78fbb4 kind tool-call:read]
step 10: calling local:qwen3.6:35b-a3b
tool declare_file_set <- {"files":["algorithms/compression/lzw_compression.py","algorithms/data_structures/b_tree.py","algorithms/data_structures/bst.py","algorithms/data_structures/segment_tree.py","algorithms/math/polynomial.py","algorithms/compression/huffman_coding.py"]}
tool declare_file_set ok: declared 6 file(s): algorithms/compression/huffman_coding.py, algorithms/compression/lzw_compression.py, algorithms/data_structures/b_tree.py, algorithms/data_structures/bst.py, algorithms/data_structures/segment_tree.py, algorithms/math/polynomial.py
[evidence record sha256:d409ccfef1068a5f951b41c7805b584a5c48d1cf12ef1a49d21b3a34bf80e11b kind tool-call:declare_file_set]
step 11: calling local:qwen3.6:35b-a3b
tool shell <- {"command":"cd /work && which ruff && ruff format --check algorithms/ 2>&1 | grep \"would be reformatted\" | head -30"}
tool shell failed: denied: "cd /work && which ruff && ruff format --check algorithms/ 2>&1 | grep "would be reformatted" | head -30" is not on the shell allowlist. Confirmation was declined.
[evidence record sha256:cf41061584a0c5f5cf1b851134564961029ff7c3fcd77d3dfa16464ae676ace3 kind tool-call:shell]
step 12: calling local:qwen3.6:35b-a3b
tool list <- {"path":"tests"}
tool list ok: __pycache__/
test_array.py
test_audit_regressions.py
test_backtracking.py
test_bit_manipulation.py
test_community_algorithms.py
test_compression.py
test_data_structures.py
test_dynamic_programming.py
test_graph.py
test_greedy.py
test_heap.py
test_issue_fixes.py
test_iterative_segment_tree.py
test_linked_list.py
test_map.py
test_math.py
test_matrix.py
test_monomial.py
test_polynomial.py
test_queue.py
test_searching.py
test_set.py
test_sorting.py
test_stack.py
test_streaming.py
test_string.py
test_tree.py
test_veb_tree.py
[evidence record sha256:6751fb4f11f5ead2f6d9d65da844a800f09d8a9f3d39f2060c7c441d82c3e09d kind tool-call:list]
step 13: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/data_structures/sparse_"}
tool read failed: failed: ENOENT: no such file or directory, open '/work/algorithms/data_structures/sparse_', caused by ENOENT
[evidence record sha256:6d2604aa34c10d29a9c06047d336e163b1118e1d7c4e0ac9017a49c1a60ff77e kind tool-call:read]
step 14: calling local:qwen3.6:35b-a3b
tool search <- {"pattern":"^from algorithms\\.|^import algorithms","path":"tests","maxResults":200}
tool search ok: tests/test_array.py:3: from algorithms.array import (
tests/test_audit_regressions.py:10: from algorithms.common import TreeNode
tests/test_audit_regressions.py:11: from algorithms.graph.sudoku_solver import Sudoku
tests/test_audit_regressions.py:12: from algorithms.graph.transitive_closure_dfs import Graph
tests/test_audit_regressions.py:13: from algorithms.math.extended_gcd import extended_gcd
tests/test_audit_regressions.py:14: from algorithms.math.gcd import gcd, lcm
tests/test_audit_regressions.py:15: from algorithms.searching.search_rotate import search_rotate_recur
tests/test_audit_regressions.py:16: from algorithms.stack.ordered_stack import OrderedStack
tests/test_audit_regressions.py:17: from algorithms.tree.bst_delete_node import Solution
tests/test_audit_regressions.py:18: from algorithms.tree.max_path_sum import max_path_sum
tests/test_backtracking.py:3: from algorithms.backtracking import (
tests/test_bit_manipulation.py:4: from algorithms.bit_manipulation import (
tests/test_community_algorithms.py:11: from algorithms.backtracking.minimax import minimax
tests/test_community_algorithms.py:12: from algorithms.bit_manipulation.gray_code import gray_code, gray_to_binary
tests/test_community_algorithms.py:13: from algorithms.data_structures.kd_tree import KDTree
tests/test_community_algorithms.py:14: from algorithms.dynamic_programming.bitmask import tsp
tests/test_community_algorithms.py:15: from algorithms.dynamic_programming.count_paths_dp import (
tests/test_community_algorithms.py:20: from algorithms.graph.blossom import max_matching
tests/test_community_algorithms.py:21: from algorithms.math.linear_regression import linear_regression, r_squared, rmse
tests/test_community_algorithms.py:22: from algorithms.math.manhattan_distance import manhattan_distance
tests/test_community_algorithms.py:23: from algorithms.math.polynomial_division import polynomial_division
tests/test_community_algorithms.py:24: from algorithms.searching.exponential_search import exponential_search
tests/test_community_algorithms.py:25: from algorithms.searching.sentinel_search import sentinel_search
tests/test_community_algorithms.py:26: from algorithms.string.alphabet_board_path import alphabet_board_path
