UVa100 The 3n+1 problem

The 3n + 1 problem

 

Background

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

 

The Problem

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 printed22 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 isprinted) for any integralinput 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 determinethe number of numbers printed (including the 1). For a given n this iscalled the cycle-length of n. In the example above, the cyclelength of 22 is 16.

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

 

 

The Input

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

You should process all pairs of integers and for eachpair determine the maximum cycle length over all integers between andincluding i and j.

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

 

The Output

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

 

Sample Input

 

1 10
100 200
201 210
900 1000

 

Sample Output

 

1 10 20
100 200 125
201 210 89
900 1000 174

UVa上的第一道题，弄了好一会才过。。。

思路：这题是uva第一道，这题主要的问题在于如何利用以前计算过的结果，如果每次都重新计算就会浪费很多时间，还有就是要注意

题目中的输入两个数大小并不是按顺序给的。要自己调整一下，但是在输出的时候还要原样输出。

我尝试着把判断偶数和除2运算都用位运算完成结果发现时间没有得到任何优化。

闲话少叙，贴代码就走人。。

Code：

#include
int arr[10001];

int main()
{
    int a,b;
    int i;
    arr[1]=1;
    arr[2]=2;
    for(i=3;i<10001;i++)
    {
        long long temp=i;
        int cnt=0;
        while(1)
        {
            if(temp&(0x01))
            {
                temp*=3;
                temp+=1;
                cnt++;
            }
            else
            {
                cnt++;
                temp>>=1;
            }
            if(tempb)
        {
            t=a;
            a=b;
            b=t;
        }
        int max=0;
        for(i=a;i<=b;i++)
        {
            if(max