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2 ^ n complexity algorithm
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2 ^ n complexity algorithm
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I need to implement and test an algorithm with a 2^n complexity. I have been trying to find one for a while. If there is any way I can acheive this by implementation -- with a exact complexity of 2^n that would be optimal. If anyone knows of a location I can find an example, or could help me implement one, that would be awesome :-). The basic operation can be anything, but a single statment like i++; would be best.
Generate all subsets of a set with n elements.
Added. The simplest way of generating all the subsets of S = {a0, a1, ..., an-1} is probably to translate between the binary representation of the rank and the subset.
Take S = {a0, a1, a2}.
rank binary subset
0 000 {}
1 001 {a0}
2 010 {a1}
3 011 {a0, a1}
4 100 {a2}
5 101 {a0, a2}
6 110 {a1, a2}
7 111 {a0, a1, a2}
So, a 1 in the binary means the corresponding element is in the subset. A 0 means the element is not in the subset.
But you should also lookup Gray code.
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