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.
ref:
水中的鱼: [LeetCode] Unique Paths II 解题报告
[解题思路]
和Unique Path一样的转移方程：
Step[i][j] = Step[i-1][j] + Step[i][j-1] if Array[i][j] ==0
or = 0 if Array[i][j] =1
or = 0 if Array[i][j] =1
public class Solution { public int uniquePathsWithObstacles(int[][] obstacleGrid) { int m = obstacleGrid.length; int n = obstacleGrid[0].length; int[][] steps = new int[m+1][n+1]; for(int i = 0; i < n+1; i++){ steps[m][i] = 0; } for(int i = 0; i < m+1; i++){ steps[i][n] = 0; } steps[m-1][n] =1; for(int i = m-1; i>= 0; i--){ for(int j = n-1; j >=0; j--){ if(obstacleGrid[i][j] == 1){ steps[i][j] = 0; }else { steps[i][j] = steps[i+1][j] + steps[i][j+1]; } } } return steps[0][0]; } }