Spaghetti sort

Spaghetti sort is a linear-time, analog algorithm for sorting a sequence of items, introduced by A. K. Dewdney in his Scientific American column.^[1]^[2]^[3] This algorithm sorts a sequence of items requiring O(n) stack space in a stable manner. It requires a parallel processor, which is assumed to be able to find the maximum of a sequence of items in O(1) time.

Algorithm

For simplicity, assume we are sorting a list of natural numbers. The sorting method is illustrated using uncooked rods of spaghetti:

For each number x in the list, obtain a rod of length x. (One practical way of choosing the unit is to let the largest number m in the list correspond to one full rod of spaghetti. In this case, the full rod equals m spaghetti units. To get a rod of length x, break a rod in two so that one piece is of length x units; discard the other piece.)
Once you have all your spaghetti rods, take them loosely in your fist and lower them to the table, so that they all stand upright, resting on the table surface. Now, for each rod, lower your other hand from above until it meets with a rod—this one is clearly the longest. Remove this rod and insert it into the front of the (initially empty) output list (or equivalently, place it in the last unused slot of the output array). Repeat until all rods have been removed.

Analysis

Preparing the n rods of spaghetti takes linear time. Lowering the rods on the table takes constant time, O(1). This is possible because the hand, the spaghetti rods and the table work as a fully parallel computing device. There are then n rods to remove so, assuming each contact-and-removal operation takes constant time, the worst-case time complexity of the algorithm is O(n).

References

^ Dewdney, A. K. (June 1984), "On the spaghetti computer and other analog gadgets for problem solving", Scientific American, vol. 250, no. 6, pp. 19–26
^ Stauffer, Dietrich (May 15, 1999), Annual Reviews of Computational Physics VI, World Scientific, p. 260, ISBN 981-02-3563-1
^ Adamatzky, Andrew (July 1, 2006), From Utopian to Genuine Unconventional Computers, Luniver Press, p. 96, ISBN 0-9551170-9-7

External links

[1] Dewdney, A. K. (June 1984), "On the spaghetti computer and other analog gadgets for problem solving", Scientific American, vol. 250, no. 6, pp. 19–26

[2] Stauffer, Dietrich (May 15, 1999), Annual Reviews of Computational Physics VI, World Scientific, p. 260, ISBN 981-02-3563-1

[3] Adamatzky, Andrew (July 1, 2006), From Utopian to Genuine Unconventional Computers, Luniver Press, p. 96, ISBN 0-9551170-9-7

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v t e Sorting algorithms
Theory	Computational complexity theory Big O notation Total order Lists Inplacement Stability Comparison sort Adaptive sort Sorting network Integer sorting X + Y sorting Transdichotomous model Quantum sort
Exchange sorts	Bubble sort Cocktail shaker sort Odd–even sort Comb sort Gnome sort Proportion extend sort Quicksort
Selection sorts	Selection sort Heapsort Smoothsort Cartesian tree sort Tournament sort Cycle sort Weak-heap sort
Insertion sorts	Insertion sort Shellsort Splaysort Tree sort Library sort Patience sorting
Merge sorts	Merge sort Cascade merge sort Oscillating merge sort Polyphase merge sort
Distribution sorts	American flag sort Bead sort Bucket sort Burstsort Counting sort Interpolation sort Pigeonhole sort Proxmap sort Radix sort Flashsort
Concurrent sorts	Bitonic sorter Batcher odd–even mergesort Pairwise sorting network Samplesort
Hybrid sorts	Block merge sort Introsort Kirkpatrick–Reisch sort Merge-insertion sort Powersort Timsort Spreadsort
Other	Topological sorting Pre-topological order Pancake sorting Spaghetti sort
Impractical sorts	Stooge sort Slowsort Bogosort