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.

这道题感觉是个经典的dp题目。dp就是建一个二维数组然后看看每个步骤结果应该是怎样的。

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

这道题需要注意的是有的时候数组会变成一维的，这个时候总数只有一个，可以通过一开始判断返回，也可以把path[0][0]赋值为1来包含长度为2，维度为1的情况。

这道题还有数学解法。。。在此先不深究了，到时候有时间再回顾吧。。。