1. 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.

Note: m and n will be at most 100.

2. 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.

3. Explanation

4. Code

public class LeetCode0063 {
    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        if (obstacleGrid == null || obstacleGrid.length == 0 || obstacleGrid[0].length == 0) {
            return 0;
        }

        if (obstacleGrid[0][0] == 1) {
            return 0;
        }

        int m = obstacleGrid.length;
        int n = obstacleGrid[0].length;

        int[][] dp = new int[m][n];

        dp[0][0] = 1;

        for (int i = 1; i < m; i++) {
            if (obstacleGrid[i][0] == 1) {
                dp[i][0] = 0;
            } else {
                dp[i][0] = dp[i - 1][0];
            }
        }

        for (int j = 1; j < n; j++) {
            if (obstacleGrid[0][j] == 1) {
                dp[0][j] = 0;
            } else {
                dp[0][j] = dp[0][j - 1];
            }
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                if (obstacleGrid[i][j] == 1) {
                    dp[i][j] = 0;
                } else {
                    dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
                }
            }
        }
        return dp[m - 1][n - 1];
    }

    public static void main(String[] args) {
        LeetCode0063 leetcode = new LeetCode0063();
        int[][] obstacleGrid = new int[][] { { 0, 0, 0 }, { 0, 1, 0 }, { 0, 0, 0 } };
        System.out.println(leetcode.uniquePathsWithObstacles(obstacleGrid));
    }
}