第五届ACM大学生程序设计竞赛:Full Binary Tree

Full Binary Tree

Time Limit: 2000ms Memory limit: 65536K 有疑问？点这里^_^

题目描述

In computer science, a binary tree is a tree data structure in which each node has at most two children. Consider an infinite full binary tree (each node has two children except the leaf nodes) defined as follows. For a
node labelled v its left child will be labelled 2 * v and its right child will be labelled 2 * v + 1. The root is labelled as 1.

You are given n queries of the form i, j. For each query, you have to print the length of the shortest path between node labelled i and node labelled j.

输入

First line contains n(1 ≤ n ≤ 10^5), the number of queries. Each query consists of two space separated integers i and j(1 ≤ i, j ≤ 10^9) in one line.

输出

For each query, print the required answer in one line.

示例输入

5
1 2
2 3
4 3
1024 2048
3214567 9998877

示例输出

1
2
3
1
44

提示

来源

2014年山东省第五届ACM大学生程序设计竞赛

题目意思:

一个满二叉树,给你两个节点,求出这两个节点间的长度.

简单来说要先找到两个节点的最近的公共祖先.这样经过的路程才是可求的最短的路径.现在已知两个节点,只需不停的最大数除以二,直到a==b,这个时候表示已经达到最近的公共祖先.每次除的时候,ans+1,记录路径的长度.最后当a==b时,所求的即为俩个节点间的距离.

#include <iostream>

using namespace std;

int main()
{
int t;
cin>>t;
while(t--)
{
int a,b;
cin>>a>>b;
if(a<b)
swap(a,b);
int ans=0;
while(a!=b)
{
while(a>b)
{
a>>=1;
ans++;
}
swap(a,b);
}
cout<<ans<<endl;
}
return 0;
}