two_wisemen_and_two_numbers.cc

#include <iostream>
#include <set>
#include <utility>

using namespace std;

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

void main() {
  set<int> good_sums;
  // Operations done by second wiseman.
  for (int a = 2; a <= 100; ++a) {
    for (int b = 2; b <= 100; ++b) {
      int sum = a + b;
      int mul = a * b;
      bool good_sum = true;
      for (int a2 = 2; a2 <= sum - 2; ++a2) {
        int 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<int> good_muls;
  for (int a_1 = 2; a_1 <= 100; ++a_1) {
    for (int a_2 = 2; a_2 <= 100; ++a_2) {
      if (!IsPrime(a_1) || !IsPrime(a_2)) continue;
      int a1 = a_1 * a_2;
      if (a1 > 100) continue;
      for (int b1 = 2; b1 <= 100 - a1; ++b1) {
        if (!IsPrime(b1)) continue;
        if (b1 * a_2 > 100) continue;
        if ((good_sums.count(a1 + b1) > 0 && good_sums.count(a_1 + b1 * a_2) == 0 && good_sums.count(a_2 + b1 * a_1) == 0) ||
            (good_sums.count(a1 + b1) == 0 && good_sums.count(a_1 + b1 * a_2) > 0 && good_sums.count(a_2 + b1 * a_1) == 0) ||
            (good_sums.count(a1 + b1) == 0 && good_sums.count(a_1 + b1 * a_2) == 0 && good_sums.count(a_2 + b1 * a_1) > 0)) {
          good_muls.insert(a1 * b1);
        }
      }
    }
  }
  cout << "Answers" << endl;
  for (auto it = good_sums.begin(); it != good_sums.end(); ++it) {
    int good_muls_count = 0;
    int ans_a = 0, ans_b = 0;
    for (auto a2 = 2; a2 <= *it - 2; ++a2) {
      int b2 = *it - a2;
      if (a2 > b2 || a2 > 100 || b2 > 100) continue;
      if (good_muls.count(a2 * b2) > 0) {
        ++good_muls_count;
        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;
    }
  }
}