LeetCode OJ:Unique Paths II

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.

备忘录法：

class Solution {
public:
int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
const int m=obstacleGrid.size();
const int n=obstacleGrid[0].size();
f=vector<vector<int>>(m+1,vector<int>(n+1,-1));
return dfs(obstacleGrid,m,n);
}
private:
vector<vector<int>> f;
int dfs(vector<vector<int>> &obst,int x,int y){
if(x<1||y<1)return 0;

if(obst[x-1][y-1])return 0;
if(x==1&&y==1)return 1;
if(f[x][y]>-1)return f[x][y];

f[x][y] = dfs(obst,x-1,y)+dfs(obst,x,y-1);
return f[x][y];
}
};

动态规划：

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