HDU1032:The 3n + 1 problem

Problem DescriptionProblems 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.  

InputThe 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. 

OutputFor 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

 

 

題意:題的大意是輸入兩個數(注意,這裡沒有說第一個數一定要小與第二個數),然後對這兩個數之間的所有整數包括端點的數,進行一種規律運算,並求出運算的次數,比較所有的數規律運算次數,輸出最大的.

#include <iostream>using namespace std;int main(){    int a,b,t,i,max;    while(cin >> a >> b)    {        cout << a << " " << b << " ";        if(a>b)//大小不確定        {            t = a;            a = b;            b = t;        }        max = 0;        for(i = a; i<=b; i++)        {            int n = i, sum = 1;            while(n-1)//等於1時就結束            {                if(n%2)                    n = 3*n+1;                else                    n = n/2;                sum++;            }            if(sum>max)            max = sum;        }        cout << max << endl;    }    return 0;}