unique_paths_with_obstacles.cpp

/*
    You are given an m x n integer array grid. There is a robot initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

    An obstacle and space are marked as 1 or 0 respectively in grid. A path that the robot takes cannot include any square that is an obstacle.

    Return the number of possible unique paths that the robot can take to reach the bottom-right corner.

    The testcases are generated so that the answer will be less than or equal to 2 * 109.

    Example 1:
    Input: obstacleGrid = [[0,0,0],[0,1,0],[0,0,0]]
    Output: 2
    Explanation: There is one obstacle in the middle of the 3x3 grid above.
    There are two ways to reach the bottom-right corner:
    1. Right -> Right -> Down -> Down
    2. Down -> Down -> Right -> Right
*/

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