Step by Step solution about How to resolve the algorithm Magic squares of doubly even order step by step in the Go programming language

The provided Go code generates and prints a magic square of a given dimension d, which is a square matrix where the sum of each row, column, and diagonal is equal to a constant known as the magic constant. The code takes an integer d as input and returns a 2D slice representing the magic square.

1. Constant and Variables:

• The code defines a constant dimensions with a value of 8, indicating the desired dimension of the magic square.
• It declares a variable bits with the value 0x9669, a bitmask used for generating the magic square pattern.
• size stores the total number of cells in the square, calculated as d * d.
• mult is set to d / 4, which is used to determine the bit position for accessing the bitmask.

2. setupMagicSquareData Function:

• This function takes an integer d representing the dimension of the square and returns a 2D slice [][]int representing the magic square.
• It checks if d is less than 4 or not divisible by 4, which are invalid dimensions for a magic square, and returns an error if true.
• The function initializes an empty 2D slice output to store the square data.
• It iterates over each row and column in the square using nested loops (outer loop for rows and inner loop for columns).
• For each cell, it calculates the bit position bitPos based on the column and row indices and the mult value.
• Using bitwise operations on the bits bitmask, it determines whether to set the cell value to i+1 or size-i. This pattern generates the magic square.
• The cell values are appended to their respective rows in output.

3. arrayItoa Function:

• This function takes an integer array input and returns a string array where each integer is converted to a string.
• It uses the fmt.Sprintf function to format each integer into a string with a fixed width of 4 characters.
• The formatted strings are appended to the output array.

4. main Function:

• The main function calls setupMagicSquareData(dimensions) with the constant dimensions (8) to generate the magic square data.
• If there is an error, it prints the error and exits.
• It calculates the magic constant using the formula (dimensions * (dimensions*dimensions + 1)) / 2.
• It iterates over the rows of the magic square data and prints each row as a space-separated string using strings.Join and arrayItoa.
• Finally, it prints the calculated magic constant.

package main

import (
	"fmt"
	"log"
	"strings"
)

const dimensions int = 8

func setupMagicSquareData(d int) ([][]int, error) {
	var output [][]int
	if d < 4 || d%4 != 0 {
		return [][]int{}, fmt.Errorf("Square dimension must be a positive number which is divisible by 4")
	}
	var bits uint = 0x9669 // 0b1001011001101001
	size := d * d
	mult := d / 4
	for i, r := 0, 0; r < d; r++ {
		output = append(output, []int{})
		for c := 0; c < d; i, c = i+1, c+1 {
			bitPos := c/mult + (r/mult)*4
			if (bits & (1 << uint(bitPos))) != 0 {
				output[r] = append(output[r], i+1)
			} else {
				output[r] = append(output[r], size-i)
			}
		}
	}
	return output, nil
}

func arrayItoa(input []int) []string {
	var output []string
	for _, i := range input {
		output = append(output, fmt.Sprintf("%4d", i))
	}
	return output
}

func main() {
	data, err := setupMagicSquareData(dimensions)
	if err != nil {
		log.Fatal(err)
	}
	magicConstant := (dimensions * (dimensions*dimensions + 1)) / 2
	for _, row := range data {
		fmt.Println(strings.Join(arrayItoa(row), " "))
	}
	fmt.Printf("\nMagic Constant: %d\n", magicConstant)
}