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 → 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.

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;
}

 

Advertisements

About Khuram Ali

Programming... Programming and Programming...!!!

Posted on July 3, 2013, in Project Euler and tagged , , , , , . Bookmark the permalink. 1 Comment.

  1. #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;

    }

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: