Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

The correctness of the BM pattern matching algorithm follows from the fact that
each time the method makes a shift, it is guaranteed not to "skip" over any possible
matches. For last(c) is the location of the last occurrence of c in P.
The worst-case running time of the BM algorithm is O(nm+|σ|). Namely, the
computation of the last function takes time O(m+|σ|) and the actual search for the
pattern takes O(nm) time in the worst case, the same as the brute-force algorithm.
An example of a text-pattern pair that achieves the worst case is
The worst-case performance, however, is unlikely to be achieved for English text,
for, in this case, the BM algorithm is often able to skip large portions of text. (See
Figure 12.4.) Experimental evidence on English text shows that the average number
of comparisons done per character is 0.24 for a five-character pattern string.
Figure 12.4: An example of a Boyer-Moore execution
on English text.
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