leetcode ---Unique Paths

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?（二维图像，只能往右或下走一步，从左上角到右下角一共多少种走法？）方法一：确定到任意一个点能有多少种走法？当x=0或y=0时，只能有一种；当x！=0 且 y！=0时，有 matrix[y][x]=matrix[y-1][x] + matrix[y][x-1]种走法；用 （上+左）代码：
public class Solution {
int[][] matrix;
public int uniquePaths(int m, int n) {
matrix = new int
[m];
for(int y=0; y<n; y++) {
for(int x=0; x<m; x++) {
//Fill top row and left most row with 1s
if(x == 0 || y==0) matrix[y][x]=1;
else {
matrix[y][x]=matrix[y-1][x] + matrix[y][x-1]; //相当于把每个点的走法种类都表示出来
}
}
}
return matrix[n-1][m-1]; //返回的时候要注意，不要越界
}
}方法二：知道从左上到右下，一共有m+n-2步，就分为两类，一类是右（m-1）步；一类是下（n-1）步； 题目转换为：在m+n-2步中，挑选哪些步是右（下）的

代码：

public class Solution {

public int uniquePaths(int m, int n) {

long result = 1;
for(int i=0;i<Math.min(m-1,n-1);i++)
result = result*(m+n-2-i)/(i+1);                  //公式
return (int)result;

}

}