/*
Author: X
Date: 04/27/2015
Purpose: Creates a 3x3 magic square. It's a magic square if the sum of the elements in each row, in each column, and in the two
diagonals is the same value (see the magic square below).
Algorithm:
1. 2D array of 3 * 3.
2. Array is filled with unique values (1-9) that are generated randomly.
3. Checks if the random number generated has been previously generated in the arrack.
4. If the number is unique, it is stored in the array.
5. The array is displayed.
6. Check if the array is a magic square.
7. Keep looping steps until magic square is found.
*/
//Includes
#include <iostream>
#include <ctime>
#include <cstdlib>
//Functions
int checkUnique(); // Function to check if the random number generated is a unique number, i.e if the number is not previously generated in the 2D array.
int magicSquare(); // Function to check if the 2D array is a magic square. Checks if sum of each row and sum of each column and diagonal are equal.

using namespace std;

bool checkUnique(int s[][3], int num){
  for (int i = 0; i < 3; i++){
    for(int j = 0; j < 3; j++){
      if (s[i][j] == 0)
        return true;
      else if (s[i][j] == num)
        return false;
    }
  }
  return true;
}

void initializeArr(int s[][3], int size = 3){
  // Code to generate a randum number.
  bool uniq = false;
  int num;

  // Iterate through the 2D array
  for (int i = 0; i < 3; i++){
    for (int j = 0; j < 3; j++){
      // Generates a number until it is unique.
      while (uniq == false){
        num = rand() % 9 + 1;
        uniq = checkUnique(s, num);
      }
      s[i][j] = num;
      uniq = false;
    }
  }
}

void displayArr(int s[][3], int size = 3){
  // Iterate through the 2D array and display the element
  for (int i = 0; i < 3; i++){
    for (int j = 0; j < 3; j++){
      cout << s[i][j] << "\t";
    }
    cout << endl;
  }
}

bool magicSquare(int s[][3], int size = 3){
  // Value to store diagonals
  int d1=0, d2=0;

  // Calulating the sum of each row and assigning it to subscript 3
  for (int i = 0; i < 3; i++){
    for (int j = 0; j < 3; j++){
      s[i][3] += s[i][j];
    }
  }

  // Calculating the sum of each col and assigning to to subscript 3
  for (int j = 0; j < 3; j++){
    for (int i = 0; i < 3; i++){
      s[3][j] += s[i][j];
    }
  }

  // Calculating the sum of the diagonal
  for (int i = 0, j = 0; i < 3; i++, j++){
    d1 += s[i][j];
  }
  for (int i = 3, j = 0; j < 3; i--, j++){
    d2 += s[i][j];
  }

  // See if the sum of everything are equal
  if (s[0][2] == d1 && s[1][2] == d1 && s[2][0] == d1 && s[2][1] == d1 && d1 == d2)
    return true;
  else
    return false;
}

void zeroArr(int s[][3], int size = 3){
  for (int i = 0; i < 3; i++){
    for (int j = 0; j < 3; j++){
      s[i][j] = 0;
    }
  }
}

int main(){
    srand(time(NULL)); //called at the beginning of main so
  // Create the 2D 3x3 array
  int square [3][3] = {0};
  bool mSq = false;

  // Continue creating a new matrix until a magic square is found
  while (mSq == false){
    // Function call to fill in the array
    initializeArr(square);
    displayArr(square);
    // Function call to determine if it is a magic square
    mSq = magicSquare(square);
    if (mSq == true)
{

    displayArr(square);
      cout << "Magic Square!" << endl;
}
    else{
      cout << "Not a Magic Square!" << endl;
      // Zero out the array
      zeroArr(square);
    }
  }

  return 0;
}