PROBTRES - The 3n plus 1 problem V2
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.
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 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.
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).
1 10 20
100 200 125
201 210 89
900 1000 174
The tests for this problem are **wrong**. You have to use **32-bit Unsigned** integers to force overflow in order to pass the tests. also, mentioned in http://discuss.spoj.com/t/wa-3n-1-problem-probtnpo/9780/2Last edit: 2016-02-18 02:50:07
I am getting AC on simpler version and WA on this one using python 2.7. Anyone know what the issue might be considering the language is type-less?
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.
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.
Hossam El-Deen Goodname:
how does the input terminate?
Its that it doesnt overflow an unsigned int... java only provides signed int.
also known as the Collatz sequence
I am having issues with Java for V2. It is not getting accepted while I am able to get it working for V1.
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.