Pigeonhole sort

Pigeonhole sort
Pigeonhole sort
Class Sorting algorithm
Data structure Array
Worst case performance O(N + n), where N is the range of key values and n is the input size
Worst case space complexity O(N * n)

Pigeonhole sorting, also known as count sort (not to be confused with counting sort), is a sorting algorithm that is suitable for sorting lists of elements where the number of elements (n) and the number of possible key values (N) are approximately the same.[1] It requires O(n + N) time.

The pigeonhole algorithm works as follows:

  1. Given an array of values to be sorted, set up an auxiliary array of initially empty "pigeonholes," one pigeonhole for each key through the range of the original array.
  2. Going over the original array, put each value into the pigeonhole corresponding to its key, such that each pigeonhole eventually contains a list of all values with that key.
  3. Iterate over the pigeonhole array in order, and put elements from non-empty pigeonholes back into the original array.

For example, suppose we were sorting these value pairs by their first element:

  • (5, "hello")
  • (3, "pie")
  • (8, "apple")
  • (5, "king")

For each value between 3 and 8 we set up a pigeonhole, then move each element to its pigeonhole:

  • 3: (3, "pie")
  • 4:
  • 5: (5, "hello"), (5, "king")
  • 6:
  • 7:
  • 8: (8, "apple")

We then iterate over the pigeonhole array in order and move them back to the original list.

The difference between pigeonhole sort and counting sort is that in counting sort, the auxiliary array does not contain lists of input elements, only counts:

  • 3: 1
  • 4: 0
  • 5: 2
  • 6: 0
  • 7: 0
  • 8: 1

Using this information we can perform a series of exchanges on the input array that puts it in order, moving items only once. Pigeonhole sort, in contrast, moves items twice: once onto the pigeonhole/bucket array and again onto the destination array. [2]

For arrays where N is much larger than n, bucket sort is a generalization that is more efficient in space and time.

See also


  1. ^ NIST's Dictionary of Algorithms and Data Structures: pigeonhole sort
  2. ^ Black, Paul E. (2006-06-19). ""pigeonhole sort", in Dictionary of Algorithms and Data Structures [online"]. U.S. National Institute of Standards and Technology. http://www.itl.nist.gov/div897/sqg/dads/HTML/pigeonholeSort.html. Retrieved 2009-04-26. 

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См. также в других словарях:

  • Pigeonhole — may refer to:*Pigeonholes, nesting spaces formed in a dovecote (also spelt dovecot or doocot ) *Pigeonhole, one of the boxes in a pigeon coop *Pigeonhole principle, a mathematical principle *Pigeonhole sort, a sorting algorithm *Pigeonhole… …   Wikipedia

  • sort — 1. noun 1) what sort of book is it? Syn: type, kind, nature, manner, variety, class, category, style; caliber, quality, form, group, set, bracket, genre, species, family, order …   Thesaurus of popular words

  • pigeonhole — [n] compartment box, carrel, chamber, corner, cranny, cubbyhole, cubicle, hole, niche, nook, place, pocket, recess, section, slot, stall; concept 434 pigeonhole [v] categorize; shelve assort, class, classify, defer, delay, dismiss, file, group,… …   New thesaurus

  • pigeonhole — I verb allocate, allot, arrange, assort, bracket, break down, catalogue, categorize, class, collocate, divide, docket, file, form into classes, grade, group, index, label, list, methodize, name, order, organize, place, place in a category, put in …   Law dictionary

  • pigeonhole — *assort, sort, classify Analogous words: systematize, methodize, organize, arrange, *order …   New Dictionary of Synonyms

  • sort — n *type, kind, stripe, kidney, ilk, description, nature, character sort vb *assort, classify, pigeonhole Analogous words: arrange, methodize, systematize, *order: cull, pick, *choose, select …   New Dictionary of Synonyms

  • sort — [n] type, variety array, batch, battery, body, brand, breed, category, character, class, clutch, denomination, description, family, genus, group, ilk, kind, likes, likes of*, lot, make, nature, number, order, parcel, quality, race, set, species,… …   New thesaurus

  • sort — I verb allocate, allot, apportion, arrange, array, assign places to, assort, catalogue, categorize, class, classify, collocate, deal, digerere, disentangle, distribute, divide, file, grade, graduate, group, methodize, order, organize, parcel out …   Law dictionary

  • sort out — verb 1. arrange or order by classes or categories (Freq. 3) How would you classify these pottery shards are they prehistoric? • Syn: ↑classify, ↑class, ↑sort, ↑assort, ↑separate • Derivationally relate …   Useful english dictionary

  • sort — Synonyms and related words: adjust, ailing, alphabetize, analyze, appraise, arrange, array, assess, assort, batch, battery, blood, body, body build, bolt, brand, break down, breed, bulk, cast, catalog, catalogue, categorize, category, character,… …   Moby Thesaurus

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