62. Unique Paths

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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.

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Hide Similar Problems (M) Unique Paths II (M) Minimum Path Sum (H) Dungeon Game

解题思路：这是一道非常经典的动态规划的题目，根据前面的结果得到后面的结果。

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

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