Magic Square confusion - c++

Question

#include <iostream>
#include <iomanip>
#include <cstdlib>
using namespace std ;
int main()
{
const int maxsize=21 ;
int magq[maxsize][maxsize] ;
int size ;
cout << "Magic Square" << endl ;
cout << "Size (odd): " ;
cin >> size ;
if( size<=0 || size>maxsize)
{
cout << "Size to big" << endl ;
exit(1) ;
}
if( 1!=size%2)
{
cout << "Not an odd nr. " << endl ;
exit(1) ;
}
for( int x=0; x<size; x++)
for( int y=0; y<size; y++)
magq[x][y] = 0 ;
// In the lecture it is said to put the nr. 1 in the first row middle column
int x=(size-1)/2 ;
int y=0 ;
magq[x][y]=1 ; //As we can clearly see here magq[x][y] for i.e size=5 is magq[2][0]
// which is not first row middle column
for( int z=2; z<=size*size; z++)
{
int xneu=(x+1)%size ; // oder: x<size-1 ? x+1 : 0
int yneu=y>0 ? y-1 : size-1 ;
if (0!=magq[xneu][yneu])
{
xneu=x ;
yneu=y+1 ;
if (yneu==size)
{
cout << "Boundary met under?!" << endl ;
yneu=0 ;
}
}
x=xneu ;
y=yneu ;
if( 0!=magq[x][y])
{
cout << "............some meaningless text!" << endl ;
cout << "Nr.: " << z << " Field: " << x << ", " << y << endl ;
exit(1) ;
}
// cout << "Feld " << x << " " << y << " Zahl " << z << endl ;
magq[x][y]=z ;
}
for( int y=0; y<size; y++)
{
for( int x=0; x<size; x++)
cout << setw(5) << magq[x][y] ;
cout << endl ;
}
int diag1=0, diag2=0 ;
for( int i=0; i<size; i++)
{
diag1 += magq[i][i] ;
diag2 += magq[i][size-1-i] ;
}
cout << "Sum: (diag1, diag2, erwartet) "
<< diag1 << " " << diag2 << " " << (size*(size*size+1))/2 << endl ;
return 0 ;
}
Can someone explain to me how is he moving in the matrix, in this exercise?
If we follow his initial notation then for n=5 (for example)
for z=2, xneu=3 and yneu=4, that is totally the reverse of the position 4,3 in which the number 2 should be stored. (Assuming that the index for rows and Column starts from 0 and ends at 4).
Can anyone explain to me, how are we moving in this program?

Answer 1

This program is about creating a magic square according to the "de la Loubère" method. There is a very good explanation on Wikipedia here. Or, because I saw some German text here.
The mechanism is totally simple. Always Go up and right (take boundaries into account). If t´his place is already filled, then go one down.
The links show a step by step example.
Your confusion about the "Middle" comes from the fact that you assume array index 2 to be not the middle. But it is. Array indicess in C++ start wirth 0. So, if you have an odd number and make a integer division by 2, you will always get an even number, because the 0.5 part is truncated.
3/2=1, 5/2=2, 7/2=3 and so on. And with the example of 5, we will receive a 2 which is the middle of indeces 0,1,2,3,4.
This should answer your question.
Additionally, I will show you a different solution
#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <array>
// The maximumn dimension of the magic square
constexpr size_t MaxDimension{ 21u };
// Some abbreviations for less typing work. Square will be implemented as a 2 dimensional std::array
using Square = std::array< std::array <int, MaxDimension>, MaxDimension>;
// Create a magic square following the method of "De-la-Loubère"
void createMagicSquare(Square& square, int sizeOfSquare) {
// Reset all values in the square to 0
square = {};
// Starting row and column. Set to upper middle cell
int row{}; int column{ sizeOfSquare / 2};
// This will wrap a position if it leaves the boundary of the square
auto wrap = [&sizeOfSquare](const int position) { return (position + sizeOfSquare) % sizeOfSquare; };
// Now build the magic square and fill it with all numbers
for (int runningNumber{ 1 }; runningNumber <= (sizeOfSquare * sizeOfSquare); ++runningNumber) {
// Write number into cell at current position
square[row][column] = runningNumber;
// If the upper right cell is occupied
if (square[wrap(row-1)][wrap(column+1)] != 0) {
// Then just go one rowe down
row = wrap(row + 1);
}
else {
// Next position will be upper right
row = wrap(row - 1);
column = wrap(column + 1);
}
}
}
// Output of the magic square
void display(Square& square, int sizeOfSquare)
{
constexpr int Width = 4;
std::cout << "\nThe Magic square is: \n\n";
for (int row = 0; row < sizeOfSquare; ++row) {
for (int column = 0; column < sizeOfSquare; ++column)
std::cout << std::setw(Width) << square[row][column];
std::cout << "\n\n";
}
}
int main()
{
// Give instruction what to do
std::cout << "Enter The Size of the Magic Square (odd number (<=21): ";
// Read user inpuit and make sure that it is a correct value
if (int sizeOfSquare{}; (std::cin >> sizeOfSquare) and (sizeOfSquare <= MaxDimension) and (sizeOfSquare%2)) {
// Define the empty square
Square square{};
// Fill it with magic numbers
createMagicSquare(square, sizeOfSquare);
// Show result
display(square, sizeOfSquare);
}
else std::cerr << "\nError: Wrong Input\n";
}