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?
Note: m and n will be at most 100.
Example 1:
Input: m = 3, n = 2Output: 3Explanation:From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:1. Right -> Right -> Down2. Right -> Down -> Right3. Down -> Right -> Right
Example 2:
Input: m = 7, n = 3Output: 28
动态规划，当前值和左边格子与上边格子的状态有关；状态仅与当前行和上一行有关，并且由于是从上往下、从左往右遍历的，可以只使用一维数组存储。
class Solution { public int uniquePaths(int m, int n) { int[] dp = new int[n]; dp[0] = 1; for(int i = 0; i < m; i++){ for(int j = 1; j < n; j++){ dp[j] += dp[j-1]; } } return dp[n-1]; }}