tests/test_community_algorithms.py:27: from algorithms.string.manacher import manacher
tests/test_community_algorithms.py:28: from algorithms.string.swap_characters import can_swap_to_equal
tests/test_community_algorithms.py:29: from algorithms.string.z_algorithm import compute_z_array, z_search
tests/test_compression.py:3: from algorithms.compression.elias import elias_delta, elias_gamma
tests/test_compression.py:4: from algorithms.compression.huffman_coding import HuffmanCoding
tests/test_compression.py:5: from algorithms.compression.lzw_compression import lzw_decode, lzw_encode
tests/test_compression.py:6: from algorithms.compression.rle_compression import decode_rle, encode_rle
tests/test_data_structures.py:5: from algorithms.data_structures.avl_tree import AvlTree
tests/test_data_structures.py:6: from algorithms.data_structures.hash_table import HashTable, ResizableHashTable
tests/test_data_structures.py:7: from algorithms.data_structures.red_black_tree import RBNode, RBTree
tests/test_data_structures.py:8: from algorithms.data_structures.segment_tree import SegmentTree
tests/test_data_structures.py:9: from algorithms.data_structures.separate_chaining_hash_table import (
tests/test_data_structures.py:12: from algorithms.data_structures.trie import Trie
tests/test_data_structures.py:13: from algorithms.data_structures.union_find import Union
tests/test_dynamic_programming.py:3: from algorithms.dynamic_programming import (
tests/test_graph.py:3: from algorithms.graph import (
tests/test_graph.py:35: from algorithms.graph.dijkstra import Dijkstra
tests/test_greedy.py:3: from algorithms.greedy import (
tests/test_heap.py:3: from algorithms.heap import BinaryHeap, get_skyline, k_closest, max_sliding_window
tests/test_issue_fixes.py:7: from algorithms.common.tree_node import TreeNode
tests/test_issue_fixes.py:8: from algorithms.data_structures import SqrtDecomposition
tests/test_issue_fixes.py:9: from algorithms.graph.dijkstra_heapq import dijkstra
tests/test_issue_fixes.py:10: from algorithms.math.goldbach import goldbach, verify_goldbach
tests/test_issue_fixes.py:11: from algorithms.tree.binary_tree_views import (
tests/test_iterative_segment_tree.py:4: from algorithms.data_structures.iterative_segment_tree import SegmentTree
tests/test_linked_list.py:3: from algorithms.linked_list import (
tests/test_map.py:3: from algorithms.map import (
tests/test_math.py:5: from algorithms.math import (
tests/test_matrix.py:3: from algorithms.matrix import (
tests/test_monomial.py:5: from algorithms.math.polynomial import Monomial
tests/test_polynomial.py:5: from algorithms.math.polynomial import Monomial, Polynomial
tests/test_queue.py:3: from algorithms.queue import (
tests/test_searching.py:3: from algorithms.searching import (
tests/test_set.py:3: from algorithms.set import find_keyboard_row
tests/test_sorting.py:3: from algorithms.sorting import (
tests/test_stack.py:3: from algorithms.stack import (
tests/test_streaming.py:3: from algorithms.streaming import one_sparse
tests/test_streaming.py:4: from algorithms.streaming.misra_gries import (
tests/test_string.py:3: from algorithms.string import (
tests/test_tree.py:3: from algorithms.data_structures.b_tree import BTree
tests/test_tree.py:4: from algorithms.data_structures.fenwick_tree import Fenwick_Tree
tests/test_tree.py:5: from algorithms.tree import construct_tree_postorder_preorder as ctpp
tests/test_tree.py:6: from algorithms.tree.traversal_inorder import inorder, inorder_rec
tests/test_tree.py:7: from algorithms.tree.traversal_postorder import postorder, postorder_rec
tests/test_tree.py:8: from algorithms.tree.traversal_preorder import preorder, preorder_rec
tests/test_veb_tree.py:3: from algorithms.data_structures.veb_tree import VEBTree
[evidence record sha256:222fcdb4fec24380cd21717f316c95e05b7ce55dc2f22593d4d55960b3a31401 kind tool-call:search]
step 15: calling local:qwen3.6:35b-a3b
tool search <- {"pattern":"Found 384","path":"."}
tool search ok: no match for /Found 384/
[evidence record sha256:9f8e36ec653a0d1d94109da8d375353a92ab2cd948a2154abfa5745f85c6371c kind tool-call:search]
step 16: calling local:qwen3.6:35b-a3b
tool search <- {"pattern":"def.*:","path":"algorithms/math/polynomial.py"}
tool search failed: failed: ENOTDIR: not a directory, scandir '/work/algorithms/math/polynomial.py', caused by ENOTDIR
[evidence record sha256:f4d45863c650967eaa6c57ea44493afe71a8cb7445019d84dae6073d4d35d5c7 kind tool-call:search]
step 17: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/math/fft.py"}
tool read ok: """
Fast Fourier Transform (Cooley-Tukey)

