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uva-100-The 3n + 1 problem

2024-07-30 18:10:47   226人阅读

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=36 

 

The 3n + 1 problem 

Background

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.

The Problem

Consider the following algorithm:

  		1. 		 input n 
 		2. 		 print n 
 		3. 		 if n = 1 then STOP 
 		4. 		 		 if n is odd then  tex2html_wrap_inline44  
 		5. 		 		 else  tex2html_wrap_inline46  
 		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 nthis 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.

The 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 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 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 10 
100 200 
201 210 
900 1000

Sample Output

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

 解题思路：题目的意思是让你求出在n到m之间进行3n+1计算步数最大的数，由于n达到100W，所以暴力的方法会超时，我们首先想到的就是打表预处理1到100W每个数字进行3n+1操作的步数，然后直接求n到m之间的max步数即可。

关于3n+1问题请走任意门-》http://en.wikipedia.org/wiki/Collatz_conjecture

 

 1 #include <stdio.h>
 2 
 3 #define MAXN 1000100
 4 
 5 int a[MAXN];
 6 
 7 int fun(long long n){
 8     int res = 1;
 9     while(1){
10         if(n == 1){
11             break;
12         }
13         if(n%2 == 0){
14             n/=2;
15         }
16         else{
17             n = 3 * n + 1;
18         }
19         res++;
20     }
21     return res;
22 }
23 
24 int main(){
25         int n, m, i, t, ans, x, y;
26         for(i = 1; i < MAXN; i++){
27             a[i] = fun((long long)i );
28         }
29         while(scanf("%d %d", &n, &m) != EOF){
30             x = n, y = m;
31             if(n > m){t = n, n = m, m = t;};
32             ans = -1;
33             for(i = n; i <=m; i++){
34                 ans = ans > a[i] ? ans : a[i];
35             }
36             printf("%d %d %d\n", x, y, ans);
37         }
38         return 0;

39 } 

uva-100-The 3n + 1 problem


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