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Spaghetti sort

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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. 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.

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

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).

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