Unique Paths II 解答

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.

Solution

Similar with "Unique Paths", there are two differences to be considered:

1. for dp[0][i] and dp[i][0], if there exists previous element which equals to 1, then the rest elements are all unreachable.

2. for dp[i][j], if it equals to 1, then it's unreachable.

public class Solution {
    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        if (obstacleGrid == null)
            return 0;
        int m = obstacleGrid.length, n = obstacleGrid[0].length;
        int[][] dp = new int[m][n];
        // Check first element
        if (obstacleGrid[0][0] == 1)
            return 0;
        else
            dp[0][0] = 1;
        // Left column
        for (int i = 1; i < m; i++) {
            if (obstacleGrid[i][0] == 1)
                dp[i][0] = 0;
            else
                dp[i][0] = dp[i - 1][0];
        }
        // Top row
        for (int i = 1; i < n; i++) {
            if (obstacleGrid[0][i] == 1)
                dp[0][i] = 0;
            else
                dp[0][i] = dp[0][i - 1];
        }
        // Inside
        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];
    }
}