How to resolve the algorithm Magic squares of doubly even order step by step in the ALGOL 68 programming language

Published on 12 May 2024 09:40 PM
#Algol 68

How to resolve the algorithm Magic squares of doubly even order step by step in the ALGOL 68 programming language

Table of Contents

Problem Statement

A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant).
A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction.

Create a magic square of   8 × 8.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Magic squares of doubly even order step by step in the ALGOL 68 programming language

Source code in the algol programming language

BEGIN # Magic squares of doubly even order #
    PROC doubly even magic square = ( INT n )[,]INT:
         IF n MOD 4 /= 0 THEN
            # not a doubly even number #
            [ 1 : 0, 1 : 0 ]INT empty square;
            empty square
         ELSE
            # ok to create the square #
            [ 1 : 4, 1 : 4 ]INT pattern;
            FOR r TO 4 DO
                FOR c TO 4 DO
                    pattern[ r, c ] := IF ( ( c = 1 OR c = 4 ) AND ( r = 1 OR r = 4 ) )
                                       OR ( ( c = 2 OR c = 3 ) AND ( r = 2 OR r = 3 ) )
                                       THEN 1
                                       ELSE 0
                                       FI
                OD
            OD;
            [ 1 : n, 1 : n ]INT result;
            INT s  = n * n, m = n OVER 4;
            INT i := 0;
            FOR r TO n DO
                FOR c TO n DO
                    result[ r, c ] := IF pattern[ ( r - 1 ) OVER m + 1, ( c - 1 ) OVER m + 1 ] = 1
                                      THEN i + 1
                                      ELSE s - i
                                      FI;
                    i +:= 1
                OD
            OD;
            result
         FI # doubly eben magic square # ;
    # test doubly even magic square #
    FOR order FROM 8 BY 4 TO 12 DO
        # calculate the field width for the elements of the square #
        INT w := 1, v := order * order;
        WHILE ( v OVERAB 10 ) > 0 DO w +:= 1 OD;
        # construct the square #
        [,]INT square = doubly even magic square( order );
        print( ( "magic square -- n = ", whole( order, 0 ), newline ) );
        FOR r FROM 1 LWB square TO 1 UPB square DO
            FOR c FROM 2 LWB square TO 2 UPB square DO
                print( ( " ", whole( square[ r, c ], - w ) ) )
            OD;
            print( ( newline ) )
        OD;
        print( ( "magic constant = ", whole( ( ( ( order * order ) + 1 ) * order ) OVER 2, 0 ), newline ) )
    OD
END

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