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2. The sorting of a file Such a restriction will evidently have serious consequences on the sorting method to be used, but it is unavoidable if the number of cards to be laid out is larger than the available table. Before proceeding, we introduce some terminology and notation to be used throughout this chapter. If we are given n items a0, a1, ... , an-1 sorting consists of permuting these items into an array ak0, ak1, ... , ak[n-1] such that, given an ordering function f f(ak0) ≤ f(ak1) ≤ ... ≤ 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.

Simultaneously decrementing k and j does not affect Q(i), and, since sk1 = pj-1 had been established, and P(i, j) holds prior to decrementing j, then P(i, j) holds after it as well. In the second branch, it is sufficient to show that the statement i := i + ds[i-1] never falsifies the invariant Q(i) because P(i, j) is satisfied automatically after the remaining assignments. Q(i) is satisfied after incrementing i provided that before the assignment Q(i+ds[i-1]) is guaranteed. Since we know that Q(i) holds, it suffices to establish ~R(i+h) for h = 1 ..

E. (i > N-M) OR (j >= M). Moreover, from the structure of the loop it follows that the two operands cannot hold simultanelously, and j cannot exceed M. e. a complete match is found in position i. Analysis of straight string search. This algorithm operates quite effectively, if we can assume that a mismatch between character pairs occurs after at most a few comparisons in the inner loop. This is likely to be the case, if the cardinality of the item type is large. For text searches with a character set size of 128 we may well assume that a mismatch occurs after inspecting 1 or 2 characters only.

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