poj 1095 Trees Made to Order 卡特兰数

这题用到了卡特兰数，详情见：http://www.cnblogs.com/jackge/archive/2013/05/19/3086519.html

解体思路详见：http://blog.csdn.net/lvlu911/article/details/5425974

代码如下：

 

#include<iostream>
#include<stdio.h>
#include<algorithm>
#include<iomanip>
#include<cmath>
#include<cstring>
#include<vector>
#define ll __int64
#define pi acos(-1.0)
#define MAX 50000
using namespace std;
int an[19]={1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012,
742900,2674440,9694845,35357670,129644790,477638700};
void fun(int n,int k)
{
    if(n==1){
        cout<<'X';
        return;
    }
    int i,sum=0;
    for(i=0;sum<k;i++)
        sum+=an[i]*an[n-i-1];
    i--;
    sum-=an[i]*an[n-i-1];
    k-=sum;
    if(i){
        cout<<'(';
        fun(i,(k-1)/an[n-i-1]+1);
        cout<<')';
    }
    cout<<'X';
    if(n-i-1){
        cout<<'(';
        fun(n-i-1,(k-1)%an[n-i-1]+1);
        cout<<')';
    }
}
int main(){
    int n,m,sum,i;
    while(cin>>n&&n){
        sum=0;
        for(i=1;sum<n;i++)
            sum+=an[i];
        i--;
        fun(i,n-sum+an[i]);
        cout<<endl;
    }
    return 0;
}