【leetcode】【62】Unique Paths

一、问题描述

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?

二、问题分析

最基础的DP问题。除了第0行（只能从左边到达）和第0列（只能从上边到达）之外，其余位置都有两种到达方式（上边和左边），显然状态转移方程为dp[i][j] = dp[i][j-1] + dp[i-1][j];

三、Java AC代码

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