Algorithms and Data Structures

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N.Wirth. Algorithms and Data Structures. Oberon version 140 7 w3 1 5 5 12 NIL w2 w1 Fig. 4.10. Insertion in ordered list Referring to Fig. 4.10, we determine the condition under which the scan continues to proceed to the next element; it consists of two factors, namely, (w1 # NIL) & (w1.key < x) The resulting search procedure is: PROCEDURE search (x: INTEGER; VAR root: Word); (* ADenS432_List3 *) VAR w1, w2, w3: Word; BEGIN (*w2 # NIL*) w2 := root; w1 := w2.next; WHILE (w1 # NIL) & (w1.key < x) DO w2 := w1; w1 := w2.next END; (* (w1 = NIL) OR (w1.key >= x) *) IF (w1 = NIL) OR (w1.key > x) THEN (*new entry*) NEW(w3); w2.next := w3; w3.key := x; w3.count := 1; w3.next := w1 ELSE INC(w1.count) END END search In order to speed up the search, the continuation condition of the while statement can once again be simplified by using a sentinel. This requires the initial presence of a dummy header as well as a sentinel at the tail. It is now high time to ask what gain can be expected from ordered list search. Remembering that the additional complexity incurred is small, one should not expect an overwhelming improvement. Assume that all words in the text occur with equal frequency. In this case the gain through lexicographical ordering is indeed also nil, once all words are listed, because the position of a word does not matter if only the total of all access steps is significant and if all words have the same frequency of occurrence. However, a gain is obtained whenever a new word is to be inserted. Instead of first scanning the entire list, on the average only half the list is scanned. Hence, ordered list insertion pays off only if a concordance is to be generated with many distinct words compared to their frequency of occurrence. The preceding examples are therefore suitable primarily as programming exercises rather than for practical applications. The arrangement of data in a linked list is recommended when the number of elements is relatively small
N.Wirth. Algorithms and Data Structures. Oberon version 141 (< 50), varies, and, moreover, when no information is given about their frequencies of access. A typical example is the symbol table in compilers of programming languages. Each declaration causes the addition of a new symbol, and upon exit from its scope of validity, it is deleted from the list. The use of simple linked lists is appropriate for applications with relatively short programs. Even in this case a considerable improvement in access method can be achieved by a very simple technique which is mentioned here again primarily because it constitutes a pretty example for demonstrating the flexibilities of the linked list structure. A characteristic property of programs is that occurrences of the same identifier are very often clustered, that is, one occurrence is often followed by one or more reoccurrences of the same word. This information is an invitation to reorganize the list after each access by moving the word that was found to the top of the list, thereby minimizing the length of the search path the next time it is sought. This method of access is called list search with reordering, or — somewhat pompously — self-organizing list search. In presenting the corresponding algorithm in the form of a procedure, we take advantage of our experience made so far and introduce a sentinel right from the start. In fact, a sentinel not only speeds up the search, but in this case it also simplifies the program. The list must initially not be empty, but contains the sentinel element already. The initialization statements are NEW(sentinel); root := sentinel Note that the main difference between the new algorithm and the straight list search is the action of reordering when an element has been found. It is then detached or deleted from its old position and inserted at the top. This deletion again requires the use of two chasing pointers, such that the predecessor w2 of an identified element w1 is still locatable. This, in turn, calls for the special treatment of the first element (i.e., the empty list). To conceive the linking process, we refer to Fig. 4.11. It shows the two pointers when w1 was identified as the desired element. The configuration after correct reordering is represented in Fig. 4.12, and the complete new search procedure is listed below. sentinel root X1 3 U2 A0 2 7 G5 6 NIL w2 w1 Fig. 4.11. List before re-ordering sentinel root X1 3 U2 2 A0 8 G5 6 NIL w2 w1 Fig. 4.12. List after re-ordering
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Algorithms and Data Structures

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