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[n][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
}
}

leetcode ---Unique Paths

原文：http://www.cnblogs.com/neversayno/p/5215334.html