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Definition
A trie is a rooted tree used for storing associative arrays where keys are usually strings. Edges are often labeled by individual symbols. Then common prefixes are factorized. Each node of the trie is associated with a prefix of a string of the set of strings: concatenation of the labels of the path from the root to the node. The root is associated with the empty string. Strings of the set are stored in terminal nodes (leaves) but not in internal nodes. A trie can be seen as a Deterministic Finite Automaton.
Tries can be compacted. To get a compact trie from a trie, internal nodes with exactly one successor are removed. Then labels of edges between remaining nodes are concatenated. Thus:
Edges are labeled by strings.
Internal nodes have at least two children.
Edges outgoing an internal node are labeled by strings starting with different symbols.
Historical Background
Tries were first recommended by de la Briandais [1]. The word “trie” comes from...
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Recommended Reading
de la Briandais R., File searching using variable length keys. In Proc. Western Joint Computer Conference., 1959, pp. 295–298.
Crochemore M., Hancart C., and Lecroq T. Algorithms on Strings. Cambridge University Press, Cambridge, 2007.
Fredkin E. Trie memory. Commun. ACM, 3(9):490–499, 1960.
Gonnet G.H. and Baeza-Yates R. Handbook of Algorithms and Data Structures – In Pascal and C, 2nd edn. Addison-Wesley, 1991.
Gusfield D. Algorithms on strings, trees and sequences. Cambridge University Press, Cambridge, 1997.
Knuth D.E. The Art of Computer Programming, Volume 3: Sorting and Searching, 3rd edn. Addison-Wesley, 1997, Section 6.3: Digital Searching, pp. 492–512.
Morrison D.R. PATRICIA – Practical Algorithm to Retrieve Information Coded in Alphanumeric, J. ACM, 15(4):514–534, 1968.
Sedgewick R. and Flajolet Ph. An Introduction to the Analysis of Algorithms, Addison-Wesley, 1996.
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Crochemore, M., Lecroq, T. (2009). Trie. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_1143
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