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Unformatted text preview: 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 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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This note was uploaded on 09/06/2009 for the course CIS 11274 taught by Professor Howell during the Spring '09 term at Kansas State University.
- Spring '09