Question:

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.

Thinking:

This question is similar with Unique Paths, and it’s the same methed to use dynamic programming. Only one difference is that we should check if it’s a obstacle. And if it’s a obstacle, its value of dp should be 0.

Solution:

public class Solution {
    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        int lr = obstacleGrid.length;
        if (lr == 0)
            return 0;
        int lc = obstacleGrid[0].length;
        int[][] dp = new int[lr][lc];
        if (obstacleGrid[0][0] == 1){
            return 0;
        }
        dp[0][0] = 1;

        for (int i = 1; i < lr; i++){
            if (obstacleGrid[i][0] == 1)
                break;
            dp[i][0] = 1;
        }
        for (int i = 1; i < lc; i++){
            if (obstacleGrid[0][i] == 1)
                break;
            dp[0][i] = 1;
        }

        for (int i = 1; i < lr; i++)
            for (int j = 1; j < lc; j++){
                if(obstacleGrid[i][j] == 1)
                    continue;
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }

        return dp[lr-1][lc-1];
    }
}