Unique Paths

lc 62

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).

How many possible unique paths are there?

public class Solution {
    public int uniquePaths(int m, int n) {
        int[][] result = new int[m][n];
        result[0][0] = 1;
        for (int i = 1; i < n; i++){
            result[0][i] = 1;
        }
        for (int j = 1; j < m; j++){
            result[j][0] = 1;
        }
        for(int i = 1; i < m; i++ ){
            for (int j = 1; j < n ;j++){
                result[i][j] = result[i-1][j] + result[i][j-1];
            }
        }
        return result[m-1][n-1];
    }
}

lc 63 Unique Paths 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.

[
  [0,0,0],
  [0,1,0],
  [0,0,0]
]

The total number of unique paths is 2.

public class Solution {
    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        int m = obstacleGrid.length;
        int n = obstacleGrid[0].length;
        int[][] result = new int[m][n];
        if (obstacleGrid[0][0] == 1) return 0;
        result[0][0] = 1;
        for (int i = 1; i < n; i++){
            if (obstacleGrid[0][i] == 1)
                break;
            result[0][i] = 1;
        }
        for (int j = 1; j < m; j++){
            if (obstacleGrid[j][0] == 1)
                break;
            result[j][0] = 1;
        }
        for(int i = 1; i < m; i++ ){
            for (int j = 1; j < n ;j++){
            if (obstacleGrid[i][j] == 1)
                result[i][j] = 0;
            else
                result[i][j] = result[i-1][j] + result[i][j-1];
            }
        }
        return result[m-1][n-1];

    }
}