O(n) Sorting Algorithm: Quantum Bogosort | Hacker News Reader

O(n) Sorting Algorithm: Quantum Bogosort

mathnews.uwaterloo.ca

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Some programmers on 4chan came up with a "Sleep sort" algorithm and then proceeded to optimize it, complete with example code:

http://dis.4chan.org/read/prog/1295544154

It essentially spawns a new thread for every item in the array, sleeps for an amount of time that scales with the item's value, and then prints out that item. So it's O(n + timeScale * $biggest_input)

Pretty funny / entertaining if taken lightly :P

I wish I'd seen some of this before I took a discrete optimization course. I would have loved to submit some of this.

That seems like a ridiculous implementation of a quite reasonable algorithm. Instead of spreading them out through time, you can spread the values out through space. Assume you know that you elements are all positive integers less than 100 (or can be mapped to such). Allocate an array of length 100. In O(n) time, you can read through your unsorted list, and copy each element to the appropriate location in the array. Then you can read through the array and print out the values in order.

That sounds suspiciously like an insert sort.

http://en.wikipedia.org/wiki/Insertion_sort

Similar but asymptotically different. In insertion sort, if your partialy sorted list is [1,5], and the next element to insert is a two, you would scan the list until you arrive at the five, which. In the system I described the partialy sorted list would be represented as [1,_,_,_,5], and you would update the second element so it would be [1,2,_,_,5].

EDIT: After thinking about it, you could do the insertion step in O(1) time if you use a linked list instead of an array. The part where insertion sort gets its log(n) factor is in scanning the list, which can take (on average) no less than log(n) time.

tantalor is correct in identifying this algorithm as pigeonhole sort.

https://en.wikipedia.org/wiki/Pigeonhole_sort

I remember reading into this topic a while ago. Here is a relevant Wikipedia article. I, for one, look forward to the day when we all can have all our problems solved by destroying the universe.

[]http://en.wikipedia.org/wiki/Quantum_suicide_and_immortality

Hahahaha.

What's the time-space complexity of destroying the universe?

Time O(1). Space O(n).

It doesn't really matter because in the surviving universe you don't do it.

There is only one universe, so it must be a constant, O(1)

More information about bogosort: https://en.wikipedia.org/wiki/Bogosort

I coded up a quick implementation of this in python, but in testing I found that after the algorithm was done I actually wanted a shuffled list.

I may not understand quantum computing properly, but would not this approach require N entangled qubits? If no, can someone explain how it would function on less than N qubits, for example 1? If it does require N qubits...I can imagine a classical solution with O(n) and slightly less ridiculous hardware requirements.

I think it requires N*log N un-entangled randomly initialized qubits. Please correct me if I'm wrong...

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