Tries:What Is a Trie?

What Is a Trie?

A trie (pronounced “try” and derived from the word retrieval) is a data structure that uses the digits in the keys to organize and search the dictionary. Although, in practice, we can use any radix to decompose the keys into digits, in our examples, we shall choose our radixes so that the digits are natural entities such as decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and letters of the English alphabet (a z, A Z).

Suppose that the elements in our dictionary are student records that contain fields such as student name, major, date of birth, and social security number (SS#). The key field is the social security number, which is a nine digit decimal number. To keep the example manageable, assume that the dictionary has only five elements. Table 28.1 shows the name and SS# fields for each of the five elements in our dictionary.

To obtain a trie representation for these five elements, we first select a radix that will be used to decompose each key into digits. If we use the radix 10, the decomposed digits are

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just the decimal digits shown in Table 28.1. We shall examine the digits of the key field (i.e., SS#) from left to right. Using the first digit of the SS#, we partition the elements into three groups–elements whose SS# begins with 2 (i.e., Bill and Kathy), those that begin with 5 (i.e., Jill), and those that begin with 9 (i.e., April and Jack). Groups with more than one element are partitioned using the next digit in the key. This partitioning process is continued until every group has exactly one element in it.

The partitioning process described above naturally results in a tree structure that has 10-way branching as is shown in Figure 28.1. The tree employs two types of nodes–branch nodes and element nodes. Each branch node has 10 children (or pointer/reference) fields.

These fields, child[0 : 9], have been labeled 0, 1, ··· , 9 for the root node of Figure 28.1.

root.child[i] points to the root of a subtrie that contains all elements whose first digit is i.

In Figure 28.1, nodes A, B, D, E, F, and I are branch nodes. The remaining nodes, nodes C, G, H, J, and K are element nodes. Each element node contains exactly one element of the dictionary. In Figure 28.1, only the key field of each element is shown in the element nodes

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