Sphere Online Judge

Problem hidden
This problem was hidden by Editorial Board member probably because it has incorrect language version or invalid test data, or description of the problem is not clear.

SPOJ Problem Set (tutorial)

Problem hidden on 2013-08-04 04:58:30 by Mitch Schwartz

4765. The 3n plus 1 problem V2

Problem code: PROBTRES


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 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.

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


Added by:Coach UTN FRSF
Date:2009-09-02
Time limit:1s-10s
Source limit:50000B
Memory limit:256MB
Cluster: Pyramid (Intel Pentium III 733 MHz)
Languages:All except: ERL JS PERL 6

hide comments
2013-08-04 02:58:36 Mitch Schwartz
Based on previous comments, you should be able to get AC with a 64-bit container if you take only the 32 least significant bits after each operation (i.e. perform operations mod 2^32). Anyway, the problem is hidden.
2013-08-03 23:46:40 Raziman T V
The assumption that intermediate values do not overflow 32 bit range is wrong. As a result, test data is faulty. Using unsigned int in c++ gives AC whereas using long long gives WA.
2013-06-13 07:44:03 Hossam El-Deen Goodname
@Rahul:

The input terminates with EOF (end of file). You can google how to check for EOF using cin or scanf.

Last edit: 2013-06-13 07:44:16
2012-09-20 07:31:57 Rahul
how does the input terminate?
2012-09-05 01:57:34 Adrian Maceiras
Its that it doesnt overflow an unsigned int... java only provides signed int.
2012-02-01 14:06:23 Jakub ©afin
also known as the Collatz sequence
2012-01-29 18:44:10 James Broman
I am having issues with Java for V2. It is not getting accepted while I am able to get it working for V1.

What data types are you guys using for V2? What exactly is the difference between V1 and V2?
2012-01-29 10:28:34 Saurajit
I'm having the same issue - I get AC for the simpler version, but WA for this one, even though I'm using unsigned long.
2011-06-11 07:08:10 Grandmaster
is there something wrong with the input cases ???
i mean i got a wrong answer but on a lower version of this problem it got accepted ..

sorry , figured out my problem ..
guess long long won't work


Last edit: 2011-06-11 07:18:15
2011-06-09 22:54:49 Santiago Zubieta
If no operation overflows a 32 bit integer, it means it should suffice with int, but the problem is that it gives WA even thought the original problem got ACC.
© Spoj.com. All Rights Reserved. Spoj uses Sphere Engine™ © by Sphere Research Labs.