# Project Euler Problem#14 solution in C++

## Longest Collatz sequence

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

`n` `n`/2 (`n` is even)

`n` 3`n` + 1 (`n` is odd)

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

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.

Solution:

#include <iostream> int main () { int N = 1000000; int CHECKPOINT = 800000; long long nTemp = N; int chainCount = 1; int check = 0; long long myNum = 0; for (int i = N; i > CHECKPOINT; --i) { while (nTemp != 1) { if ((nTemp%2) == 0) { nTemp = nTemp/2; }else { nTemp = (nTemp*3) + 1; } ++chainCount; } --N; nTemp = N; if (check < chainCount) { check = chainCount; myNum = nTemp; } chainCount = 1; } std::cout << "The number " << myNum << " has longest chain of " << check << std::endl; }

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Posted on July 3, 2013, in Project Euler and tagged Collatz conjecture, Collatz Problem, Longest Collatz sequence, Number Theory, Project Euler, Project Euler Problem#14 solution in C++. Bookmark the permalink. 1 Comment.

#include

using namespace std;

bool check_number(long long result, long long &chain, long long *myarray)

{

if ( myarray[result] != 0)

{

chain = chain + myarray[result];

return false;

}

else

return true;

}

#define SIZE 1000000

int main()

{

long long *myarray = new long long [SIZE](); // () will intialze everything to 0

cout << myarray[0];

bool valid = true;

long long maxchain = 0,num, result, maxnum;

long long chain;

for ( long long i = 1; i < SIZE ; i++)

{

chain = 0;

num = i;

result = 0;

valid = true;

while( result != 1 && valid)

{

if (num % 2 == 0)

{

result = num/2;

chain++;

if ( result < SIZE && result != 1)

valid = check_number(result, chain,myarray);

}

else

{

result = (3*num) + 1;

chain++;

if ( result maxchain)

{

maxnum = i;

maxchain = chain;

}

}

cout << maxnum;

}