LeetCode每日一题：unique paths

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?

问题分析

简单动态规划问题，到达dp[i][j]的方法数为dp[i-1][j]+dp[i][j-1]

代码实现

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