Package edu.princeton.cs.algs4

Class PatriciaSET

  • All Implemented Interfaces:
    Iterable<String>
    public class PatriciaSET
extends Object
implements Iterable<String>
    The PatriciaSET class provides an implementation of an unordered set, with the restriction that the items (keys) are of class String. It supports the usual add, contains, delete, size, and is-empty methods. It also provides an iterator method for iterating over all the elements in the set.

    This unordered set class implements PATRICIA (Practical Algorithm to Retrieve Information Coded In Alphanumeric). In spite of the acronym, string keys are not limited to alphanumeric content. A key may possess any string value, with one exception: a zero-length string is not permitted.

    Unlike other generic set implementations that can accept a parameterized key type, this set class can only accommodate keys of class String. This unfortunate restriction stems from a limitation in Java. Although Java provides excellent support for generic programming, the current infrastructure somewhat limits generic collection implementations to those that employ comparison-based or hash-based methods. PATRICIA does not employ comparisons or hashing; instead, it relies on bit-test operations. Because Java does not furnish any generic abstractions (or implementations) for bit-testing the contents of an object, providing support for generic keys using PATRICIA does not seem practical.

    PATRICIA is a variation of a trie, and it is often classified as a space-optimized trie. In a classical trie, each level represents a subsequent digit in a key. In PATRICIA, nodes only exist to identify the digits (bits) that distinguish the individual keys within the trie. Because PATRICIA uses a radix of two, each node has only two children, like a binary tree. Also like a binary tree, the number of nodes, within the trie, equals the number of keys. Consequently, some classify PATRICIA as a tree.

    The analysis of PATRICIA is complicated. The theoretical wost-case performance for an add, contains, or delete operation is O(N), when N is less than W (where W is the length in bits of the longest key), and O(W), when N is greater than W. However, the worst case is unlikely to occur with typical use. The average (and usual) performance of PATRICIA is approximately ~lg N for each add, contains, or delete operation. Although this appears to put PATRICIA on the same footing as binary trees, this time complexity represents the number of single-bit test operations (under PATRICIA), and not full-key comparisons (as required by binary trees). After the single-bit tests conclude, PATRICIA requires just one full-key comparison to confirm the existence (or absence) of the key (per add, contains, or delete operation).

    In practice, decent implementations of PATRICIA can often outperform balanced binary trees, and even hash tables. Although this particular implementation performs well, the source code was written with an emphasis on clarity, and not performance. PATRICIA performs admirably when its bit-testing loops are well tuned. Consider using the source code as a guide, should you need to produce an optimized implementation, for another key type, or in another programming language.

    Other resources for PATRICIA:
    Sedgewick, R. (1990) Algorithms in C, Addison-Wesley
    Knuth, D. (1973) The Art of Computer Programming, Addison-Wesley

    Author:
    John Hentosh (based on an implementation by Robert Sedgewick)

    • Constructor Detail

      • PatriciaSET

        public PatriciaSET()
        Initializes an empty PATRICIA-based set.

    • Method Detail

      • contains

        public boolean contains​(String key)
        Does the set contain the given key?
        Parameters:
        key - the key
        Returns:
        true if the set contains key and false otherwise
        Throws:
        IllegalArgumentException - if key is null
        IllegalArgumentException - if key is the empty string.

      • iterator

        public Iterator<String> iterator()
        Returns all of the keys in the set, as an iterator. To iterate over all of the keys in a set named set, use the foreach notation: for (Key key : set).
        Specified by:
        iterator in interface Iterable<String>
        Returns:
        an iterator to all of the keys in the set

      • toString

        public String toString()
        Returns a string representation of this set.
        Overrides:
        toString in class Object
        Returns:
        a string representation of this set, with the keys separated by single spaces

      • main

        public static void main​(String[] args)
        Unit tests the PatriciaSET data type. This test fixture runs a series of tests on a randomly generated dataset. You may specify up to two integer parameters on the command line. The first parameter indicates the size of the dataset. The second parameter controls the number of passes (a new random dataset becomes generated at the start of each pass).
        Parameters:
        args - the command-line arguments