Sorting by Exchanging

• Autorzy: Grzegorz Bancerek
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2011
• Tom: 19
• Numer: 2
• Strony: 93-102

Daty

wydano

2011-01-01

online

2011-07-18

Twórcy

autor

Grzegorz Bancerek

• Białystok Technical University, Poland

Bibliografia

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

Identyfikatory

DOI

10.2478/v10037-011-0015-4