/r/dailyprogrammer #365 - "Up Arrow Notation" (Knuth)

up_arrow_notation.cpp

#include <cassert>
#include <cmath>
#include <iostream>

long calc(long a, long n, long b)
{
  if (n == 1)
    return static_cast<long>(pow(a, b));
  else if (n >= 1 && b <= 0)
    return 1;

  return calc(a, n-1, calc(a, n, b-1));
}

int main(int argc, char* argv[])
{
  long a = std::stoi(argv[1]); // left-side of operator
  long n = std::stoi(argv[2]); // the factor of the arrow / number of arrows
  long b = std::stoi(argv[3]); // right-side of operator

  std::cout << "a=" << a << " n=" << n << " b=" << b << std::endl;

  long result = calc(a, n, b);

  std::cout << "Result: " << result << std::endl;

  // testing
  std::cout << "Starting tests." << std::endl;

  assert(calc(2, 1, 4)  == 16);
  assert(calc(2, 2, 3)  == 16);
  assert(calc(2, 2, 4)  == 65536);
  assert(calc(2, 3, 3)  == 65536);
  assert(calc(1, 1, 0)  == 1);
  assert(calc(1, 2, 0)  == 1);
  assert(calc(-1, 3, 3) == -1);

  std::cout << "Testing complete." << std::endl;

  return 0;
}