62. Unique Paths

问题描述
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?

解题思路
该问题给出m和n，形成一个矩阵，要求从左上角的机器人到达右下角，而且机器人每次只能走一步，且只能向右或者向下。其一共有多少不同的路线。我们可以采用动态规划的思路：对于格点(i， j)。由于只能从上格点(i-1,j)或左格点(i,j-1)到达，并且两者路径是不重复的，因此path[i][j] = path[i-1][j]+path[i][j-1]。

代码展示

#include<iostream>#include<vector>using namespace std;class Solution {public:    int uniquePaths(int m, int n) {        vector<vector<int> > path(m, vector<int>(n, 1));        for(int i = 1; i < m; i ++)        {            for(int j = 1; j < n; j ++)            {                path[i][j] = path[i-1][j] + path[i][j-1];            }        }        return path[m-1][n-1];    }};int main(){    int m, n;    cout<<"请输入m n ：";    cin>>m>>n;    Solution solution;    int result = solution.uniquePaths(m, n);    cout<<result<<endl;    return 0;}

运行结果展示