[LeetCode]-Unique PathsII 有障碍的矩阵中求两点间所有路线条数

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.

[
[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.
分析：
本题可以完全在Unique Paths 的基础上使用动态规划+滚动数组的方式实现。

只是要注意：初始f[0]的值会随着不同“层”的第一个值是否为1，所变化。

class Solution {
public:
int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
const int m=obstacleGrid.size();
const int n=obstacleGrid[0].size();

if(obstacleGrid[0][0] || obstacleGrid[m-1][n-1] ) return 0;

vector<int> f(n,0);

//需要找到第一列首个1在哪，之后f[0]均设为0
int first_col_obstacle;
for(int i=0;i<m;i++)
if(obstacleGrid[i][0]==1){
first_col_obstacle=i;
break;
}

for(int i=0;i<m;i++){
if(i>=first_col_obstacle)
f[0]=0;
else
f[0]=1;
for(int j=1;j<n;j++){
if(obstacleGrid[i][j]==1)
f[j]=0;
else
f[j]= f[j-1]+f[j];
}
}

return f[n-1];
}
};