84-counting-power-sets.md

Problem:

In this kata, you must create a function powers/Powers that takes an array, and returns the number of subsets possible to create from that list. In other words, counts the power sets.

For instance

powers([1,2,3]) => 8

...due to...

powers([1,2,3]) =>
[[],
 [1],
 [2],
 [3],
 [1,2],
 [2,3],
 [1,3],
 [1,2,3]]

Your function should be able to count sets up to the size of 500, so watch out; pretty big numbers occur there!

For comparison, my Haskell solution can compute the number of sets for an array of length 90 000 in less than a second, so be quick!

You should treat each array passed as a set of unique values for this kata.

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###Examples:

powers([])        => 1
powers([1])       => 2
powers([1,2])     => 4
powers([1,2,3,4]) => 16

Powers.powers(new int[]{});        // 1
Powers.powers(new int[]{1});       // 2
Powers.powers(new int[]{1,2});     // 4
Powers.powers(new int[]{1,2,3,4}); // 16

Kata.Powers(new int[] {})        => 1
Kata.Powers(new int[] {1})       => 2
Kata.Powers(new int[] {1,2})     => 4
Kata.Powers(new int[] {1,2,3,4}) => 16

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Inspired by this kata by xcuthulu - refer to it if you're stuck!

Solution