Problem 14

Problem 14
Filename: prob14.cc

// 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.

#include <iostream>
#include <list>

using namespace std;

const unsigned int MAX_BOUND = 1000000;

inline unsigned int nextNumber(unsigned int x)
{
  return (x%2 == 0) ? x/2 : ((3*x)+1);
}

inline size_t getSeqLength(const unsigned int x)
{
  size_t length = 0;

  for(unsigned int y=x; y != 1; y=nextNumber(y))
    {
      ++length;
    }

  // +1 for the 1 on the end
  return length + 1;
}

int main()
{
  size_t current_max = 0;
  unsigned int current = 0;

  for(int i=MAX_BOUND; i>0; --i)
    {
       size_t sl = getSeqLength(i);

      if(sl > current_max)
	{
	  current = i;
	  current_max = sl;
	}
    }

  cout << "answer: " << current << endl;
  
  return 0;
}



#if 0
void printList(const list<unsigned int> &v)
{
  for(list<unsigned int>::const_iterator i = v.begin();
      i != v.end();
      ++i)
    cout << *i << ", ";
  cout << endl;
}

inline unsigned int nextNumber(unsigned int x)
{
  return (x%2 == 0) ? x/2 : ((3*x)+1);
}

inline size_t checkValueAndRemoveSequenceFromList(list<unsigned int> &v)
{
  size_t length = 0;

  for(unsigned int y=v.front(); y != 1; y=nextNumber(y))
    {
      ++length;
      if(y%2 == 1 && y < MAX_BOUND)
	{
	  v.remove(y);
	}
    }

  // +1 for the 1 on the end
  return length + 1;
}

int main()
{
  // create the working list

  list<unsigned int> v;
  for(unsigned int i=3; i<=MAX_BOUND; i+=2)
    {
      v.push_front(i);
    }

  unsigned int current_start = -1;
  unsigned int current_max = 0;
  while(v.size() > 1)
    {
      const unsigned int working = v.front();
      const size_t length = checkValueAndRemoveSequenceFromList(v);
      if(length > current_max)
	{
	  current_start = working;
	  current_max = length;
	}
    }

  cout << "answer: " << current_start << ":(";
  cout << current_max << ")" << endl;


  return 0;
}
#endif

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