Programming a Latin Square in Delphi? - delphi

Question

I'm trying to make a Latin Square program that accepts a user-entered size of square (e.g. entering 5 will generate a Latin Square 5x5) and then output the formatted square to the user.
If you don't know what a Latin Square is or want to see the actual task I have been set, look no further.
I have slightly coded some of this, but I'm failing at the first hurdle. Teachers are providing no help, you lot are my only hope.
uses
System.SysUtils;
var
// Variables
// 2D array, size defined in main code
Square: array of array of integer;
// Integer holding the square size
SquareSize: integer;
begin
// Introduction
writeln('This program will generate a Latin Squar of a size designated by you.');
// Ask for user input, receive and store in a variable
write('Enter the size of the Latin Square (1 value): ');
readln(SquareSize);
// More user friendly garbage
writeln('Latin Square size: ', SquareSize, ' x ', SquareSize, '.');
// Calculations
// Set size of the 2D array to user designated dimensions
setlength(Square, SquareSize, SquareSize);
end.
After the last line of code (setlength) I want to set ALL values in my new 2D array to the user-entered number. I think.
Other than that, I have no clue what I'm doing.
If you want to help me, please can you try to keep it as simple as possible so I can understand it?
Sorry for any screw-ups made in this, first time on Stack Overflow.

Answer 1

The link you gave also gives the answer, see below the code.
program LatinSquare;
{$APPTYPE CONSOLE}
type
TSquare = array of array of Integer;
procedure WriteLatinSquare(var Square: TSquare; N: Integer);
var
X, Y: Integer;
begin
{ Allocate and fill the square array. }
SetLength(Square, N, N);
for Y := 0 to High(Square) do
for X := 0 to High(Square[Y]) do
Square[X, Y] := (Y + X) mod N + 1;
{ Display the Square array. }
for Y := 0 to High(Square) do
begin
for X := 0 to High(Square[Y]) do
Write(Square[X, Y]:3);
Writeln;
end;
Writeln;
end;
var
Square: TSquare;
SquareSize: Integer;
begin
SquareSize := 6;
WriteLatinSquare(Square, SquareSize);
Readln;
end.
As the link says: start with 1 2 3 4 5 6, then the next line, shift by one, so that becomes 2 3 4 5 6 1, etc... That is what the first part (with the X, Y loops) does: it fills the square.
Of course, Y + X can go over the limit of 0..5 (I add the 1 later on), so you use mod to wrap the values around, so 6 becomes 0, 7 becomes 1, etc. In effect:
1st line: 0+0=0 -> 0, 0+1=1 -> 1, 0+2=2 -> 2, 0+3=3 -> 3, 0+4=4 -> 4, 0+5=5 -> 5
2nd line: 1+0=1 -> 1, 1+1=2 -> 2, 1+2=3 -> 3, 1+3=4 -> 4, 1+4=5 -> 5, 1+5=6 -> 0
3rd line: 2+0=2 -> 2, 2+1=3 -> 3, 2+2=4 -> 4, 2+3=5 -> 5, 2+4=6 -> 0, 2+5=7 -> 1
etc...
Then you add the 1, so instead of 0 1 2 3 4 5you get 1 2 3 4 5 6.
The second part of the routine just prints the Square array.
If you don't need to save the square, it can be done in one part:
procedure WriteMagicSquare2(N: Integer);
var
X, Y: Integer;
begin
for Y := 0 to N - 1 do
begin
for X := 0 to N - 1 do
Write((Y + X) mod N + 1, ' ');
Writeln;
end;
Writeln;
end;
Output (for N = 6):
1 2 3 4 5 6
2 3 4 5 6 1
3 4 5 6 1 2
4 5 6 1 2 3
5 6 1 2 3 4
6 1 2 3 4 5

Answer 2

Assuming your in my school given this is the exact homework I have from the same book word for word. On note of the code above I will add one point, the Latin squares size should be user entered so in the last block of code change it to this:
var
Square: TSquare;
X, UserI, SquareSize: Integer;
begin
X := 0;
Writeln('type -1000 to stop the loop');
repeat
Writeln('What size square do you want?');
readln(UserI);
if UserI = -1000 then
begin
goto gotolable;
end
else
SquareSize := UserI;
WriteLatinSquare(Square, SquareSize);
writeln ('Press enter to do another Latin square');
readln;
until X = 1;
gotolable: