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F(ak[n-1]) Ordinarily, the ordering function is not evaluated according to a specified rule of computation but is stored as an explicit component (field) of each item. Its value is called the key of the item. As a consequence, the record structure is particularly well suited to represent items and might for example be declared as follows: TYPE Item = RECORD key: INTEGER; (*other components declared here*) END The other components represent relevant data about the items in the collection; the key merely assumes the purpose of identifying the items.

See fig. 10. i 0 A B C D A B N-1 string C E j 0 pattern M-1 Fig. 10. In the notations of the KMP algorithm, the alignment position of the pattern is now i-j (and not i, as was the case with the simple algorithm). The central pont of the algorithm is the comparison of s[i] and p[j], if they are equal then i and j are both increased by 1, otherwise the pattern must be shifted by assigning to j of some smaller value D. The boundary case j = 0 shows that one should provide for a shift of the pattern entirely beyond the current comparison point (so that p[0] becomes aligned with s[i+1]).

The exact analysis of the performance of KMP-search is, like the algorithm itself, very intricate. In [1-8] its inventors prove that the number of character comparisons is in the order of M+N, which suggests a substantial improvement over M*N for the straight search. They also point out the welcome property that the scanning pointer i never backs up, whereas in straight string search the scan always begins at the first pattern character after a mismatch, and therefore may involve characters that had actually been scanned already.

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