Unique Paths II

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.

  1. [
  2.   [0,0,0],
  3.   [0,1,0],
  4.   [0,0,0]
  5. ]

The total number of unique paths is 2.

Note: m and n will be at most 100.

Solution:

  1. public class Solution {
  2.   public int uniquePathsWithObstacles(int[][] obstacleGrid) {
  3.     int m = obstacleGrid.length;
  4.     int n = obstacleGrid[0].length;
  5.     int[][] dp = new int[m][n];
  7.     // first row
  8.     for (int j = 0; j < n; j++) {
  9.       if (obstacleGrid[0][j] == 1) {
  10.         break;
  11.       }
  12.       dp[0][j] = 1;
  13.     }
  15.     // first col
  16.     for (int i = 0; i < m; i++) {
  17.       if (obstacleGrid[i][0] == 1) {
  18.         break;
  19.       }
  20.       dp[i][0] = 1;
  21.     }
  23.     // others
  24.     for (int i = 1; i < m; i++) {
  25.       for (int j = 1; j < n; j++) {
  26.         if (obstacleGrid[i][j] == 0) {
  27.           dp[i][j] = dp[i-1][j] + dp[i][j-1];
  28.         }
  29.       }
  30.     }
  32.     return dp[m-1][n-1];
  33.   }
  34. }