Unique Paths II

Q: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.

A: 动态规划

int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
int m = obstacleGrid.size();
if(m==0)
return 0;
int n = obstacleGrid[0].size();

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

vector<vector<int> > count;

int i,j;
for(i=0;i<m;i++)
count.push_back(vector<int>(n));

count[0][0] = 1;

for(i=1;i<m;i++)
count[i][0] = ((obstacleGrid[i][0]==1||count[i-1][0]==0)?0:1);
for(j=1;j<n;j++)
count[0][j] = ((obstacleGrid[0][j]==1||count[0][j-1]==0)?0:1);

for(i=1;i<m;i++)
for(j=1;j<n;j++)
count[i][j] = ((obstacleGrid[i][j]==1)?0:count[i-1][j]+count[i][j-1]);

return count[m-1][n-1];

}