By Wirth N.

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**Extra info for Algorithms and data structures, Oberon version**

**Sample text**

To let x sift down by comparing x with the next item aj, and either inserting x or moving aj to the right and proceeding to the left. We note that there are two distinct conditions that may cause the termination of the sifting down process: 1. An item aj is found with a key less than the key of x. 2. The left end of the destination sequence is reached. PROCEDURE StraightInsertion; (* ADenS2_Sorts *) VAR i, j: INTEGER; x: Item; BEGIN FOR i := 1 TO n-1 DO x := a[i]; j := i; WHILE (j > 0) & (x < a[j-1]) DO a[j] := a[j-1]; DEC(j) END; a[j] := x END END StraightInsertion Analysis of straight insertion.

The following example illustrates this process. Hoola-Hoola girls like Hooligans. Hooligan Hooligan Hooligan Hooligan Hooligan Since individual character comparisons now proceed from right to left, the following, slightly modified versions of of the predicates P, R and Q are more convenient. P(i, j) = Ak: j ≤ k < M : si-M+k = pk R(i) = P(i, 0) Q(i) = Ak: M ≤ k < i : ~R(k) The loop invariant has the form Q(i) & P(i, j). It is convenient to define k = i-M+j. Then the BM-algorithm can be formulated as follows.

9 shows that the current search state is characterized by i and j. e. the condition that holds after each increase of i or j) can be chosen as follows: in the positions below i there is no match, and in the position i there is a match of the first j characters of the pattern. This is formally expressed as follows: Q(i) & P(i, j) Evidently, j = M would mean there is a required math of the entire pattern in the position i, whereas i > N M would mean that the text contains no match at all. Wirth. Algorithms and Data Structures.

### Algorithms and data structures, Oberon version by Wirth N.

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