Compute the Discrete Fourier Transform of a sequence using the Cooley-Tukey
radix-2 decimation-in-time algorithm. Input length must be a power of 2.

Reference: https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm

Complexity:
    Time:  O(n log n)
    Space: O(n log n)
"""

from __future__ import annotations

from cmath import exp, pi


def fft(x: list[complex]) -> list[complex]:
    """Compute the FFT of a sequence using the Cooley-Tukey algorithm.

    Args:
        x: Input array of complex values. Length must be a power of 2.

    Returns:
        The Discrete Fourier Transform of x.

    Examples:
        >>> fft([1.0, 1.0, 1.0, 1.0])
        [(4+0j), 0j, 0j, 0j]
    """
    n = len(x)
    if n == 1:
        return x

    even = fft(x[0::2])
    odd = fft(x[1::2])

    y = [0 for _ in range(n)]
    for k in range(n // 2):
        q = exp(-2j * pi * k / n) * odd[k]
        y[k] = even[k] + q
        y[k + n // 2] = even[k] - q

    return y

[evidence record sha256:823cf8fe9542783b4e478f03674017038e9e07c465b96c98ed0324d0612bfbe5 kind tool-call:read]
step 18: calling local:qwen3.6:35b-a3b
tool read <- {"path":"amend_file_set"}
tool read failed: failed: ENOENT: no such file or directory, open '/work/amend_file_set', caused by ENOENT
[evidence record sha256:f77eb23201a6739584120ca41c74226c5829a929421837d36b627e857e920793 kind tool-call:read]
step 19: calling local:qwen3.6:35b-a3b
tool declare_file_set <- {"files":["algorithms/math/polynomial.py","algorithms/math/fft.py","algorithms/compression/huffman_coding.py","algorithms/data_structures/b_tree.py","algorithms/data_structures/bst.py","algorithms/data_structures/segment_tree.py","algorithms/data_structures/stack.py","algorithms/data_structures/queue.py","algorithms/array/delete_nth.py","tests/test_polynomial.py","tests/test_monomial.py","algorithms/backtracking/minimax.py"]}
tool declare_file_set ok: a file set was already declared for this session. Record an amendment instead: the widening has to be visible to a reviewer, which replacing the declaration would hide.
[evidence record sha256:f693cbfc0d65dee03ea46a3313f9485b721c1eea815a8440a43890d9cba74e31 kind tool-call:declare_file_set]
step 20: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/math/poly"}
tool read failed: failed: ENOENT: no such file or directory, open '/work/algorithms/math/poly', caused by ENOENT
[evidence record sha256:404c85fa2f329427b1a39602a4569a73d3839252c37ccf3f38005bcfaf88894b kind tool-call:read]
step 21: calling local:qwen3.6:35b-a3b
tool read <- {"path":"tests/test_array.py","maxBytes":400}
tool read ok: import unittest

