zoj1062

递归类题目

#include<string>
#include<iostream>
using namespace std;
#define MAXNODE 19

int A[MAXNODE],B[MAXNODE];

string tree(int node,int index)
{
  string s("X");
  int i=0,j=node-1;
  for(;i<node;i++,j--)
  {
    int p=A[i]*A[j];
    if(index>=p)
      index-=p;
    else 
      break;
  }
  int x=index/A[j],y=index%A[j];
  if(i)
    s='('+tree(i,x)+')'+s;
  if(j)
    s=s+'('+tree(j,y)+')';
  return s;
}

int main()
{
  B[1]=(B[0]=A[0]=A[1]=1)+1;
  for(int i=2;i<MAXNODE;i++)
  {
    A[i]=0;
    for(int j=0;j<i;j++)
      A[i]+=A[j]*A[i-j-1];
    B[i]=B[i-1]+A[i];
  }
  int N;
  while(cin>>N)
  {
    int node;
    if(!N)  break;
    else 
      for(node=0;node<MAXNODE;node++)
        if(N<B[node])
          break;
    int index=N-B[node-1];
    cout<<tree(node,index)<<endl;
  }
  return 0;
}