ArithematicExpressions.cpp

#include <vector>
#include <iostream>
#include <cmath>
 
const double Epsilon = 0.00001;
 

void eval(const std::vector<double>& numbers, std::vector<bool>& used)
{
 
  if (numbers.size() == 1)
  {
    auto result = numbers.front() + Epsilon;
    
    if (fmod(result, 1) > 10*Epsilon)
      return;
 
    int index = int(result + Epsilon);
    
    if (index >= 0 && index < (int)used.size())
      used[index] = true;
 
    return;
  }
 
  
  auto next = numbers;
  for (size_t i = 0; i < numbers.size(); i++)
    for (size_t j = i + 1; j < numbers.size(); j++)
    {
     
      double a = numbers[i];
      double b = numbers[j];
 
      
      next = numbers;
      next.erase(next.begin() + j); 
      next.erase(next.begin() + i);
 
     
      next.push_back(a + b);
      eval(next, used);
      next.back() = a - b;   
      eval(next, used);
      next.back() = b - a;  
      eval(next, used);
      next.back() = a * b;   
      eval(next, used);
      if (b != 0)
      {
        next.back() = a / b; 
        eval(next, used);
      }
      if (a != 0)
      {
        next.back() = b / a; 
        eval(next, used);
      }
 
      
    }
}
 

unsigned int getSequenceLength(const std::vector<double>& numbers)
{
  
  std::vector<bool> used(1000, false);
  eval(numbers, used);
 
  unsigned int result = 0;
  while (used[result + 1])
    result++;
  return result;
}
 
int main()
{

 
  
  unsigned int numDigits;
  std::cin >> numDigits;
 
  std::vector<double> numbers(numDigits);
  for (auto& x : numbers)
    std::cin >> x;
 
  
  std::cout << getSequenceLength(numbers);
 

 
  return 0;
}