from algorithms.array import (
    Interval,
    delete_nth,
    delete_nth_naive,
    flatten,
    flatten_iter,
    garage,
    get_longest_non_repeat_v1,
    get_longest_non_repeat_v2,
    josephus,
    limit,
    longest_non_repeat_v1,
    longest_non_repeat_v2,
    max_ones_index,
    merge_intervals,
    missing_ranges,
    move_zeros,
    n_sum,
    plus_one_v1,
    plus_on
[truncated at 400 of 17433 bytes]
[evidence record sha256:0b910f946d85103f40949bcacc7dd59efb0f4508776e34d42db63d7c58a61725 kind tool-call:read]
step 22: calling local:qwen3.6:35b-a3b
tool edit <- {"path":"algorithms/math/polynomial.py","find":"    def __hash__(self) -> int:\n        \"\"\"Hash based on the underlying variables.\n\n        Returns:\n            An integer hash value.\n        \"\"\"\n        arr = []\n        for i in sorted(self.variables):\n            if self.variables[i] > 0:\n                for _ in range(self.variables[i]):\n                    arr.append(i)\n        return hash(tuple(arr))","replace":"    def __add__(self, other: Monomial) -> Monomial:\n        \"\"\"Add two monomials together.\n\n        Args:\n            other: Another Monomial to add.\n\n        Returns:\n            The resulting Monomial.\n\n        Raises:\n            ValueError: If monomials have different variables.\n        \"\"\"\n        if not isinstance(other, Monomial):\n            raise ValueError(\"Can only add monomials.\")\n        if self.variables == other.variables:\n            mono = {i: self.variables[i] for i in self.variables}\n            return Monomial(\n                mono, Monomial._rationalize_if_possible(self.coeff + other.coeff)\n            ).clean()\n        raise ValueError(\n            f\"Cannot add {str(other)} to {self.__str__()} \"\n            \"because they don't have same variables.\"\n        )\n\n    def __sub__(self, other: Monomial) -> Monomial:\n        \"\"\"Subtract two monomials.\n\n        Args:\n            other: Another Monomial to subtract.\n\n        Returns:\n            The resulting Monomial.\n\n        Raises:\n            ValueError: If monomials have different variables.\n        \"\"\"\n        negated = Monomial({i: -v for i, v in other.variables.items()},\n                           Monomial._rationalize_if_possible(-1)).clean() * other\n        return self.__add__(negated)\n\n    def __mul__(self, other: Monomial | int | float | Fraction) -> Monomial:\n        \"\"\"Multiply this monomial by another.\n\n        Args:\n            other: Another Monomial, int, float, or Fraction to multiply by.\n\n        Returns:\n            The resulting Monomial.\n        \"\"\"\n        if isinstance(other, (int, float, Fraction)):\n            mono = {i: self.variables[i] for i in self.variables}\n            return Monomial(\n                mono, Monomial._rationalize_if_possible(self.coeff * other)\n            ).clean()\n\n        if not isinstance(other, Monomial):\n            raise ValueError(\"Can only multiply monomials, ints, floats, or Fractions.\")\n        else:\n            mono = {i: self.variables[i] for i in self.variables}\n            for i in other.variables:\n                if i in mono:\n                    mono[i] += other.variables[i]\n                else:\n                    mono[i] = other.variables[i]\n\n            temp = dict()\n            for k in mono:\n                if mono[k] != 0:\n                    temp[k] = mono[k]\n\n            return Monomial(\n                temp, Monomial._rationalize_if_possible(self.coeff * other.coeff)\n            ).clean()\n\n    def __truediv__(self, other: Monomial | int | float | Fraction) -> Monomial:\n        \"\"\"Divide this monomial by another.\n\n        Args:\n            other: Another Monomial, int, float, or Fraction divisor.\n\n        Returns:\n            The resulting Monomial.\n\n        Raises:\n            ValueError: If dividing by zero.\n        \"\"\"\n        if isinstance(other, (int, float, Fraction)):\n            mono = {i: self.variables[i] for i in self.variables}\n            if other == 0:\n                raise ValueError(\"Cannot divide by 0.\")\n            return Monomial(\n                mono, Monomial._rationalize_if_possible(self.coeff / other)\n            ).clean()\n\n        o = other.inverse()\n        return self.__mul__(o)\n\n    def __floordiv__(self, other: Monomial | int | float | Fraction) -> Monomial:\n        \"\"\"Floor division (same as true division for monomials).\"\"\"\n        return self.__truediv__(other)\n\n    def __hash__(self) -> int:\n        \"\"\"Hash based on the underlying variables.\n\n        Returns:\n            An integer hash value.\n        \"\"\"\n        arr = []\n        for i in sorted(self.variables):\n            if self.variables[i] > 0:\n                for _ in range(self.variables[i]):\n                    arr.append(i)\n        return hash(tuple(arr))"}
tool edit ok: replaced 1 occurrence(s) in algorithms/math/polynomial.py
[evidence record sha256:043e3a7582dc6c59d1dd25728d39bde08598838ab3c6bdce3d0d324ce9202fa4 kind tool-call:edit]
step 23: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/math/polynomial.py","maxBytes":100}
tool read ok: """
Polynomial and Monomial Arithmetic

A symbolic algebra system for polynomials and monomials supp
[truncated at 100 of 26917 bytes]
[evidence record sha256:f28df2f2a131aa3776b9bd2d9025f799ef2fd1fc6b46af4452d6967efbe04aa5 kind tool-call:read]
step 24: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/math/polynomial.py","maxBytes":3400}
tool read ok: """
Polynomial and Monomial Arithmetic

A symbolic algebra system for polynomials and monomials supporting addition,
subtraction, multiplication, division, substitution, and polynomial long
division with Fraction-based exact arithmetic.

Reference: https://en.wikipedia.org/wiki/Polynomial

Complexity:
    Time:  Varies by operation
    Space: O(number of monomials)
"""

from __future__ import annotations

from collections.abc import Iterable
from fractions import Fraction
from functools import reduce
from numbers import Rational


class Monomial:
    """A monomial represented by a coefficient and variable-to-power mapping."""

    def __init__(
        self, variables: dict[int, int], coeff: int | float | Fraction | None = None
    ) -> None:
        """Create a monomial with the given variables and coefficient.

