Unique Paths II

Description

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.

Notice
m and n will be at most 100.

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.

Link

Lintcode_ladder

Method

1. Dp
2. x

Example

1. 1

class Solution {
public:
    /**
     * @param obstacleGrid: A list of lists of integers
     * @return: An integer
     */ 
    int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
        // write your code here
        if (obstacleGrid.empty()) {
            return 0;
        }
        int m = obstacleGrid.size();
        int n = obstacleGrid[0].size();
        vector<vector<int>> dp(m+1, vector<int>(n+1, 0));
        // may be the first block is the obstacle, so not any move is allowed
        dp[0][1] = 1;
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                // the dp[m+1][n+1], obstacleGrid[m][n],
                // the current i j in dp will be related with i-1 j-1 in obstacleGrid
                if (obstacleGrid[i-1][j-1] != 1) {
                    dp[i][j] = dp[i-1][j] + dp[i][j-1];
                }
            }
        }
        return dp[m][n];
    }
};

Similar problems

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Tags

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