[RESOLVED] Full Enumeration of a Boolean Array

[M_Saeidi]

Hi to all.

I’m completely new here. I appreciate your assistances through my question.

I have a Boolean Array like this:
Dim blnarX(1 to 100) as Boolean
Assume that every member of this array is a project that could be selected or not. In addition, these 100 members are just predefined spaces (i.e. just user knows how many projects are there). My code gets the number of projects from the user in a variable like intNumberOfProjects which is an integer smaller than 101. Since each project could be selected or not, there will be 2 ^ intNumberOfProjects different alternatives to select these projects. How can I enumerate all these alternatives by means of blnarX? For example if I (as a code writer) knew that my program should always enumerate just 3 projects, I used something like code below:

blnarX(1) = False
blnarX(2) = False
blnarX(3) = False
For intCtrI = 1 To 2
    For intCtrJ = 1 To 2
        For intCtrK = 1 To 2
            ' Main part of code comes here which evaluates the alternative.
            ' This part of code is performed for 2 ^ 3 (=8) times, which I call
            ' it full enumeration of projects. For Example, in the first iteration no
            ' project is selected and in the last iteration all projects are selected.
            blnarX(3) = not blnarX(3)
        Next intCtrK
        blnarX(2) = not blnarX(2)
    Next intCtrJ
    blnarX(1) = Not blnarX(1)
Next intCtrI

However, I don’t know how many projects the user has. Furthermore, it’s not rational to write four lines for each project. What is the solution? We also have intNumberOfProjects. I want to generalize code above.

Best Regards,
Mohammad

[anhn]

I cannot understand what you want to achieve.

With your code above, with 3 For loops from 1 to 2, that is an even number of times each line blnarX(i) = not blnarX(i) is run, you will go back to original value of blnarX(i). Nothing has been changed.

Instead of Dim blnarX(1 to 100) as Boolean
you can use dynamic array:

Dim blnarX() as Boolean
'-- and later after get input from user with intNumberOfProjects >= 1:
Redim blnarX(1 to intNumberOfProjects)

[M_Saeidi]

I cannot understand what you want to achieve.

With your code above, with 3 For loops from 1 to 2, that is an even number of times each line blnarX(i) = not blnarX(i) is run, you will go back to original value of blnarX(i). Nothing has been changed.

Instead of Dim blnarX(1 to 100) as Boolean
you can use dynamic array:

Dim blnarX() as Boolean
'-- and later after get input from user with intNumberOfProjects >= 1:
Redim blnarX(1 to intNumberOfProjects)

Thank you anhn. I didn't know Dynamic arrays. However, my main question has remained.

It's not important that blnar(i) goes back to it's original amount. I don't want them. I have an Integer Programing like this:

Max Z = a*A + b*B + c*C + ... + n* N

s.t.:
(1) A, B, C, ... , N = 0 or 1
(2) alpha*A + beta*B + ... + nue*N <= Budget

The easiest way (and of course, the most time-consuming way) for solving such a program is Full Enumeration of alternatives. In the main part of the code, first, I should check if the cost of the selected projects is possible (regarding the budget constraint) and if yes, I calculate amount of goal function Z (at the same place, i.e. main part of code). Then each time I compare the Z with a variable named sngMaxValue. If Z > sngMaxValue then (1:sngMaxValue = Z , and 2: store combination of selected projects in another variable), else (Do Nothing). After finishing all For loops, I have the best combination of the projects which gives the greatest Z. How can I escape from writing all these Fors? Please help me.

Regards,
Mohammad

[Ellis Dee]

The easiest way (and of course, the most time-consuming way) for solving such a program is Full Enumeration of alternatives.

Not possible. 2^100 possible values yields north of 1.2 nonillion permutations. If you could process a trillion per second -- which a supercomputer probably couldn't -- it would take something like 40 billion years to finish.

[M_Saeidi]

Thank you Ellis Dee for your useful post.
You are absolutely right. I think I should use some methods of integer programming like Branch and Bound, or cutting planes.