leetcode Unique Paths题解

题目描述：

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

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

中文理解：

给定一个矩形的长宽m，n，然后一个机器人从矩阵左上角走到右下角的方案有多少种，机器人只能向下走或者向右走。

解题思路：

可以使用二维矩阵来保存走到每一步的方法数，其中第一行和第一列走法均为1，其他根据递推公式path[i][j]=path[i-1][j]+path[i][j-1]。

代码（java）：

class Solution {
    public int uniquePaths(int m, int n) {
        int[][] path=new int[m][n];
        for(int i=0;i