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Powerset algorithm

 
Tyler Long
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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
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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.
 
Tyler Long
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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
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Do you understand what a power set is?
 
fred rosenberger
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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.
 
Tyler Long
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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
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Yes, that's correct!
 
Tyler Long
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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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