csu2140—A Rational Sequence（递归）

题目链接：传送门

H(1946): A Rational Sequence

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Description

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:

A rational 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,…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 to compute the nth element of the sequence, F(n). Does this problem sound familiar? Well it should! But we changed it a little!

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, and the index, N, of the sequence element to compute (1 <= N <= 2147483647).

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 numerator of the fraction, followed immediately by a forward slash (‘/’) followed immediately by the denominator of the fraction. Inputs will be chosen so neither the numerator nor the denominator will overflow an 32-bit unsigned integer.

Sample Input

41 12 43 114 1431655765

Sample Output

1 1/12 1/33 5/24 2178309/1346269

解题思路：对于二叉树的结点n，左结点为2n，右结点为2n+1

对于当前给出的结点编号递归向上回到起点，然后从起点向下计算出结点的数值

额，当时竟然找了半天规律，太菜了

#include <cstdio>  #include <cstring>  #include <cmath>  #include <iostream>  #include <queue>#include <set>#include <string>#include <stack>#include <algorithm>#include <map>using namespace std;  typedef long long ll;const int N = 10007;const int M = 100000000;const int INF = 0x3fffffff;const int mod = 1e9+7;const double Pi = acos(-1.0);const double sm = 1e-9;typedef pair<int,int> PA; PA getValue( int p ){PA s;if( p == 1 ) return PA(1,1);PA t = getValue(p/2);if( p%2 == 0 ){s.first = t.first;s.second = t.first+t.second;}else{s.first = t.first+t.second;s.second = t.second;}return s;}int main(){int T;scanf("%d",&T);while( T-- ){int n,m;scanf("%d%d",&n,&m);PA ans = getValue(m);printf("%d %d/%d\n",n,ans.first,ans.second);}return 0;}