The word frequency counter， as previously implemented， takes several minutes to count the frequency of words in the author’s manuscript for this textbook on a Raspberry Pi. Most of the time

　　is spent building the list of words and re-sorting the list in order of word frequency. Most of the

　　time for both of these operations is spent in searching for the word in the list before incrementing its count or inserting it in the list. There are more efficient ways to build ordered lists of data.

　　Since the code is well modularized using an ADT， the internal mechanism of the list can be

　　modified without affecting the main program. A major improvement can be made by changing

　　the data structure from a linked list to a binary tree. Fig. 6.1 shows an example binary tree

　　storing word frequency counts. The time required to insert into a linked list is O（N）， but the

　　time required to insert into a binary tree is O（log2 N）。 To give some perspective， the author’s

　　manuscript for this textbook contains about 125，000 words. Since log2（125，000） 《 17， we

　　would expect the linked list implementation to require about 125，000

　　17 ≈ 7353 times as long as a

　　binary tree implementation to process the author’s manuscript for this textbook. In reality，