Find the 2nd largest element in an array with minimum number of comparisons

Question

For an array of size N, what is the number of comparisons required?

Answer 1

The accepted solution by sdcvvc in C++11.

#include 
#include 
#include 
#include 
#include 

using std::vector;
using std::cout;
using std::endl;
using std::random_shuffle;
using std::min;
using std::max;

vector create_tournament(const vector& input) {
  // make sure we have at least two elements, so the problem is interesting
  if (input.size() <= 1) {
    return input;
  }

  vector result(2 * input.size() - 1, -1);

  int i = 0;
  for (const auto& el : input) {
    result[input.size() - 1 + i] = el;
    ++i;
  }

  for (uint j = input.size() / 2; j > 0; j >>= 1) {
    for (uint k = 0; k < 2 * j; k += 2) {
      result[j - 1 + k / 2] = min(result[2 * j - 1 + k], result[2 * j + k]);
    }
  }

  return result;
}

int second_smaller(const vector& tournament) {
  const auto& minimum = tournament[0];
  int second = INT_MAX;

  for (uint j = 0; j < tournament.size() / 2; ) {
    if (tournament[2 * j + 1] == minimum) {
      second = min(second, tournament[2 * j + 2]);
      j = 2 * j + 1;
    }
    else {
      second = min(second, tournament[2 * j + 1]);
      j = 2 * j + 2;
    }
  }

  return second;
}

void print_vector(const vector& v) {
  for (const auto& el : v) {
    cout << el << " ";
  }
  cout << endl;
}

int main() {

  vector a;
  for (int i = 1; i <= 2048; ++i)
    a.push_back(i);

  for (int i = 0; i < 1000; i++) {
    random_shuffle(a.begin(), a.end());
    const auto& v = create_tournament(a);
    assert (second_smaller(v) == 2);
  }

  return 0;
}