Randomly filled Array

[cindy2]

Hi,

I need a 2D array with 9 by 9 elements. The problem is that every column must be randomly filled with the numbers 1 To 9 (Or 0 To 8). But every row must contain exactly one 1, one 2 and one 3.

Can somebody please help me with building this array?

Cindy

[kadghar]

I need a 2D array with 9 by 9 ...

I see, something like a Sudoku, but without the 3x3 squares.

I dont know if there is an easy way, but with some DOs and FORs you can achieve it, something like this should work for the first column, you can use something like that for the next ones.

Dim i As Integer
Dim m As Integer
Dim IO As Boolean
Dim Arr(1 To 9, 1 To 9) As Integer
arr(1,1) = int (rnd * 9) + 1
i = 2
Do
    IO = False
    arr(1,i) = int (rnd*9) + 1
    m = 1
    Do 
        If arr(1,m) = arr(1,i) Then 
            IO = True
            Exit Loop
        End If
        m = m + 1
        If m = i Then Exit Do
    Loop
    If IO = False Then i = i + 1 
    If i = 10 Then Exit Do
Loop

I think there should be some method for sampling without replacement in wikipedia.

HTH

[cindy2]

... with some DOs and FORs ...

I have written a code that produces a 9 by 9 array that contains randomly one "1" in each column and row: So there are never two or more "1" 's in a row or column. My code looks like this:

    Dim j As Integer
    Dim k As Integer = 8
    Dim i As Integer
    Dim x As Integer
 
    Dim Arr(8, 8) As Integer
    x = Int(Rnd() * 9)
    Arr(x, 0) = 1
 
    For i = 1 To 8
        j = Int(Rnd() * 9)
        k = 0
        Do
            Arr(j, i) = 1
            If Arr(j, i) = Arr(j, k) Then
                Arr(j, i) = 0
                j = Int(Rnd() * 9)
                k = 0
            Else
                k = k + 1
                If k = i Then Exit Do
            End If
        Loop
    Next

The next thing I want to do, is to add the numbers "2" in the same way and of course without overwriting the "1" 's. Can you please help me?

Cindy

[kadghar]

The next thing I want to do, is to add the numbers "2" in the same way and of course without overwriting the "1" 's. Can you please help me?

Hi Cindy, I've made the code that adds all the numbers but there's a small problem here, the algorithm doesn't guarantee that you'll be making a valid arrangement. e.g. while assigning number "4" this might happen:

0 0 3 1 2 4 0 0 0
0 4 0 2 0 3 0 1 0
0 0 4 3 0 1 2 0 0
0 0 0 4 1 2 3 0 0
0 3 0 0 4 0 0 2 1
1 0 0 0 3 0 4 0 2
2 0 0 0 0 0 1 3 4
0 1 2 0 0 0 0 4 3
3 2 1 0 0 0 0 0 0

So you won't have a chance to write a 4 in the last line. I think the right way should be generating an ordered array like this:

1 2 3 4 5 6 7 8 9
2 3 4 5 6 7 8 9 1
3 4 5 6 7 8 9 1 2
4 5 6 7 8 9 1 2 3
5 6 7 8 9 1 2 3 4
6 7 8 9 1 2 3 4 5
7 8 9 1 2 3 4 5 6
8 9 1 2 3 4 5 6 7
9 1 2 3 4 5 6 7 8

and then randomly switch rows and columns a random number of times.

HTH

[cindy2]

and then randomly switch rows and columns a random number of times.

HTH

Thanks for your reply

I thought of that too, that there may be some inconsisticy while the array is building up.

In this case only the numbers 1 to 3 have to be at different rows and columns, so I won't encounter inconsistencies. But I want a general solution so that if I want the numbers 1 To 4 at different rows and columns, I only have to make little adjustments to the code.

I'm pretty new to vb2005, so I dont't know how to swap columns and rows until the requirements fit. Can you please help me?

Cindy

[cindy2]

Hi Cindy, I've made the code that adds all the numbers but there's a small problem here, the algorithm doesn't guarantee that you'll be making a valid arrangement. e.g. while assigning number "4" this might happen:

Hi kadghar,

My code produces now a random 9 by 9 array: Both the numbers "1" and "2" are randomized. But even with two random numbers in a 9 by 9 array there will be eventualy an invalid arrangement. So you'r right, The best way is to swap rows and columns until the requierments fit. Can you help me with that please?

Cindy

[kadghar]

Hi kadghar,

My code produces now a random 9 by 9 array: Both the numbers "1" and "2" are randomized. But even with two random numbers in a 9 by 9 array there will be eventualy an invalid arrangement. So you'r right, The best way is to swap rows and columns until the requierments fit. Can you help me with that please?

Cindy

Yeap, sorry i didnt answer before, i've been offline for 2 days and now i've a lot of work at the office.

to generate the initial array do something like

dim arr(8,8) as integer
dim i as integer
dim j as integer
 
for i=0 to 8
    for j = 0 to 8
        arr(i,j) = ((i + j) mod 9 ) +1
    next
next

Depends on de version of vb you are using if you have the mod function. in case you dont, just create it for positive numbers, its quite easy:

public function mod(dou1 as double, dou2 as double) as double
    mod = dou1 - int (dou1/dou2) * dou2
end function

and use mod(i+j , 9 ) + 1 instead.

