Unique Paths II
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题目:
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
.
解析:
承接上一道题,在原来的基础增加障碍物而已,只要使用DP找到答案,如果在(i,j)上有障碍,则DP I=0。
时间为O(nm),空间为o(nm)。代码如下
程序:
class Solution {
public:
int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
int m = obstacleGrid.size() , n = obstacleGrid[0].size();
vector<vector<int>> dp(m+1,vector<int>(n+1,0));
dp[0][1] = 1;
for(int i = 1 ; i <= m ; ++i)
for(int j = 1 ; j <= n ; ++j)
if(!obstacleGrid[i-1][j-1])
dp[i][j] = dp[i-1][j]+dp[i][j-1];
return dp[m][n];
}
};
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