This is a slight variation on a specification of iterative binary search due to Bentley and is from column four of Programming Pearls (Addison-Wesley 1986).
We are to determine whether the sorted array X[1..N] contains the element T. We calculate P, the position of T in X. When P is zero, T is not in X[1..N]. Otherwise, 1<=P<=N and T=X[P].
We know that N>gt;=0 and that X <= X <= ... <= X[N]. When N=0 the array is empty. The types of T and the elements of X are the same.
Binary search solves the problem by keeping track of a range within the array in which T must be if it is anywhere in the array. Initially, the range is the entire array. The range is shrunk by comparing its middle element to to T and discarding half the arrange. The process continues until T is discovered in the array or until the range in which it must lie is known to be empty.
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Source text last modified Mon Nov 10 08:57:45 1997.
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