62. Unique Paths

题目：

A robot is located at the top-left corner of a m x ngrid (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.

链接： http://leetcode.com/problems/unique-paths/

题解： 

dp的经典问题，每次向右或向下走一步。第一行或者第一列走到头只有一种方法，所以初始化为1，转移方程是dp[i][j] = dp[i - 1][j] + dp[i][j - 1]

Time Complexity O(m * n)， Space Complexity O(m * n)。

public class Solution {

    public 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]; } }

测试：