admin管理员组文章数量:1558087
Problem Description
Aunt Lizzie takes half a pill of a certain medicine every day. She starts with a bottle that contains N pills.
On the first day, she removes a random pill, breaks it in two halves, takes one half and puts the other half back into the bottle.
On subsequent days, she removes a random piece (which can be either a whole pill or half a pill) from the bottle. If it is half a pill, she takes it. If it is a whole pill, she takes one half and puts the other half back into the bottle.
In how many ways can she empty the bottle? We represent the sequence of pills removed from the bottle in the course of 2N days as a string, where the i-th character is W if a whole pill was chosen on the i-th day, and H if a half pill was chosen (0 <= i < 2N). How many different valid strings are there that empty the bottle?
Input
The input will contain data for at most 1000 problem instances. For each problem instance there will be one line of input: a positive integer N <= 30, the number of pills initially in the bottle. End of input will be indicated by 0.
Output
For each problem instance, the output will be a single number, displayed at the beginning of a new line. It will be the number of different ways the bottle can be emptied.
Sample Input
6
1
4
2
3
30
0
Sample Output
132
1
14
2
5
3814986502092304
解析:卡特林(Catalan)数(可以百度)
#include<iostream>
using namespace std;
long long catalan(int n)
{
long long count=1;
for(int i=1,j=2*n;i<=n;i++,j--)
count=count*j/i;
return count;
}
int main()
{
int n;
while(cin>>n)
{
if(n==0) break;
cout<<catalan(n)/(n+1)<<endl;
}
return 0;
}
版权声明:本文标题:hdu4165Pills 内容由热心网友自发贡献,该文观点仅代表作者本人, 转载请联系作者并注明出处:https://m.elefans.com/dongtai/1727341892a1109515.html, 本站仅提供信息存储空间服务,不拥有所有权,不承担相关法律责任。如发现本站有涉嫌抄袭侵权/违法违规的内容,一经查实,本站将立刻删除。
发表评论