How do you implement the bottom-up and top-down approach in this problem?

Question

I am given a grid or n * n. I need to find how many routes I can take to get from grid[0][0] to grid[n - 1][n - 1]. However in the grid there will be the letter 'H' in some of the spaces. If there is an "H", I cannot cross that place. I can only go to the right of down. I need to use the top-down approach and the bottom-up approach but I don't know how to do that. Here is an example:

grid = [['.', '.', '.', '.'],
       ['.', '.', '.', 'H'],
       ['.', '.', 'H', '.'],
       ['.', '.', '.', '.']]

I need to go from the first element to the last element without going through the 'H's. The answer to this example is 4.

score 0 · Accepted Answer · answered Jun 14 '22 at 14:15

Here they have the solution https://www.geeksforgeeks.org/count-number-ways-reach-destination-maze/

R = 4
C = 4
def countPaths(maze):
     
    if (maze[0][0] == -1):
        return 0
 
    for i in range(R):
        if (maze[i][0] == 0):
            maze[i][0] = 1
 
        else:
            break
 
    for i in range(1, C, 1):
        if (maze[0][i] == 0):
            maze[0][i] = 1
 
        else:
            break

    for i in range(1, R, 1):
        for j in range(1, C, 1):
             
            if (maze[i][j] == -1):
                continue

            if (maze[i - 1][j] > 0):
                maze[i][j] = (maze[i][j] +
                              maze[i - 1][j])
 

            if (maze[i][j - 1] > 0):
                maze[i][j] = (maze[i][j] +
                              maze[i][j - 1])
 
    if (maze[R - 1][C - 1] > 0):
        return maze[R - 1][C - 1]
    else:
        return 0
 

if __name__ == '__main__':
    maze = [[0, 0, 0, 0],
            [0, -1, 0, 0],
            [-1, 0, 0, 0],
            [0, 0, 0, 0 ]]
    print(countPaths(maze))

How do you implement the bottom-up and top-down approach in this problem?

1 Answers1