LeetCode - 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?

这是简单的排列组合问题，即从m+n步中，随便选取其中m步往下走，另外n步往右走。可以直接用公式或者递归实现。递归公式也不难得到：C（m，n）=C（m-1，n）+ C（m，n-1）。但是递归效率较低，可以采用二维数组表示网格中从起点到该格点当前可行的路径数，利用v[i][j]=v[i-1][j]+v[i][j-1]递推关系得到终点的路径数。

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