How to resolve the algorithm Magic squares of odd order step by step in the Seed7 programming language

Published on 12 May 2024 09:40 PM
#Seed7

How to resolve the algorithm Magic squares of odd order step by step in the Seed7 programming language

Table of Contents

Problem Statement

A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square.

For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number.
You should demonstrate the generator by showing at least a magic square for   N = 5.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Magic squares of odd order step by step in the Seed7 programming language

Source code in the seed7 programming language

$ include "seed7_05.s7i";

const func integer: succ (in integer: num, in integer: max) is
  return succ(num mod max);

const func integer: pred (in integer: num, in integer: max) is
  return succ((num - 2) mod max);

const proc: main is func
  local
    var integer: size is 3;
    var array array integer: magic is 0 times 0 times 0;
    var integer: row is 1;
    var integer: column is 1;
    var integer: number is 0;
  begin
    if length(argv(PROGRAM)) >= 1 then
      size := integer parse (argv(PROGRAM)[1]);
    end if;
    magic := size times size times 0;
    column := succ(size div 2);
    for number range 1 to size ** 2 do
      magic[row][column] := number;
      if magic[pred(row, size)][succ(column, size)] = 0 then 
        row := pred(row, size);
        column := succ(column, size);
      else
        row := succ(row, size);
      end if;
    end for;
    for key row range magic do
      for key column range magic[row] do
        write(magic[row][column] lpad 4);
      end for;
      writeln;
    end for;
  end func;

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