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URL: http://github.com/TheAlgorithms/Python/commit/bc8df6de3143b417c4d174200fd7edd0dbba4ce3

s" /> [pre-commit.ci] pre-commit autoupdate (#11322) · TheAlgorithms/Python@bc8df6d · GitHub
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[pre-commit.ci] pre-commit autoupdate (#11322)
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](astral-sh/ruff-pre-commit@v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](pre-commit/mirrors-mypy@v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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‎.pre-commit-config.yaml‎

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- id: auto-walrus
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- repo: https://github.com/astral-sh/ruff-pre-commit
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rev: v0.2.2
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rev: v0.3.2
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hooks:
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- id: ruff
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- id: ruff-format
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- id: validate-pyproject
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- repo: https://github.com/pre-commit/mirrors-mypy
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rev: v1.8.0
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rev: v1.9.0
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hooks:
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- id: mypy
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‎backtracking/all_combinations.py‎

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"""
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In this problem, we want to determine all possible combinations of k
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numbers out of 1 ... n. We use backtracking to solve this problem.
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In this problem, we want to determine all possible combinations of k
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numbers out of 1 ... n. We use backtracking to solve this problem.
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Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!))),
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Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!))),
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"""
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from __future__ import annotations
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from itertools import combinations

‎backtracking/all_permutations.py‎

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"""
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In this problem, we want to determine all possible permutations
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of the given sequence. We use backtracking to solve this problem.
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In this problem, we want to determine all possible permutations
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of the given sequence. We use backtracking to solve this problem.
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Time complexity: O(n! * n),
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where n denotes the length of the given sequence.
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Time complexity: O(n! * n),
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where n denotes the length of the given sequence.
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"""
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from __future__ import annotations
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‎backtracking/all_subsequences.py‎

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Time complexity: O(2^n),
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where n denotes the length of the given sequence.
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"""
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from typing import Any

‎backtracking/coloring.py‎

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"""
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Graph Coloring also called "m coloring problem"
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consists of coloring a given graph with at most m colors
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such that no adjacent vertices are assigned the same color
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Graph Coloring also called "m coloring problem"
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consists of coloring a given graph with at most m colors
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such that no adjacent vertices are assigned the same color
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Wikipedia: https://en.wikipedia.org/wiki/Graph_coloring
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Wikipedia: https://en.wikipedia.org/wiki/Graph_coloring
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"""
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‎backtracking/hamiltonian_cycle.py‎

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"""
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A Hamiltonian cycle (Hamiltonian circuit) is a graph cycle
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through a graph that visits each node exactly once.
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Determining whether such paths and cycles exist in graphs
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is the 'Hamiltonian path problem', which is NP-complete.
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A Hamiltonian cycle (Hamiltonian circuit) is a graph cycle
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through a graph that visits each node exactly once.
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Determining whether such paths and cycles exist in graphs
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is the 'Hamiltonian path problem', which is NP-complete.
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Wikipedia: https://en.wikipedia.org/wiki/Hamiltonian_path
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Wikipedia: https://en.wikipedia.org/wiki/Hamiltonian_path
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‎backtracking/minimax.py‎

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leaves of game tree is stored in scores[]
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height is maximum height of Game tree
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"""
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from __future__ import annotations
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import math

‎backtracking/n_queens.py‎

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"""
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The nqueens problem is of placing N queens on a N * N
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chess board such that no queen can attack any other queens placed
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on that chess board.
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This means that one queen cannot have any other queen on its horizontal, vertical and
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diagonal lines.
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The nqueens problem is of placing N queens on a N * N
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chess board such that no queen can attack any other queens placed
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on that chess board.
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This means that one queen cannot have any other queen on its horizontal, vertical and
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diagonal lines.
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solution = []

‎backtracking/n_queens_math.py‎

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for another one or vice versa.
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‎backtracking/sudoku.py‎

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have solved the puzzle. else, we backtrack and place another number
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in that cell and repeat this process.
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"""
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Matrix = list[list[int]]

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