Unique Paths

题目名称
Unique Paths—LeetCode链接

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.

分析
  之前遇到一个类似的题目，求最短路径和的问题Minimum Path Sum，大家可以参考一下。这里采用动态规划算法：
  path[i][j] = path[i-1][j] + path[i][j-1]

C++代码

/************************************************************** Copyright:武汉大学计算机学院B507 Author:Ryan Date:2015-10-30 Email:[email protected] Description:Unique Paths **************************************************************/
#include<iostream>
#include<vector>
using namespace std;

int uniquePaths(int m, int n) {
   //初始化一个m x n的二维向量，所有初始值为1
   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=10,n=8;
    cout<<"Unique paths:"<<uniquePaths(m,n)<<endl;
    return 0;
}

总结
  现在用动态规划（Dynamic Programming）解决问题越来越得心应手了。