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1-twoup - The Selection Problem Given an array of numbers...

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The Selection Problem Given an array of numbers, we wish to find the k th smallest. What if k is larger than n ? Can the algorithm change the array? If the elements are not all distinct, what exactly do we mean by the “ k th smallest”? To answer these and possibly other questions, we need a formal specification . 1 Algorithm Specifications An algorithm specification consists of three parts: a precondition : a statement of the assumptions we make about the input to the algorithm and the environment in which it will be executed; a postcondition : a statement of the required result of executing the algorithm, assuming the precondition is satisfied; and a function header giving a name and parameter list. We say that an algorithm meets its specification if the postcondition is satisfied whenever the precondition is satisfied. 2

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Specification for the Selection Problem Precondition: A [1 ..n ] is an array of Number s, 1 k n , k and n are Nat s.
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