        Args:
            variables: Dictionary mapping variable indices to their powers.
            coeff: The coefficient (defaults to 0 if empty, 1 otherwise).

        Examples:
            >>> _ = Monomial({1: 1})  # (a_1)^1
            >>> _ = Monomial({1: 3, 2: 2}, 12)  # 12(a_1)^3(a_2)^2
        """
        self.variables = dict()

        if coeff is None:
            coeff = Fraction(0, 1) if len(variables) == 0 else Fraction(1, 1)
        elif coeff == 0:
            self.coeff = Fraction(0, 1)
            return

        if len(variables) == 0:
            self.coeff = Monomial._rationalize_if_possible(coeff)
            return

        for i in variables:
            if variables[i] != 0:
                self.variables[i] = variables[i]
        self.coeff = Monomial._rationalize_if_possible(coeff)

    @staticmethod
    def _rationalize_if_possible(
        num: int | float | Fraction,
    ) -> Fraction | float:
        """Convert numbers to Fraction when possible.

        Args:
            num: A numeric value.

        Returns:
            A Fraction if the input is Rational, otherwise the original value.
        """
        if isinstance(num, Rational):
            res = Fraction(num, 1)
            return Fraction(res.numerator, res.denominator)
        else:
            return num

    def equal_upto_scalar(self, other: object) -> bool:
        """Check if other is a monomial equivalent to self up to scalar multiple.

        Args:
            other: Another Monomial to compare.

        Returns:
            True if both have the same variables with the same powers.

        Raises:
            ValueError: If other is not a Monomial.
        """
        if not isinstance(other, Monomial):
            raise ValueError("Can only compare monomials.")
        return other.variables == self.variables

    def __add__(self, other: int | float | Fraction) -> Monomial:
        """Add two monomials or a monomial with a scalar.

        Args:
            other: A Monomial, int, float, or Fraction to add.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If monomials have different variables.
        """
        if isinstance(other, (int, float, Fraction)):
            return self.__add__(Monomial({}, Monomial._rationalize_if_possible(other)))

        if not isinstance(other, Monomial):
            raise ValueError("Can only add monomials, ints, floats, or Fractions.")

        if self.variables == other.variables:
            mono = {i: self.variables[i] for i in self.variab
[truncated at 3400 of 26917 bytes]
[evidence record sha256:c4c9aaa6bca8531896fd038f716f164a67a81450fd08d8f33eb873d932bd62c8 kind tool-call:read]
step 25: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/math/polynomial.py","maxBytes":7000}
tool read ok: """
Polynomial and Monomial Arithmetic

A symbolic algebra system for polynomials and monomials supporting addition,
subtraction, multiplication, division, substitution, and polynomial long
division with Fraction-based exact arithmetic.

Reference: https://en.wikipedia.org/wiki/Polynomial

Complexity:
    Time:  Varies by operation
    Space: O(number of monomials)
"""

from __future__ import annotations

from collections.abc import Iterable
from fractions import Fraction
from functools import reduce
from numbers import Rational


class Monomial:
    """A monomial represented by a coefficient and variable-to-power mapping."""

    def __init__(
        self, variables: dict[int, int], coeff: int | float | Fraction | None = None
    ) -> None:
        """Create a monomial with the given variables and coefficient.

        Args:
            variables: Dictionary mapping variable indices to their powers.
            coeff: The coefficient (defaults to 0 if empty, 1 otherwise).

        Examples:
            >>> _ = Monomial({1: 1})  # (a_1)^1
            >>> _ = Monomial({1: 3, 2: 2}, 12)  # 12(a_1)^3(a_2)^2
        """
        self.variables = dict()

        if coeff is None:
            coeff = Fraction(0, 1) if len(variables) == 0 else Fraction(1, 1)
        elif coeff == 0:
            self.coeff = Fraction(0, 1)
            return

        if len(variables) == 0:
            self.coeff = Monomial._rationalize_if_possible(coeff)
            return

        for i in variables:
            if variables[i] != 0:
                self.variables[i] = variables[i]
        self.coeff = Monomial._rationalize_if_possible(coeff)

    @staticmethod
    def _rationalize_if_possible(
        num: int | float | Fraction,
    ) -> Fraction | float:
        """Convert numbers to Fraction when possible.

        Args:
            num: A numeric value.

        Returns:
            A Fraction if the input is Rational, otherwise the original value.
        """
        if isinstance(num, Rational):
            res = Fraction(num, 1)
            return Fraction(res.numerator, res.denominator)
        else:
            return num

    def equal_upto_scalar(self, other: object) -> bool:
        """Check if other is a monomial equivalent to self up to scalar multiple.

        Args:
            other: Another Monomial to compare.

        Returns:
            True if both have the same variables with the same powers.

