Function fabricator

Prompt

Your task is to create Python functions based on the provided natural language requests. The requests will describe the desired functionality of the function, including the input parameters and expected return value. Implement the functions according to the given specifications, ensuring that they handle edge cases, perform necessary validations, and follow best practices for Python programming. Please include appropriate comments in the code to explain the logic and assist other developers in understanding the implementation. [function description]

Sample query

Your task is to create Python functions based on the provided natural language requests. The requests will describe the desired functionality of the function, including the input parameters and expected return value. Implement the functions according to the given specifications, ensuring that they handle edge cases, perform necessary validations, and follow best practices for Python programming. Please include appropriate comments in the code to explain the logic and assist other developers in understanding the implementation. I want a function that can solve a Sudoku puzzle. The function should take a 9x9 Sudoku grid as input, where empty cells are represented by the value 0. The function should solve the puzzle using a backtracking algorithm and return the solved grid. If the puzzle is unsolvable, it should return None. The function should also validate the input grid to ensure it is a valid Sudoku puzzle.

Sample response

Here's a Python function that solves a Sudoku puzzle using a backtracking algorithm and validates the input grid:

def is_valid_sudoku(grid):
    """
    Check if the given Sudoku grid is valid.
    """
    # Check rows
    for row in grid:
        if not is_valid_row(row):
            return False

    # Check columns
    for col in range(9):
        column = [grid[row][col] for row in range(9)]
        if not is_valid_row(column):
            return False

    # Check 3x3 subgrids
    for i in range(0, 9, 3):
        for j in range(0, 9, 3):
            subgrid = [grid[x][y] for x in range(i, i+3) for y in range(j, j+3)]
            if not is_valid_row(subgrid):
                return False

    return True

def is_valid_row(row):
    """
    Check if a row is valid (no duplicates except for 0).
    """
    seen = set()
    for num in row:
        if num != 0:
            if num in seen:
                return False
            seen.add(num)
    return True

def solve_sudoku(grid):
    """
    Solve the Sudoku puzzle using backtracking.
    """
    if not is_valid_sudoku(grid):
        return None

    empty_cell = find_empty_cell(grid)
    if not empty_cell:
        return grid

    row, col = empty_cell
    for num in range(1, 10):
        if is_safe(grid, row, col, num):
            grid[row][col] = num
            if solve_sudoku(grid):
                return grid
            grid[row][col] = 0  # Backtrack if the current configuration is invalid
    return None

def find_empty_cell(grid):
    """
    Find the first empty cell (cell with value 0) in the Sudoku grid.
    """
    for i in range(9):
        for j in range(9):
            if grid[i][j] == 0:
                return (i, j)
    return None

def is_safe(grid, row, col, num):
    """
    Check if it's safe to place 'num' in the given position.
    """
    # Check row
    if num in grid[row]:
        return False

    # Check column
    if num in [grid[i][col] for i in range(9)]:
        return False

    # Check 3x3 subgrid
    start_row, start_col = 3 * (row // 3), 3 * (col // 3)
    for i in range(start_row, start_row + 3):
        for j in range(start_col, start_col + 3):
            if grid[i][j] == num:
                return False

    return True

This code defines several helper functions:

1. is_valid_sudoku(grid): Checks if the given Sudoku grid is valid according to Sudoku rules.
2. is_valid_row(row): Checks if a given row in the Sudoku grid is valid (no duplicates except for 0).
3. solve_sudoku(grid): Solves the Sudoku puzzle using backtracking.
4. find_empty_cell(grid): Finds the first empty cell (cell with value 0) in the Sudoku grid.
5. is_safe(grid, row, col, num): Checks if it's safe to place a number in a given position in the Sudoku grid.

The solve_sudoku function starts solving the Sudoku puzzle by recursively trying to fill each empty cell with a valid number. If a solution is found, it returns the solved grid. If the puzzle is unsolvable, it returns None.