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Powerset algorithm

Tyler Long
Greenhorn

Joined: Mar 02, 2007
Posts: 4
Hi.

I need help writing a program that will print the powerset of a set/array. I basically just need the idea/algorithm of how to print it. If I knew where to start I'm certain I could code it.

Could someone please point me in the right direction?
Ernest Friedman-Hill
author and iconoclast
Marshal

Joined: Jul 08, 2003
Posts: 24183
    
  34

Hi,

Welcome to JavaRanch!

Let's say there are N elements in the set. The powerset of a set contains 2^N elements, so a 32-element set gives rise to a 4-billion element powerset.

Now imagine an N-bit integer. Let each bit in the number represent one specific element e in the original set. There is one element E in the powerset for each value this integer can take. For each value of the integer, the 1-bits correspond to the elements e of the original set that belong to this powerset element E, and the 0-bits corresponds to elements not in E.

So to print the powerset, you use either a real integer or long, or an array of booleans or any other representation you like of an integer. Then you "count", one value at a time, and for each value of the integer, you compute the corresponding element E of the powerset and print it.


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Tyler Long
Greenhorn

Joined: Mar 02, 2007
Posts: 4
Originally posted by Ernest Friedman-Hill:
Hi,

Welcome to JavaRanch!

Let's say there are N elements in the set. The powerset of a set contains 2^N elements, so a 32-element set gives rise to a 4-billion element powerset.

Now imagine an N-bit integer. Let each bit in the number represent one specific element e in the original set. There is one element E in the powerset for each value this integer can take. For each value of the integer, the 1-bits correspond to the elements e of the original set that belong to this powerset element E, and the 0-bits corresponds to elements not in E.

So to print the powerset, you use either a real integer or long, or an array of booleans or any other representation you like of an integer. Then you "count", one value at a time, and for each value of the integer, you compute the corresponding element E of the powerset and print it.


I do not understand this.
Thanks for the help anyway.
David McCombs
Ranch Hand

Joined: Oct 17, 2006
Posts: 212
Do you understand what a power set is?


"Should array indices start at 0 or 1? My compromise of 0.5 was rejected without, I thought, proper consideration."- Stan Kelly-Bootle
fred rosenberger
lowercase baba
Bartender

Joined: Oct 02, 2003
Posts: 11229
    
  16

what Ernest is saying is that you can use the bits in an integer (or long) as "flags" for whether or not to include an element. say you have 3 elements.

2 ^ 3 = 8.

so, you need to count from 0 - 7 (giving you the 8 powerset elements).

as you count, you look at which bits in your counter are on. so when you get to say 3, your counter looks like this:

000000...000011 (the exact number of 0's depends on your use of an int vs. a long, but it doesn't matter).

so, from this, you know to include the 1st and the 2nd elements of the original set ( the set called e) as the elements of one of your powerset (E elements.


There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
Tyler Long
Greenhorn

Joined: Mar 02, 2007
Posts: 4
Is this right? And I do this up until 16? 2^4?

Let's say I had the set {Grapes, Apples, Oranges, Pears}.

0001 {Grapes}

0010 {Apples}

0011 {Grapes, Apples}

0100 {Oranges}

0101 {Grapes, Oranges}

0110 {Apples, Oranges}

0111 {Grapes, Apples, Oranges}

1000 {Pears}
Ernest Friedman-Hill
author and iconoclast
Marshal

Joined: Jul 08, 2003
Posts: 24183
    
  34

Yes, that's correct!
Tyler Long
Greenhorn

Joined: Mar 02, 2007
Posts: 4
Originally posted by Ernest Friedman-Hill:
Yes, that's correct!


Thank you very much. I really appreciate your help.

You taught me something new.
 
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subject: Powerset algorithm