Step by Step solution about How to resolve the algorithm Magic squares of odd order step by step in the Julia programming language

This code implements a function called magicsquareodd that generates an odd-order magic square. A magic square is a square matrix where the sum of each row, column, and diagonal is the same.

The magicsquareodd function takes one argument, base, which must be an odd integer greater than or equal to 3. It starts by creating a square matrix filled with zeros and sets the initial position to the top-left corner (row 1, column 1). It then iterates through the numbers from 1 to the square of the base, assigning each number to the current position in the matrix.

The function uses a specific algorithm to determine the next position in the matrix. If the cell to the right of the current position is empty, the next position is to the right. If the cell to the right is not empty, the next position is one row down and one column to the left.

If the next position is outside the bounds of the matrix, the function wraps around to the beginning of the next row. This ensures that all cells in the matrix are filled.

Once the function has assigned all the numbers to the matrix, it returns the resulting magic square.

The main program calls the magicsquareodd function for odd values of base from 3 to 7 and prints the resulting magic squares.

Here is an example output for base = 5:

Magic square with size 5 - magic constant = 65
----------------------------------------------------
5  1  24  25  20
4  20  19  18  21
21  18  17  16  22
22  17  16  15  23
23  16  15  14  24

# v0.6.0

function magicsquareodd(base::Int)
    if base & 1 == 0 || base < 3; error("base must be odd and >3") end

    square = fill(0, base, base)
    r, number = 1, 1
    size = base * base

    c = div(base, 2) + 1
    while number ≤ size
        square[r, c] = number
        fr = r == 1 ? base : r - 1
        fc = c == base ? 1 : c + 1
        if square[fr, fc] != 0
            fr = r == base ? 1 : r + 1
            fc = c
        end
        r, c = fr, fc
        number += 1
    end

    return square
end

for n in 3:2:7
    println("Magic square with size $n - magic constant = ", div(n ^ 3 + n, 2))
    println("----------------------------------------------------")
    square = magicsquareodd(n)
    for i in 1:n
        println(square[i, :])
    end
    println()
end