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Unique Paths

Dynamic Programming

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.

C++代码:

#include<iostream>using namespace std;class Solution {public:    int uniquePaths(int m, int n) {        if(m==0||n==0)            return 0;        int path[m][n];        path[0][0]=0;        int i,j;        for(i=0;i<m;i++)            path[i][0]=1;        for(j=0;j<n;j++)            path[0][j]=1;        for(i=1;i<m;i++)        {            for(j=1;j<n;j++)                path[i][j]=path[i-1][j]+path[i][j-1];        }        return path[m-1][n-1];    }};int main(){    Solution s;    cout<<s.uniquePaths(3,7)<<endl;}

 

Unique Paths