And then i think you can use randomize to change the seed of the generator and make between 50 and 100 events, do something like:

dim n as integer
randomize 
n=rnd*50 + 51
 
for i = 1 to n
    arr = swap (arr, int(rnd*8), int(rnd*8), int(rnd * 2)+1)
next

i dont know if there's an easy way, but you can create a function like

swap ( swArr, Index1 , Index2, Dimension)

with a couple of FOR or DO and a dummy one-dimensioned array

[cindy2]

And then i think you can use randomize to change the seed of the generator and make between 50 and 100 events, do something like:

dim n as integer
randomize 
n=rnd*50 + 51
 
for i = 1 to n
    arr = swap (arr, int(rnd*8), int(rnd*8), int(rnd * 2)+1)
next

i dont know if there's an easy way, but you can create a function like

swap ( swArr, Index1 , Index2, Dimension)

with a couple of FOR or DO and a dummy one-dimensioned array

Thanks for your reply,

I'm sorry I'm still asking you about the same issue I 'm troubled with. The problem is not to make an ordered array. And even randomize the array is not the real problem. The biggest challenge for me is to make the requirements fit, and when they fit to stop the procedure. I haven't a clue how to mennage that. I also don't understand what you mean with n-times events. Because you still don't know if the requierments will fit in that amount of events...do you? Please, can you help me again? ...Almost forgot: What do you mean with a dummy one-dimensional array

Cindy

[kadghar]

... The biggest challenge for me is to make the requirements fit, and when they fit to stop the procedure. I haven't a clue how to mennage that. I also don't understand what you mean with n-times events...

What do you mean with requirements?? If you want the array to have always numbers 1 to 9 without repeating any in columns and rows, all you have to do is with the original array i gave you... the 123456789 , 23456781 ... and swap its rows and cols, it will always preserve this property... nice isnt it?

n-times mean that you can swap columns or lines a random number of times, lets say n times, where n will be a random number (lets say betwen 50 and 100), so
n= int (rnd * 51 + 50)

but you can do it 30 times or the number you like.

Almost forgot: What do you mean with a dummy one-dimensional array
Cindy

I mean an array that you will dispose after you used it while swaping columns

lets say you want to swap column 2 and 4

what you should do is copy column 2 into this "dummy array" then copy column 4 into column 2 and then "dummy array" into column 4

[cindy2]

What do you mean with requirements?? If you want the array to have always numbers 1 to 9 without repeating any in columns and rows, all you have to do is with the original array i gave you... the 123456789 , 23456781 ... and swap its rows and cols, it will always preserve this property... nice isnt it?

Thank you very much! My code produces now a random array by swapping rows and colums of an ordered array. It looks very nice, but as you probebly know, the array is not really random. Let's take a look at a much simpler ordered array:

1234
2341
3412
4123

Indeed, you can swap rows and colums and the requierments (:every row and column can only have each number just ones) will always fit. But with this initial ordered array you can never make the following array:

3142
4321
1234
2413

So the requierments do fit, but the array can never be made by swapping. My question is: Do you have suggestions to make a really random array? I succeeded in making an array with two random numbers in a x by x array. But it did requiere a lot of code to make just two numbers random.

Cindy

[kadghar]

Thank you very much! My code produces now a random array by swapping rows and colums of an ordered array. It looks very nice, but as you probebly know, the array is not really random. Let's take a look at a much simpler ordered array:

1234
2341
3412
4123

Indeed, you can swap rows and colums and the requierments (:every row and column can only have each number just ones) will always fit. But with this initial ordered array you can never make the following array:

3142
4321
1234
2413

So the requierments do fit, but the array can never be made by swapping. My question is: Do you have suggestions to make a really random array? I succeeded in making an array with two random numbers in a x by x array. But it did requiere a lot of code to make just two numbers random.

Cindy

instead of thinking of
1234
2341
3412
4123

as a base array, think of it as an "index map"

so generate a random vector, something that could look like:

Arr = {3,2,1,4}

and use (imagine indexes go from 1 to 4)
arr(1)arr(2)arr(3)arr(4)
arr(2)arr(3)arr(4)arr(1)
arr(3)arr(4)arr(1)arr(2)
arr(4)arr(1)arr(2)arr(3)

so the original array will look like:

3214
2143
1432
4321

And you can swap its columns and rows.
This way you can increase the posibilities. even then it'll have some restrictions.

HTH

By the way, take a look to this thread. It has a similar problem, and the solution there has even more restrictions, if you can find a way to make some better arrays will be great.

[cindy2]

3214
2143
1432
4321

And you can swap its columns and rows.
This way you can increase the posibilities. even then it'll have some restrictions.

HTH

By the way, take a look to this thread. It has a similar problem, and the solution there has even more restrictions, if you can find a way to make some better arrays will be great.

That's a good idea, using different index-arrays. I don't want to sound "hard to please", but I want a really random array. I made some examples (on paper), with different index-arrays. It's still impossible to make the array I have written above. So, do you have other suggestions for me?
BTW I looked at the thread of Sudoku.

Cindy

[kadghar]

... I don't want to sound "hard to please", ...

oh no!! how can you even say it!!! :P just kidding

I dont know how many permutations this problem has, but in case you find it out, you'll have to have a "basic structure" for each one, so you could randomly chose one of this structures in the begining, use it as a map of indexes and make the swaps..

But at least we have now two basic structures, my 1234 etc... and your imposible one.

If you find another case unreachable by any of these two we already have, you can use it as a third one... and so on.

[Killer42]

Sorry to drop into the thread so late, but have you tried reading through the Wikipedia entry on magic squares?