Unique Paths

题目
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?

答案

class Solution {
    public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        dp[m - 1][n - 1] = 1;
        for(int i = m - 1; i >= 0; i--) {
            for(int j = n - 1; j >= 0; j--) {
                int right_paths = 0, down_paths = 0;
                // Skip finish grid
                if(i == m - 1 && j == n - 1) continue;
                // right
                if(j < n - 1)
                    right_paths = dp[i][j + 1];
                // down
                if(i < m - 1)
                    down_paths = dp[i + 1][j];
                dp[i][j] = right_paths + down_paths;
            }
        }
        return dp[0][0];
    }
}
``