Description

Follow up for "Unique Paths":

Now consider if some obstacles are added to the grids. How many unique paths would there be?

An obstacle and empty space is marked as 1 and 0 respectively in the grid.

For example,
There is one obstacle in the middle of a 3x3 grid as illustrated below.

[
[0,0,0],
[0,1,0],
[0,0,0]
]

The total number of unique paths is 2.

Note: m and n will be at most 100.

Solution

DP

class Solution {
    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        if (obstacleGrid == null || obstacleGrid.length == 0 
            || obstacleGrid[0].length == 0) {
            return 0;
        }
        
        int m = obstacleGrid.length;
        int n = obstacleGrid[0].length;
        if (obstacleGrid[0][0] == 1 || obstacleGrid[m - 1][n - 1] == 1) {
            return 0;
        }    
        
        int[][] path = new int[m][n];
        path[0][0] = 1;
        
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (obstacleGrid[i][j] != 0) {
                    path[i][j] = 0;
                } else {
                    if (i > 0) path[i][j] += path[i - 1][j];
                    if (j > 0) path[i][j] += path[i][j - 1];
                }
            }
        }
        
        return path[m - 1][n - 1];
    }
}