leetcode Unique Paths II

Unique Paths II

Total Accepted: 2092 Total
Submissions: 8049My Submissions

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.

I actually submitted the code with TLE using DFS. DP is the right solution:

class Solution {
 public:
  int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
    int m = obstacleGrid.size(), n = m == 0 ? 0 : obstacleGrid[0].size(), count = 0;
    if (m == 0 || n == 0)
      return count;
    vector<vector<int>> dp(m, vector<int>(n, 0));
    int i, j;
    if (obstacleGrid[0][0] == 1)
      return 0;
    else
      dp[0][0] = 1;
    for (j = 1; j < n; ++j)
      dp[0][j] = dp[0][j - 1] & (obstacleGrid[0][j] == 0);
    for (i = 1; i < m; ++i)
      dp[i][0] = dp[i - 1][0] & (obstacleGrid[i][0] == 0);
    
    for (i = 1; i < m; ++i)
      for (j = 1; j < n; ++j)
        if (obstacleGrid[i][j] == 0)
          dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
        else
          dp[i][j] = 0;
    return dp[m - 1][n - 1];

  }
};