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:
Using dynamic programming:public class Solution { public int uniquePathsWithObstacles(int[][] obstacleGrid) { int[][] numberOfPaths = new int[obstacleGrid.length][obstacleGrid[0].length]; numberOfPaths[0][0] = obstacleGrid[0][0]==0 ? 1 : 0; for (int i=0; i<obstacleGrid.length; i++) { for (int j=0; j<obstacleGrid[0].length; j++) { if (obstacleGrid[i][j]==0) { numberOfPaths[i][j] += i>0 ? numberOfPaths[i-1][j] : 0; numberOfPaths[i][j] += j>0 ? numberOfPaths[i][j-1] : 0; } } } return numberOfPaths[obstacleGrid.length-1][obstacleGrid[0].length-1]; } }
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