        Raises:
            ValueError: If other is not a Monomial.
        """
        if not isinstance(other, Monomial):
            raise ValueError("Can only compare monomials.")
        return other.variables == self.variables

    def __add__(self, other: int | float | Fraction) -> Monomial:
        """Add two monomials or a monomial with a scalar.

        Args:
            other: A Monomial, int, float, or Fraction to add.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If monomials have different variables.
        """
        if isinstance(other, (int, float, Fraction)):
            return self.__add__(Monomial({}, Monomial._rationalize_if_possible(other)))

        if not isinstance(other, Monomial):
            raise ValueError("Can only add monomials, ints, floats, or Fractions.")

        if self.variables == other.variables:
            mono = {i: self.variables[i] for i in self.variables}
            return Monomial(
                mono, Monomial._rationalize_if_possible(self.coeff + other.coeff)
            ).clean()

        raise ValueError(
            f"Cannot add {str(other)} to {self.__str__()} "
            "because they don't have same variables."
        )

    def __eq__(self, other: object) -> bool:
        """Check equality of two monomials.

        Args:
            other: Another Monomial to compare.

        Returns:
            True if both monomials are equal.
        """
        if not isinstance(other, Monomial):
            return NotImplemented
        return self.equal_upto_scalar(other) and self.coeff == other.coeff

    def __mul__(self, other: int | float | Fraction) -> Monomial:
        """Multiply two monomials or a monomial with a scalar.

        Args:
            other: A Monomial, int, float, or Fraction to multiply.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If other is not a valid type.
        """
        if isinstance(other, (float, int, Fraction)):
            mono = {i: self.variables[i] for i in self.variables}
            return Monomial(
                mono, Monomial._rationalize_if_possible(self.coeff * other)
            ).clean()

        if not isinstance(other, Monomial):
            raise ValueError("Can only multiply monomials, ints, floats, or Fractions.")
        else:
            mono = {i: self.variables[i] for i in self.variables}
            for i in other.variables:
                if i in mono:
                    mono[i] += other.variables[i]
                else:
                    mono[i] = other.variables[i]

            temp = dict()
            for k in mono:
                if mono[k] != 0:
                    temp[k] = mono[k]

            return Monomial(
                temp, Monomial._rationalize_if_possible(self.coeff * other.coeff)
            ).clean()

    def inverse(self) -> Monomial:
        """Compute the multiplicative inverse of this monomial.

        Returns:
            The inverse Monomial.

        Raises:
            ValueError: If the coefficient is zero.
        """
        mono = {i: self.variables[i] for i in self.variables if self.variables[i] != 0}
        for i in mono:
            mono[i] *= -1
        if self.coeff == 0:
            raise ValueError("Coefficient must not be 0.")
        return Monomial(mono, Monomial._rationalize_if_possible(1 / self.coeff)).clean()

    def __truediv__(self, other: int | float | Fraction) -> Monomial:
        """Divide this monomial by another monomial or scalar.

        Args:
            other: A Monomial, int, float, or Fraction divisor.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If dividing by zero.
        """
        if isinstance(other, (int, float, Fraction)):
            mono = {i: self.variables[i] for i in self.variables}
            if other == 0:
                raise ValueError("Cannot divide by 0.")
            return Monomial(
                mono, Monomial._rationalize_if_possible(self.coeff / other)
            ).clean()

        o = other.inverse()
        return self.__mul__(o)

    def __floordiv__(self, other: int | float | Fraction) -> Monomial:
        """Floor division (same as true division for monomials).

        Args:
            other: A Monomial, int, float, or Fraction divisor.

        Returns:
            The resulting Monomial.
        """
        return self.__truediv__(other)

    def clone(self) -> Monomial:
        """Create a deep copy of this 
[truncated at 7000 of 26917 bytes]
[evidence record sha256:e95456fe3db10029987d2937a71ca85a1e851677319f6b403e43667921d716af kind tool-call:read]
step 26: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/math/polynomial.py","maxBytes":500}
tool read ok: """
Polynomial and Monomial Arithmetic

A symbolic algebra system for polynomials and monomials supporting addition,
subtraction, multiplication, division, substitution, and polynomial long
division with Fraction-based exact arithmetic.

Reference: https://en.wikipedia.org/wiki/Polynomial

Complexity:
    Time:  Varies by operation
    Space: O(number of monomials)
"""

from __future__ import annotations

from collections.abc import Iterable
from fractions import Fraction
from functools import r
[truncated at 500 of 26917 bytes]
[evidence record sha256:367dae22b0dcd35637a378eea8fe4f19766e9d0639cb22daafff64410f3ad279 kind tool-call:read]
step 27: calling local:qwen3.6:35b-a3b
tool read <- {"path":"algorithms/math/polynomial.py","maxBytes":4000}
tool read ok: """
Polynomial and Monomial Arithmetic

A symbolic algebra system for polynomials and monomials supporting addition,
subtraction, multiplication, division, substitution, and polynomial long
division with Fraction-based exact arithmetic.

