Sorting by Exchanging

Grzegorz Bancerek

Formalized Mathematics (2011)

  • Volume: 19, Issue: 2, page 93-102
  • ISSN: 1426-2630

Abstract

top
We show that exchanging of pairs in an array which are in incorrect order leads to sorted array. It justifies correctness of Bubble Sort, Insertion Sort, and Quicksort.

How to cite

top

Grzegorz Bancerek. "Sorting by Exchanging." Formalized Mathematics 19.2 (2011): 93-102. <http://eudml.org/doc/267513>.

@article{GrzegorzBancerek2011,
abstract = {We show that exchanging of pairs in an array which are in incorrect order leads to sorted array. It justifies correctness of Bubble Sort, Insertion Sort, and Quicksort.},
author = {Grzegorz Bancerek},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {93-102},
title = {Sorting by Exchanging},
url = {http://eudml.org/doc/267513},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Grzegorz Bancerek
TI - Sorting by Exchanging
JO - Formalized Mathematics
PY - 2011
VL - 19
IS - 2
SP - 93
EP - 102
AB - We show that exchanging of pairs in an array which are in incorrect order leads to sorted array. It justifies correctness of Bubble Sort, Insertion Sort, and Quicksort.
LA - eng
UR - http://eudml.org/doc/267513
ER -

References

top
  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. [2] Grzegorz Bancerek. Ordinal arithmetics. Formalized Mathematics, 1(3):515-519, 1990. 
  3. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  4. [4] Grzegorz Bancerek. Sequences of ordinal numbers. Formalized Mathematics, 1(2):281-290, 1990. 
  5. [5] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Formalized Mathematics, 6(1):93-107, 1997. 
  6. [6] Grzegorz Bancerek. Mizar analysis of algorithms: Preliminaries. Formalized Mathematics, 15(3):87-110, 2007, doi:10.2478/v10037-007-0011-x.[Crossref] 
  7. [7] Grzegorz Bancerek. Veblen hierarchy. Formalized Mathematics, 19(2):83-92, 2011, doi: 10.2478/v10037-011-0014-5.[Crossref] Zbl1276.03044
  8. [8] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  9. [9] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996. 
  10. [10] Czesław Byliński. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990. 
  11. [11] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  12. [12] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  13. [13] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  14. [14] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  15. [15] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  16. [16] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  17. [17] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003. 
  18. [18] Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990. 
  19. [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  20. [20] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001. 
  21. [21] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  22. [22] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.