two_wisemen_and_two_numbers_v2.cc

#include <iostream>
#include <set>
#include <vector>
#include <utility>
#include <stdint.h>

using namespace std;
typedef int64_t i64;

bool IsPrime(i64 n) {
  if (n == 2) return true;
  if (n % 2 == 0) return false;
  for (i64 i = 3; i * i <= n; i += 2) {
    if (n % i == 0) return false;
  }
  return true;
}

void main() {
  set<i64> good_sums;
  // Operations done by second wiseman.
  for (i64 a = 2; a <= 100; ++a) {
    for (i64 b = 2; b <= 100; ++b) {
      i64 sum = a + b;
      i64 mul = a * b;
      bool good_sum = true;
      for (i64 a2 = 2; a2 <= sum - 2; ++a2) {
        i64 b2 = sum - a2;
        if (IsPrime(a2) && IsPrime(b2)) {
          good_sum = false;
          //std::cout << "a2 = " << a2 << ", b2 = " << b2 << std::endl;
        }
      }
      if (good_sum) {
        good_sums.insert(sum);
      }
    }
  }
  cout << "GoodSums" << endl;
  for (auto it = good_sums.begin(); it != good_sums.end(); ++it) {
    cout << *it << " ";
  }
  cout << endl;
  // Operations done by second wiseman.
  set<i64> good_muls;
  for (i64 m_1 = 2; m_1 <= 100; ++m_1) {
    if (!IsPrime(m_1)) continue;
    for (i64 m_2 = m_1; m_2 <= 100; ++m_2) {
      if (!IsPrime(m_2)) continue;
      for (i64 m_3 = m_2; m_3 <= 100; ++m_3) {
        if (!IsPrime(m_3)) continue;
        set<i64> possible_sums;
        possible_sums.insert(m_1 + m_2 * m_3);
        possible_sums.insert(m_2 + m_1 * m_3);
        possible_sums.insert(m_3 + m_1 * m_2);
        i64 num_good_sums = 0;
        for (auto it = possible_sums.begin(); it != possible_sums.end(); ++it) {
          if (good_sums.count(*it) > 0) ++num_good_sums;
        }
        if (num_good_sums == 1) good_muls.insert(m_1 * m_2 * m_3);

        for (i64 m_4 = m_3; m_4 <= 100; ++m_4) {
          if (!IsPrime(m_4)) continue;

          set<i64> possible_sums;
          possible_sums.insert(m_1 + m_2 * m_3 * m_4);
          possible_sums.insert(m_2 + m_1 * m_3 * m_4);
          possible_sums.insert(m_3 + m_1 * m_2 * m_4);
          possible_sums.insert(m_4 + m_1 * m_2 * m_4);
          possible_sums.insert(m_1 * m_2 + m_3 * m_4);
          possible_sums.insert(m_1 * m_3 + m_2 * m_4);
          possible_sums.insert(m_1 * m_4 + m_2 * m_3);
          i64 num_good_sums = 0;
          for (auto it = possible_sums.begin(); it != possible_sums.end(); ++it) {
            if (good_sums.count(*it) > 0) ++num_good_sums;
          }
          if (num_good_sums == 1) good_muls.insert(m_1 * m_2 * m_3 * m_4);
        }
      }
    }
  }

  cout << "Answers" << endl;
  for (auto it = good_sums.begin(); it != good_sums.end(); ++it) {
    i64 good_muls_count = 0;
    i64 ans_a = 0, ans_b = 0;
    vector<i64> muls;
    for (auto a2 = 2; a2 <= *it - 2; ++a2) {
      i64 b2 = *it - a2;
      if (a2 > b2 || a2 > 100 || b2 > 100) continue;
      if (good_muls.count(a2 * b2) > 0) {
        ++good_muls_count;
        muls.push_back(a2 * b2);
        ans_a = a2, ans_b = b2;
      }
    }
    if (good_muls_count == 1) {
      cout << "a = " << ans_a << ", b = " << ans_b << ", sum = " << (ans_a + ans_b) << ", mul = " << (ans_a * ans_b) << endl;
      /*
      for (int i = 0; i < muls.size(); ++i) {
        cout << muls[i] << " ";
      }
      cout << endl;
      */
    }
  }
}