4.28 leetcode -28 unique-paths

题目描述

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.

这也是一题动态规划的题目，设定一个二维的数组，每个格子都可以由其他格子走过来，然后可以算得最终的种类。

class Solution {public:    int uniquePaths(int m, int n) {        int** path;        path = (int **)malloc(m*sizeof(int*));        if(m == 0 || n == 0)            return 0;        for(int i = 0;i < m;i++)            {            path[i] = (int *)malloc(n*sizeof(int));            for(int j = 0; j < n;j ++)                {                if(j == 0|| i == 0)                    path[i][j] = 1;                else                    path[i][j] = path[i][j-1] + path[i-1][j];            }        }        return path[m-1][n-1];    }};