# 【纽约区域赛】-E-A Rational Sequence （递归，满二叉树）

E   A Rational Sequence

A sequence of positive rational numbers is defined as follows:

An infinite full binary tree labeled by positive rational numbers is defined by:

 The label of the root is 1/1.

 The left child of label p/q is p/(p+q).

 The right child of label p/q is (p+q)/q.

The top of the tree is shown in the following figure: The sequence is defined by doing a level order (breadth first) traversal of the tree (indicated by the
light dashed line). So that:

F(1) = 1/1, F(2) = 1/2, F(3) = 2/1, F(4) = 1/3, F(5) = 3/2, F(6) = 2/3, …

Write a program which finds the value of n for which F(n) is p/q for inputs p and q.
Greater New York Regional E • A Rational Sequence

Input

The first line of input contains a single integer P, (1  P  1000), which is the number of data sets
that follow. Each data set should be processed identically and independently.

Each data set consists of a single line of input. It contains the data set number, K, a single space, the
numerator, p, a forward slash (/) and the denominator, q, of the desired fraction.

Output

For each data set there is a single line of output. It contains the data set number, K, followed by a
single space which is then followed by the value of n for which F(n) is p/q. Inputs will be chosen so n
will fit in a 32-bit integer.

Sample Input Sample Output

1 1/1
2 1/3
3 5/2
4 2178309/1346269

1 1
2 4
3 11
4 1431655765

``````#include <cstdio>
#include <stack>
#include <queue>
#include <cmath>
#include <vector>
#include <cstring>
#include <algorithm>
using namespace std;
#define CLR(a,b) memset(a,b,sizeof(a))
#define INF 0x3f3f3f3f
#define LL long long
LL h;
LL search(LL a,LL b)		//返回当前节点，前面节点的个数 (再加上上面所有节点的个数((1<<h)-1)即可)
{
h++;
if(a==b)			//当返回根结点时，根节点前面没有节点，所以是 0
return 0;
if(a>b)
return (search(a-b,b))*2;
if(a<b)
return (search(a,b-a))*2-1;
}
int main()
{
int u;
LL k,a,b;
scanf("%d",&u);
while(u--)
{
h=0;
scanf("%lld %lld/%lld",&k,&a,&b);
printf("%lld %lld\n",k,search(a,b)+((LL)1<<h)-1);
}
return 0;
}
``````

原文作者：满二叉树
原文地址: https://blog.csdn.net/Bear1998/article/details/59589617
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