Description:

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

Now consider if some obstacles are added to the grids. How many unique paths would there be?

An obstacle and space is marked as 1 and 0 respectively in the grid.

How many possible unique paths are there?

Solution:

Time Complexity : O(n^2)
Space Complexity: O(n^2)

var uniquePathsWithObstacles = function(obstacleGrid) {
    const m = obstacleGrid.length;
    const n = obstacleGrid[0].length
    // Create dp array
    const dp = Array(m + 1).fill(0).map(() => Array(n + 1).fill(0));
    dp[0][1] = 1

    for(let i = 1; i < m+1; i++) {
        for(let j = 1; j < n+1; j++){
            // Add value to dp array if the cell we are looking at in the grid is not blocked
            dp[i][j] = obstacleGrid[i-1][j-1]===0 ? dp[i-1][j]+dp[i][j-1] : 0 
        }
    }
    return dp[m][n]
};