HDOJ1032 The 3n+1 Problem（趣味数字——"角谷猜想"实现）

The 3n + 1 problem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 40189    Accepted Submission(s): 14697

Problem Description

Problems in Computer Science are often classified as belonging to a certain class of problems (e.g., NP, Unsolvable, Recursive). In this problem you will be analyzing a property of an algorithm whose classification is not known for all possible inputs.

Consider the following algorithm: 


    1.      input n

    2.      print n

    3.      if n = 1 then STOP

    4.           if n is odd then n <- 3n + 1

    5.           else n <- n / 2

    6.      GOTO 2


Given the input 22, the following sequence of numbers will be printed 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 

It is conjectured that the algorithm above will terminate (when a 1 is printed) for any integral input value. Despite the simplicity of the algorithm, it is unknown whether this conjecture is true. It has been verified, however, for all integers n such that 0 < n < 1,000,000 (and, in fact, for many more numbers than this.) 

Given an input n, it is possible to determine the number of numbers printed (including the 1). For a given n this is called the cycle-length of n. In the example above, the cycle length of 22 is 16. 

For any two numbers i and j you are to determine the maximum cycle length over all numbers between i and j. 

 

Input

The input will consist of a series of pairs of integers i and j, one pair of integers per line. All integers will be less than 1,000,000 and greater than 0. 

You should process all pairs of integers and for each pair determine the maximum cycle length over all integers between and including i and j. 

You can assume that no opperation overflows a 32-bit integer.

 

Output

For each pair of input integers i and j you should output i, j, and the maximum cycle length for integers between and including i and j. These three numbers should be separated by at least one space with all three numbers on one line and with one line of output for each line of input. The integers i and j must appear in the output in the same order in which they appeared in the input and should be followed by the maximum cycle length (on the same line). 

 

Sample Input

1 10100 200201 210900 1000

 

Sample Output

1 10 20100 200 125201 210 89900 1000 174

 

Source

UVA

【分析】"角谷猜想"实现。

题意：输入两个数i和j，对于[i, j]上上的每个数x，若x是奇数，则x=3*x+1; 若x是偶数，则x=x/2，直到x为1为止。求出此闭区间上包括x和1在内的最大循环圈的长度（如给出的22：22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1，循环圈长度为16）。

        需要注意i和j的大小关系并未指定，应该分i<=j 和 i>j 两种情况讨论。最后输出i、j和最大循环圈长度。

#include <stdio.h>typedef long long ll;ll m,n;void swap(ll *a,ll *b){ll t;t=*a;*a=*b;*b=t;}int main(){ll i,tm,tn;ll len,maxl,temp;while(scanf("%lld %lld",&m,&n)!=EOF){tm=m;       //用tm和tn保存输入的m和n，便于后续操作 tn=n;if(m>n)swap(&m,&n);maxl=0;for(i=m;i<=n;i++){temp=i;len=1;while(temp!=1){len++;if(temp%2==0)temp/=2;elsetemp=3*temp+1;}if(len>maxl)maxl=len;}if(tm>tn)printf("%lld %lld %lld\n",n,m,maxl);elseprintf("%lld %lld %lld\n",m,n,maxl);}return 0;}