#include <iostream>
#include <stdlib.h>     /* srand, rand */
#include <time.h>       /* time */
#include <math.h>

using namespace std;

// prototypes
int add(int, int);  // no variable names, no function body
int sub(int, int);
int mul(int, int);
int _div(int, int);
int pow(int, int);
int soe(int);

int main() {
  srand(time(NULL));

  // local variables
  int a = rand() % 10;  // this is assignment to variable `a`
  int b = rand() % 10;
  soe(8);
  // cout << a << " ^ " << b << " = " << pow(a, b);
}

int add(int x, int y) {
  return x + y;
}

int sub(int x, int y) {
  return x - y;
}

int mul(int x, int y) {
  return x * y;
}

int _div(int x, int y) {
  if (y == 0) { // equivalence is not the same as assignment
    cout << "Cannot divide by zero!" << endl;
  }
  return x / y;
}

int pow(int base, int power) {  // 2^(1/2) == sqrt(2)
  // we handle no decimals
  if (power < 0) {
    cout << "This function does not support returing negative values." << endl;
    return -1;
  }

  // local variable to store the result
  int soln = 1; // intialized to zero.

  // do the looping
  for (int i = 0; i < power; i++) {
    soln *= base;
  }

  return soln;
}

int soe(int n) {
  // Input: an integer n > 1.
  if (n < 1) {
    cout << "Negative values aren't considered." << endl;
  }

  //Let A be an array of Boolean values, indexed by integers 2 to n,
  //initially all set to true.
  int* arr = new int[n - 1];

  for (int i = 0; i < n; i++) {
    arr[i] = 1;
    cout << arr[i] << " ";
  }

// for i = 2, 3, 4, ..., not exceeding √n:
//    if A[i] is true:
  for (int i = 2; i < sqrt(n); i++) {
    if (arr) {
      for (int j = i; j < n; j++) {
        arr[j] = 0;
      }
    }
  }

  //  Output: all i such that A[i] is true.
  for (int i = 0; i < n; i++) {
    if (arr[i]) {
      cout << i << " ";
    }
  }
  return 0;
}

// ------ Advanced
// sin
// cos
// tan