Added validate sudoku board function (#9881)

* Added algorithm to deeply clone a graph

* Fixed file name and removed a function call

* Removed nested function and fixed class parameter types

* Fixed doctests

* bug fix

* Added class decorator

* Updated doctests and fixed precommit errors

* Cleaned up code

* Simplified doctest

* Added doctests

* Code simplification

* Created function which validates sudoku boards

* Update matrix/validate_sudoku_board.py

* Fixed precommit errors

* Removed file accidentally included

* Improved readability and simplicity

* Add timeit benchmarks

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update validate_sudoku_board.py

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

matrix/validate_sudoku_board.py

@@ -0,0 +1,107 @@
+"""
+LeetCode 36. Valid Sudoku
+https://leetcode.com/problems/valid-sudoku/
+https://en.wikipedia.org/wiki/Sudoku
+
+Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be
+validated according to the following rules:
+
+- Each row must contain the digits 1-9 without repetition.
+- Each column must contain the digits 1-9 without repetition.
+- Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9
+  without repetition.
+
+Note:
+
+A Sudoku board (partially filled) could be valid but is not necessarily
+solvable.
+
+Only the filled cells need to be validated according to the mentioned rules.
+"""
+
+from collections import defaultdict
+
+NUM_SQUARES = 9
+EMPTY_CELL = "."
+
+
+def is_valid_sudoku_board(sudoku_board: list[list[str]]) -> bool:
+    """
+    This function validates (but does not solve) a sudoku board.
+    The board may be valid but unsolvable.
+
+    >>> is_valid_sudoku_board([
+    ...  ["5","3",".",".","7",".",".",".","."]
+    ... ,["6",".",".","1","9","5",".",".","."]
+    ... ,[".","9","8",".",".",".",".","6","."]
+    ... ,["8",".",".",".","6",".",".",".","3"]
+    ... ,["4",".",".","8",".","3",".",".","1"]
+    ... ,["7",".",".",".","2",".",".",".","6"]
+    ... ,[".","6",".",".",".",".","2","8","."]
+    ... ,[".",".",".","4","1","9",".",".","5"]
+    ... ,[".",".",".",".","8",".",".","7","9"]
+    ... ])
+    True
+    >>> is_valid_sudoku_board([
+    ...  ["8","3",".",".","7",".",".",".","."]
+    ... ,["6",".",".","1","9","5",".",".","."]
+    ... ,[".","9","8",".",".",".",".","6","."]
+    ... ,["8",".",".",".","6",".",".",".","3"]
+    ... ,["4",".",".","8",".","3",".",".","1"]
+    ... ,["7",".",".",".","2",".",".",".","6"]
+    ... ,[".","6",".",".",".",".","2","8","."]
+    ... ,[".",".",".","4","1","9",".",".","5"]
+    ... ,[".",".",".",".","8",".",".","7","9"]
+    ... ])
+    False
+    >>> is_valid_sudoku_board([["1", "2", "3", "4", "5", "6", "7", "8", "9"]])
+    Traceback (most recent call last):
+        ...
+    ValueError: Sudoku boards must be 9x9 squares.
+    >>> is_valid_sudoku_board(
+    ...        [["1"], ["2"], ["3"], ["4"], ["5"], ["6"], ["7"], ["8"], ["9"]]
+    ...  )
+    Traceback (most recent call last):
+        ...
+    ValueError: Sudoku boards must be 9x9 squares.
+    """
+    if len(sudoku_board) != NUM_SQUARES or (
+        any(len(row) != NUM_SQUARES for row in sudoku_board)
+    ):
+        error_message = f"Sudoku boards must be {NUM_SQUARES}x{NUM_SQUARES} squares."
+        raise ValueError(error_message)
+
+    row_values: defaultdict[int, set[str]] = defaultdict(set)
+    col_values: defaultdict[int, set[str]] = defaultdict(set)
+    box_values: defaultdict[tuple[int, int], set[str]] = defaultdict(set)
+
+    for row in range(NUM_SQUARES):
+        for col in range(NUM_SQUARES):
+            value = sudoku_board[row][col]
+
+            if value == EMPTY_CELL:
+                continue
+
+            box = (row // 3, col // 3)
+
+            if (
+                value in row_values[row]
+                or value in col_values[col]
+                or value in box_values[box]
+            ):
+                return False
+
+            row_values[row].add(value)
+            col_values[col].add(value)
+            box_values[box].add(value)
+
+    return True
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+    from timeit import timeit
+
+    testmod()
+    print(timeit("is_valid_sudoku_board(valid_board)", globals=globals()))
+    print(timeit("is_valid_sudoku_board(invalid_board)", globals=globals()))