Lattice paths

Problem 15

Starting in the top left corner of a 2×2 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 20×20 grid?

Answer:

137846528820

Completed on Wed, 26 Oct 2016, 14:59

题解：组合问题。在每一个路径中，都会有20次横向和20次纵向移动。如果把横向移动记为1，纵向移动记为0，那么问题就变成一个40位数字中有20个1和20个0的组合数。所以答案就是C（20,40）。


代码：


#include<cstdio>
#include<iostream>
using namespace std;

int main()
{
  long long ans1=1;
  int j=1;
  for(int i=21;i<=40;i++)
  {
    ans1=(ans1*i)/j;
    j++;
    if(j>20)break;
  }
  cout<<ans1<<endl;
  return 0;
}