Data Structures: Theory and PracticeComputer Science and Applied Mathematics: Data Structures: Theory and Practice focuses on the processes, methodologies, principles, and approaches involved in data structures, including algorithms, decision trees, Boolean functions, lattices, and matrices. The book first offers information on set theory, functions, and relations, and graph theory. Discussions focus on linear formulas of digraphs, isomorphism of digraphs, basic definitions in the theory of digraphs, Boolean functions and forms, lattices, indexed sets, algebra of sets, and order pair and related concepts. The text then examines strings, trees, and paths and cycles in digraphs. Topics include algebra of strings, Markov algorithms, algebraic structures, languages and grammars, decision trees and decision tables, trees as grammatic markers, shortest path problems, and representation of prefix formulas. The publication ponders on digraphs of programs, arrays, pushdown stores, lists, and list structures, and organization of files. Concerns include scatter storage techniques, files and secondary storage, representation of digraphs as list structures, storage of arrays, and sparse matrices. |
Contents
Set Theory | 3 |
1c Complement of a Set | 9 |
le Algebra of Sets as an Axiomatic Theory | 15 |
Copyright | |
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a₁ a₂ abstract algebra adjacency matrix algebra of sets arcs originating array Assume axioms b₁ binary block Boolean algebra Boolean form called circuit column Consider contains corresponding cycle datum defined DEFINITION denote diagram digraph of Figure document equivalence relation example Exercise exists finite flowchart flowchart digraph formula Fortran given grammar graph hash address Hence indegree index terms integers IPOP isomorphism K-formula k₁ language lattice lexicographic order list element list store list structure Markov algorithm n₁ node base operations ordered pairs partially ordered sets path matrix permutation pointer problem procedure processing proof reachable representation represented rule S-expression S₁ Section semigroup sequence shortest path Snobol sort tree specified stack statement storage string sublist subroutine subscript subset substring switches symbols terminal nodes THEOREM theory Type variables vector words write x₁ zero