Longest Collatz Sequence - Prokect Euler #14

Question

The following iterative sequence is defined for the set of positive integers:

n → n/2 (n is even) n → 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following sequence:

13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.

Which starting number, under one million, produces the longest chain?

NOTE: Once the chain starts the terms are allowed to go above one million.

This is the task and this is my solution:

     #include <iostream>
     using namespace std;

     int n;
     int start_n;
     bool n_even = false;
     int sequence_length = 0;
     int longest_sequence = 0;
     int longest_sequence_number;

     int main()
     {
     for (n = 2; n <= 1000000; n++)
     {
    start_n = n;

    cout << n << endl;

    do
    {
        sequence_length += 1;
        if (n % 2 == 0)
        {
            n_even = true;
        }
        else
        {
            n_even = false;
        }

        if (n_even == true)
        {
            n = n / 2;
        }
        else
        {
            n = 3 * n + 1;
        }
    } while (n == 1);

    if (sequence_length > longest_sequence)
    {
        longest_sequence = sequence_length;
        longest_sequence_number = start_n;
        sequence_length = 0;
    }
    else
    {
        sequence_length = 0;
    } 
}

cout << "Number with the longest sequence: " << longest_sequence_number << endl;

int end;
cin >> end;

}

I tested both the evaluation of the sequence and the generation of n independently, and both work. However, when i put them together the floor loop generates 2, 5, 17, 53, 161, 485, 1457, 4373, 13121, 39365, 118097, 354293 and says the number with the longest sequence is 2.

Is there a problem with my for loop, do while loop, or both?

The `do ... while (n == 1);` doesn't seem to be correct. Note that `do-while` is not the same as `repeat-until` from other languages. — Bo Persson, Feb 14 '16 at 12:30

score 1 · Accepted Answer · answered Feb 14 '16 at 12:30

1

There are at least 2 problems in your code i can spot right away:

Inside your "sequence-generation" you change n, which you also use as counter in your for-loop. Don't do this, better change your for-loop to increment start_n and use n for the sequence or vice versa.
Your sequence continues while(n==1) - shouldn't it be while(n!=1) ?

answered Feb 14 '16 at 12:30

Anedar

4,235
1
23
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Ah yes thank you for pointing out the while problem. And sorry, but i'm unclear on what you mean by changing the n to start_n. – sanorpetro Feb 14 '16 at 12:45
1

your for-loop iterates over n. Then you copy n into start_n. And then you modify n (with the corrected while-loop) until n==1. The for-loop will increase it to 2 again, the sequence will modify it until its 1 - this is an infinite loop. Let your for-loop iterate over start_n, then copy it into n, then modify n (not the for-loop-variable!) – Anedar Feb 14 '16 at 12:50
I renamed the n inside the for parameters to gen_n and then assigned n to gen_n. I tested it for the largest sequence under 1000 which belonged to 871, however when i set it to a million it seemingly stops just after gen_n == 100,000. Help? – sanorpetro Feb 14 '16 at 13:11

Longest Collatz Sequence - Prokect Euler #14

1 Answers1