The Algorithm Design Manual
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Programming Challenges

The Stony Brook Algorithm Repository

Steven Skiena
Stony Brook University
Dept. of Computer Science

1.1.5 Set Data Structures

Problem Input | Problem Output

INPUT                    OUTPUT

Input Description: A universe of objects U = \{ u_1,...,u_n\}, and a collection of subsets S_1,...,S_m, S_i \subset U.

Problem: Represent each subset so as to efficiently (1) test whether u_i \in S_j, (2) find the union or intersection of S_i and S_j, (3) insert or delete members of S_i.

Excerpt from The Algorithm Design Manual: We distinguish sets from two other kinds of objects: strings and dictionaries. If there is no fixed-size universal set, a collection of objects is best thought of as a dictionary. If the order does matter in a subset, i.e. if {A,B,C} is not the same as {B,C,A}, then your structure is more profitably thought of as a string.

When each subset has cardinality exactly two, they form edges in a graph whose vertices are the universal set. A system of subsets with no restrictions on the cardinality of its members is called a hypergraph. It often can be profitable to consider whether your problem has a graph-theoretical analogy, like connected components or shortest path in a hypergraph.

Your primary alternatives for representing arbitrary systems of subsets are:


  • Standard Template library in C++ form SGI (C++) (rating 10)
  • Java Collections (Java) (rating 9)
  • LEDA - A Library of Efficient Data Types and Algorithms (C++) (rating 8)
  • GNU Classpath: an GNU Java API Library (Java) (rating 8)
  • REDUCE Computer Algebra System Computer Algebra System (Lisp) (rating 7)
  • Bruno R. Preiss's books with source (C++,Java,C#) (rating 6)

  • Recommended Books

    Data Structures and Algorithm Analysis in C++ (3rd Edition) by Mark Allen Weiss Algorithms in C++: Fundamentals, Data Structures, Sorting, Searching by Robert Sedgewick The Art of Computer Programming: Fundamental Algorithms by Donald Knuth
    Davenport-Schinzel sequences and their geometric applications by M. Sharir and P. Agarwal Data Structures and Network Algorithms by R. Tarjan

    Related Problems

    Generating Partitions
    Generating Subsets
    Graph Data Structures
    Minimum Spanning Tree
    Set Cover

    This page last modified on 2008-07-10 .