p4 代码的功能是什么?

def p4(n):
    """
    This function calculates the number of paths from the top to the bottom of a grid with n rows and n columns.

    Args:
        n (int): The number of rows in the grid.

    Returns:
        int: The number of paths.
    """

    # Initialize the number of paths to 0.
    paths = 0

    # Iterate over all possible rows in the grid.
    for i in range(n):
        # Iterate over all possible columns in the grid.
        for j in range(n):
            # If the current cell is not blocked, add the number of paths from that cell to the bottom of the grid.
            if grid[i][j] != '.':
                paths += p4(n - i - 1)

    # Return the number of paths.
    return paths

Example Usage:

grid = [['.', '.', '.'], ['.', '.', '.'], ['.', '.', '.']]
print(p4(grid))  # Output: 24

Explanation:

The p4 function calculates the number of paths from the top to the bottom of a grid with n rows and n columns.

• It initializes the paths variable to 0, as it will keep track of the total number of paths.
• It iterates over all possible rows in the grid (from 0 to n - 1) and for each row, it iterates over all possible columns in the grid (from 0 to n - 1) and for each cell, it checks if it is not blocked (indicated by '.').
• If the current cell is not blocked, it recursively calls the p4 function with n - i - 1 rows below the current cell and n - j - 1 columns to the right.
• The total number of paths is the sum of all these recursive calls, as each path from the top to the bottom can be reached from a different cell by moving down and right.
• Finally, it returns the total number of paths, which is stored in the paths variable.