63.寻找路径第二弹

Unique Paths II

问题描述：

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]]

测试代码（python）：

import numpy as npclass Solution(object):       def uniquePathsWithObstacles(self, obstacleGrid):        """        :type obstacleGrid: List[List[int]]        :rtype: int        """        if obstacleGrid[0][0]==1:            return 0        m = len(obstacleGrid)        n = len(obstacleGrid[0])        dp = np.zeros((m+1,n+1))        dp[0][1] = 1        for i in range(1,m+1):            for j in range(1,n+1):                if obstacleGrid[i-1][j-1]==1:                    dp[i][j] = 0                      continue                dp[i][j] = dp[i-1][j]+dp[i][j-1]        return int(dp[m][n])

性能：

测试代码（c++）：

class Solution {public:    int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) {        if(obstacleGrid[0][0]==1)            return 0;        int m = obstacleGrid.size();        int 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]==1)                {                    dp[i][j] = 0;                        continue;                }                dp[i][j] = dp[i-1][j]+dp[i][j-1];            }        }        return dp[m][n];    }};

性能：