（Problem 15）Lattice paths

Starting in the top left corner of a 22 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 2020 grid?

题目大意：

从一个22网格的左上角开始，有6条（不允许往回走）通往右下角的路。

对于2020的网格，这样的路有多少条？

// （Problem 15）Lattice paths

// Completed on Tue, 11 Feb 2014, 23:58

// Language: VC++2010

//

// 版权所有（C）acutus   (mail: [email protected]) 

// 博客地址：http://www.cnblogs.com/acutus/

#include<iostream>

#include<cmath>

using namespace std;



long long a[21][21];



int main()

{

    int i;

    for(i = 0; i < 21; i++)

    {

        a[0][i] = 1;

        a[i][0] = 1;

    }

    for (i = 1; i < 21; i++)

        for (int j = 1; j < 21; j++)

            a[i][j] = a[i][j-1] + a[i-1][j];

    cout<<a[20][20]<<endl;

    return 0;

}

Answer:

137846528820