LeetCode -- Unique Paths

Posted 2020-06-16

Question:

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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

 

 Analysis:

一个机器人在 m * n 网格的左上角（由start标识），每次这个机器人只能向右或向下移动，尝试到达网格的右下角（由finish标识）。

这里有多少条可能的不同的路径？

注意： m 和 n 都小于100.

 

思路：由于之前做过求最短路径的问题，所以很容易的想到动态规划的思想。

 

Answer：

public class Solution {
    public int uniquePaths(int m, int n) {
        if(m == 0 && n == 0)
            return 0;
        if(m == 1 || n == 1) return 1;
        int[][] dp = new int[m][n];
        dp[0][0] = 1;
        for(int i=0; i<m; i++) {
            for(int j=0; j<n; j++) {
                if(i == 0 && j == 0)
                    continue;
                else if(i == 0 && j != 0)
                    dp[i][j] = dp[i][j-1];
                else if(i != 0 && j == 0)
                    dp[i][j] = dp[i-1][j];
                else 
                    dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        }
        return dp[m-1][n-1];
    }
}