Tries:Keys with Different Length

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Keys with Different Length

In the example of Figure 28.1, all keys have the same number of digits (i.e., 9).

In many applications, however, different keys have different length. This does not pose a problem unless one key is a prefix of another (for example, 27 is a prefix of 276). For applications in which one key may be a prefix of another, we normally add a special digit (say #) at the end of each key. Doing this ensures that no key is a prefix of another.

To see why we cannot permit a key that is a prefix of another key, consider the example of Figure 28.1. Suppose we are to search for an element with the key 27. Using the search strategy just described, we reach the branch node E. What do we do now? There is no next digit in the search key that can be used to reach the terminating condition (i.e., you either fall off the trie or reach an element node) for downward moves. To resolve this problem, we add the special digit # at the end of each key and also increase the number of children fields in an element node by one. The additional child field is used when the next digit equals #.

An alternative to adding a special digit at the end of each key is to give each node a data field that is used to store the element (if any) whose key exhausts at that node. So, for example, the element whose key is 27 can be stored in node E of Figure 28.1. When this alternative is used, the search strategy is modified so that when the digits of the search key are exhausted, we examine the data field of the reached node. If this data field is empty, we have no element whose key equals the search key. Otherwise, the desired element is in this data field.

It is important to note that in applications that have different length keys with the property that no key is a prefix of another, neither of just mentioned strategies is needed; the scheme described in Section 28.2 works as is.

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