Unique Path 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.

Analyse: Construct another 2*2 array to store path information. First initialize the first column and first row, then compute remaining parts.

Runtime: 4ms.

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> > path(m, vector<int>(n, 0));
        path[0][0] = 1;
        for(int i = 1; i < m; i++){ //indicate whether elements in the first column are reachable
            if(obstacleGrid[i][0] == 0 && path[i - 1][0] == 1) path[i][0] = 1;
            else path[i][0] = 0;
        }
        for(int j = 1; j < n; j++){ //indicate whether the elements in the first row are reachable
            if(obstacleGrid[0][j] == 0 && path[0][j - 1] == 1) path[0][j] = 1;
            else path[0][j] = 0;
        }
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                if(obstacleGrid[i][j] == 1) path[i][j] = 0;
                else path[i][j] = path[i - 1][j] + path[i][j - 1];
            }
        }
        return path[m - 1][n - 1];
    }
};