694 - The Collatz Sequence

  The Collatz Sequence 

An algorithm given by Lothar Collatz produces sequences of integers, and is described as follows:

Step 1:

Choose an arbitrary positive integer A as the first item in the sequence.

Step 2:

If A = 1 then stop.

Step 3:

If A is even, then replace A by A / 2 and go to step 2.

Step 4:

If A is odd, then replace A by 3 * A + 1 and go to step 2.

It has been shown that this algorithm will always stop (in step 2) for initial values ofA as large as 10⁹, but some values of A encountered in the sequence may exceed the size of an integer on many computers. In this problem we want to determine the length of the sequence that includes all values produced until either the algorithm stops (in step 2), or a value larger than some specified limit would be produced (in step 4).

Input 

The input for this problem consists of multiple test cases. For each case, the input contains a single line with two positive integers, the first giving the initial value ofA (for step 1) and the second giving L, the limiting value for terms in the sequence. Neither of these,A or L, is larger than 2,147,483,647 (the largest value that can be stored in a 32-bit signed integer). The initial value ofA is always less than L. A line that contains two negative integers follows the last case.

Output 

For each input case display the case number (sequentially numbered starting with 1), a colon, the initial value forA, the limiting value L, and the number of terms computed.

Sample Input 

 3 100 34 100 75 250 27 2147483647 101 304 101 303 -1 -1

Sample Output 

 Case 1: A = 3, limit = 100, number of terms = 8 Case 2: A = 34, limit = 100, number of terms = 14 Case 3: A = 75, limit = 250, number of terms = 3 Case 4: A = 27, limit = 2147483647, number of terms = 112 Case 5: A = 101, limit = 304, number of terms = 26 Case 6: A = 101, limit = 303, number of terms = 1
需注意的A和limit得用long long类型的，另外，在win下声明数据类型的时候应该写作 __int64 a; 输入输出的时候用 %I64d  linux下的gcc/g++里面，数据类型声明写作 long long a; 输入输出时候用 %lld 关于使用printf的输入输出，这里就有一个更囧的情况。实际上只要记住，主要的区分在于操作系统：如果在win系统下，那么无论什么编译器，一律用%I64d；如果在linux系统，一律用%lld。这是因为MS提供的msvcrt.dll库里使用的就是%I64d的方式，尽管Dev-Cpp等在语法上支持标准， （来自http://wenku.baidu.com/view/0e2d9ecda1c7aa00b52acb50）
#include <stdio.h>#include <stdlib.h>int main(void){    int i=0;    long long A,A1,limit;    while(scanf("%lld%lld",&A,&limit) ==2)    {    if(A == -1 && limit == -1) break;    int num_term = 1;    A1 = A;    i++;        while(A1 != 1)        {        if(A1 % 2 == 0)        A1 = A1 / 2;        else        A1 = A1 *3 + 1;        if(A1 > limit) break;        num_term++;        }        printf("Case %d: A = %lld, limit = %lld, number of terms = %d\n",i,A,limit,num_term);    }    return 0;}