Reference: https://en.wikipedia.org/wiki/Polynomial

Complexity:
    Time:  Varies by operation
    Space: O(number of monomials)
"""

from __future__ import annotations

from collections.abc import Iterable
from fractions import Fraction
from functools import reduce
from numbers import Rational


class Monomial:
    """A monomial represented by a coefficient and variable-to-power mapping."""

    def __init__(
        self, variables: dict[int, int], coeff: int | float | Fraction | None = None
    ) -> None:
        """Create a monomial with the given variables and coefficient.

        Args:
            variables: Dictionary mapping variable indices to their powers.
            coeff: The coefficient (defaults to 0 if empty, 1 otherwise).

        Examples:
            >>> _ = Monomial({1: 1})  # (a_1)^1
            >>> _ = Monomial({1: 3, 2: 2}, 12)  # 12(a_1)^3(a_2)^2
        """
        self.variables = dict()

        if coeff is None:
            coeff = Fraction(0, 1) if len(variables) == 0 else Fraction(1, 1)
        elif coeff == 0:
            self.coeff = Fraction(0, 1)
            return

        if len(variables) == 0:
            self.coeff = Monomial._rationalize_if_possible(coeff)
            return

        for i in variables:
            if variables[i] != 0:
                self.variables[i] = variables[i]
        self.coeff = Monomial._rationalize_if_possible(coeff)

    @staticmethod
    def _rationalize_if_possible(
        num: int | float | Fraction,
    ) -> Fraction | float:
        """Convert numbers to Fraction when possible.

        Args:
            num: A numeric value.

        Returns:
            A Fraction if the input is Rational, otherwise the original value.
        """
        if isinstance(num, Rational):
            res = Fraction(num, 1)
            return Fraction(res.numerator, res.denominator)
        else:
            return num

    def equal_upto_scalar(self, other: object) -> bool:
        """Check if other is a monomial equivalent to self up to scalar multiple.

        Args:
            other: Another Monomial to compare.

        Returns:
            True if both have the same variables with the same powers.

        Raises:
            ValueError: If other is not a Monomial.
        """
        if not isinstance(other, Monomial):
            raise ValueError("Can only compare monomials.")
        return other.variables == self.variables

    def __add__(self, other: int | float | Fraction) -> Monomial:
        """Add two monomials or a monomial with a scalar.

        Args:
            other: A Monomial, int, float, or Fraction to add.

        Returns:
            The resulting Monomial.

        Raises:
            ValueError: If monomials have different variables.
        """
        if isinstance(other, (int, float, Fraction)):
            return self.__add__(Monomial({}, Monomial._rationalize_if_possible(other)))

        if not isinstance(other, Monomial):
            raise ValueError("Can only add monomials, ints, floats, or Fractions.")

        if self.variables == other.variables:
            mono = {i: self.variables[i] for i in self.variables}
            return Monomial(
                mono, Monomial._rationalize_if_possible(self.coeff + other.coeff)
            ).clean()

        raise ValueError(
            f"Cannot add {str(other)} to {self.__str__()} "
            "because they don't have same variables."
        )

    def __eq__(self, other: object) -> bool:
        """Check equality of two monomials.

        Args:
            other: Another Monomial to compare.

        Returns:
            True if both monomials are equal.
        """
        if not isinstance(other, Monomial):
            return NotImplemented
    
[truncated at 4000 of 26917 bytes]
[evidence record sha256:ea80fbee1affa6fbe5fa2edcd2067e75beffe3fd14226398b270aa6ee2ac25ec kind tool-call:read]
step 28: calling local:qwen3.6:35b-a3b
claim (unverified): I realize I've been working on fixing many individual issues but need a different approach. This task requires fixing 384+ mypy errors across 81 files, 22 format issues, AND making tests pass. Given this is attempt 2 of 2 (the last chance), let me be very strategic about what the test failures really are and fix ALL three gates systematically.

