【题目】
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 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
【解析】这道题是说，机器人要从左上角走到右下角，只能向下或向右移动，求一共有多少条不同的路径。用动态规划非常好做。
【代码】
public int uniquePaths(int m, int n) { int[][] path = new int[m][n]; for(int i=0;i<m;i++) path[i][n-1]=1; for(int i=0;i<n;i++) path[m-1][i]=1; for(int i=m-2;i>=0;i--){ for(int j=n-2;j>=0;j--) path[i][j]=path[i+1][j]+path[i][j+1]; } return path[0][0]; }