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?

因为只能向下或者向右走，所依某一点的值就是上面方格的值 和左边的值 相加

dynamic programming.

public class Solution {    public int uniquePaths(int m, int n) {        int[][] grid=new int[100][100];        for(int i=0;i<m;i++){        	grid[i][0]=1;        }        for(int j=0;j<n;j++){        	grid[0][j]=1;        }        for(int i=1;i<m;i++){        	for(int j=1;j<n;j++){        		grid[i][j]=grid[i-1][j]+grid[i][j-1];        	}        }        return grid[m-1][n-1];    }}

leetcode Unique Paths