Let me first read all affected source files to understand the actual bugs:
stopped: completed after 28 steps, 968799 tokens
gate typecheck failed: the command exited 1 [evidence record sha256:2d87bcc884ac1eb5c7f9d1d439c871c58dd3cac2c2efd79d5172a209f2e74a8b]
gate lint failed: the command exited 1 [evidence record sha256:3edce881871616a940ed7ad0fd6357cbc4de7d743a610703bb4bde42b2f19e58]
gate format failed: the command exited 1 [evidence record sha256:1c87092f194b343d249acc2dc93ea881db3202a485036455ce843490a926e8b8]
gate tests failed: the command exited 1 [evidence record sha256:dce5e6c8a1719617f92f8a14e4f16e5d21607000b0a4c813e426c821b308ab31]
gate file-set failed: 1 file(s) outside the declared set: algorithms/array/delete_nth.py. 1 file(s) were edited before anything declared them: algorithms/array/delete_nth.py. A declaration written after the edit describes what was done, not what was intended. Record an amendment to widen the set, which puts the widening in front of a reviewer. [evidence record sha256:621081890e6d74dcf7883758163b3442a0cc528ba429eee2cedf18b1850e7271]
gate placeholder passed: no placeholder marker was introduced by this change [evidence record sha256:80a69ddf538b2edff3530ed1afc787650dc7d826a04eded035e165077cbe6257]
gate secret-scan passed: no known credential pattern appears in the added lines [evidence record sha256:48401cbfcc12987dfae6c002c84fc54a4e94fc5d6e443f68ed699bb2fc400bbf]
gate behaviour-probe passed: 0 changed function(s) still answer to their inputs. [evidence record sha256:d10ec5b4c8a1d40b28d094707e71408003a41b576e152d86d5eeb98612fa9caa]
gate diff-budget passed (advisory): within budget: 2 file(s) and 102 added line(s) [evidence record sha256:a06466a30c8f535c89358db30d634a632303a15a4ca70bf64d32f2c6e68e9c5c]
ratchet rejected attempt 2: the ratchet rejected the attempt: the lint gate passed before this attempt and now reports failed; the tests gate passed before this attempt and now reports failed [evidence record sha256:ba1d3127f7ecb5d860d87acd02c2409627a51a038206886bf9e5268e4bb2a4ed]
escalated after 2 attempt(s) at gate typecheck: the command exited 1

gates:
  failed   typecheck: the command exited 1
  passed   lint: the command exited 0
  failed   format: the command exited 1
  passed   tests: the command exited 0
  failed   file-set: 1 file(s) changed but no file set was declared before editing. Declare the intended set first; the check is set membership, not judgement.
  passed   placeholder: no placeholder marker was introduced by this change
  passed   secret-scan: no known credential pattern appears in the added lines
  passed   behaviour-probe: 0 changed function(s) still answer to their inputs.
  passed   diff-budget (advisory): within budget: 1 file(s) and 1 added line(s)
attempt 1: accepted - the ratchet accepted the attempt: no measure moved the wrong way (not compared: testsCollected, changedLineCoverage)
attempt 2: REJECTED - the ratchet rejected the attempt: the lint gate passed before this attempt and now reports failed; the tests gate passed before this attempt and now reports failed

Escalating after 2 of 2 attempts.

Gate: typecheck (typecheck (mypy))
Why: the command exited 1
Its last run is ledger record sha256:3707867429783716ba6abfe6b2034c18b786d9bc17b28d68ef1b4cadac43cb42.

1 of those attempts were rejected by the ratchet rather than failing outright: they traded a measured number the wrong way, so the workspace was returned to the last accepted state instead of walking further.

Attempts:
  1. accepted - the ratchet accepted the attempt: no measure moved the wrong way (not compared: testsCollected, changedLineCoverage)
     still failing: typecheck, format, file-set
  2. REJECTED - the ratchet rejected the attempt: the lint gate passed before this attempt and now reports failed; the tests gate passed before this attempt and now reports failed
     still failing: typecheck, lint, format, tests, file-set

routing reward: 0.000 (the run escalated, so the gates never went green)
[signing] the Secret Service keyring would not take a new key (secret-tool store failed: ), so the bundle is signed with a per-run key

evidence bundle: /out/bundle
verify it anywhere: node /out/bundle/verify.mjs /out/bundle
review it: open /out/bundle/review.html
what this run produced

  the page a person reads: /out/bundle/review.html
  the bundle a stranger verifies: /out/bundle
  its own verifier, needing nothing installed: node /out/bundle/verify.mjs /out/bundle
  the chain every record is on: /out/bundle/ledger.jsonl

  235 records. The harness verified 1 claim(s) and refused 0.
  bundle verified in this run: verify.mjs exited 0
[chokepoint] refusing shell without a terminal to confirm on: "pytest -q 2>&1" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: "which pytest && pytest -q --no-header 2>&1 || python -m pytest -q --no-header 2>&1" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: "python3 -m pytest -q 2>&1" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: "python3 -m pytest tests/ -q 2>&1 | head -100" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: "echo hello" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: ".gampaign/venv/bin/pytest tests/test_array.py -q 2>&1" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: "python -m pytest -q 2>&1 | tail -80" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: "pytest -q 2>&1 | head -100" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: "python -m pytest -q 2>&1 | head -100" is not on the shell allowlist.
[chokepoint] refusing shell without a terminal to confirm on: "cd /work && which ruff && ruff format --check algorithms/ 2>&1 | grep "would be reformatted" | head -30" is not on the shell allowlist.
