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?

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

Note: m and n will be at most 100.

 

题意：有一个m * n的二维数组，求出从(0,0)到(m-1,n-1)有多少条路，每次移动只能向下或向右

思路：

dp算法。

dp[i][j] = dp[i - 1][j] + dp[i][j - 1];

代码：

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