Euler 014 c++ Solution

Problem

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.

Answer: 837799

Solution

euler014.cpp

#include <iostream>
#include <vector>
#include <cmath>
#include <cstdint>

uint64_t next_collatz_term(uint64_t prev)
{
  uint64_t ret;
  if( 0 == (prev%2)){
    ret = prev/2;
  }else{
    ret = (3 * prev)+1;
  }
  return ret;
}

static std::vector<int> previous_counts(1000000,-1);

int count_collatz_terms_brute(uint64_t start)
{
  int count = 1;
  while( 1 != start ){
    start = next_collatz_term(start);
    count++;
  }
  return count;
}

int count_collatz_terms_opt(uint64_t start)
{
  if( 1 == start ) return 1;

  int count = 0;

  if( start < 1000000 ){
    count = previous_counts.at(start);
    if( -1 == count ){
      count = count_collatz_terms_opt(next_collatz_term(start));
      count++;
      previous_counts.at(start) = count;
    }
  }else{
    count = count_collatz_terms_brute(start);
  }

  return count;
}

uint64_t longest_collatz_sequence_brute(uint64_t max_check)
{
  int max_count = 0;
  int max_counter = 0;
  for (uint64_t i = 1; i < max_check; i++) {
      int terms = count_collatz_terms_brute(i);
      if( max_count < terms ){
        max_count = terms;
        max_counter = i;
      }
  }
  return max_counter;
}

// Optimization, store previous counts and
// skip already calculated values.
uint64_t longest_collatz_sequence_opt(uint64_t max_check)
{
  int max_count = 0;
  int max_counter = 0;

  for (uint64_t i = 2; i < max_check; i++) {
    if( -1 == previous_counts.at(i) ){
      int count = count_collatz_terms_opt(i);
      if( max_count < count ){
        max_count = count;
        max_counter = i;
      }
    }
  }

  return max_counter;
}

#if ! defined UNITTEST_MODE
int main(int argc, char const *argv[])
{
  int answer = longest_collatz_sequence_brute(1000000);
  std::cout << "Answer: " << answer
                          << '/' << count_collatz_terms_brute(answer)
                          << std::endl;

  answer = longest_collatz_sequence_opt(1000000);
  std::cout << "Answer: " << answer
                          << '/' << count_collatz_terms_opt(answer)
                          << std::endl;
}
#endif // #if ! defined UNITTEST_MODE

Euler 014 c++ Solution

Problem

Solution

See Also