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# handout6 - ECS20 Handout 6 1 An algorithm is a nite set of...

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ECS20 Handout 6 January 18, 2011 1. An algorithm is a finite set of precise instructions for performing a computation or for solving a problem. 2. Properties that algorithms generally share: Input, Output, Definiteness, Correctness, Finiteness, Effectiveness, Generality. 3. Case study 1: finding the maximum element in a finite sequence a = { a (1) ,a (2) ,...,a ( n ) } of integers. procedure find_max(a,n) imax = 1 max = a(1) for i := 2 to n if max < a(i) then imax = i max = a(i) endif endfor return (imax,max) // imax is the index (location) of the largest element max Complexity: The total number of comparisons = n - 1 = Θ( n ) 4. Case study 2: locating an element x in a list of distinct element { a 1 ,a 2 ,...,a n } of integers, or determine that it is not in the list. Pseudocode for linear sort algorithm: procedure linear_search(a,x) i := 1 while (i <= n and x /= a(i) ) i := i + 1 endwhile if i <= n then location := i else location := 0 endif return location // the subscript of the term that equals x, // or is 0 if x is not found Complexity: The (average) number of comparisons = n 2 = Θ( n ) 1

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5. Case study 3: locating an element
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handout6 - ECS20 Handout 6 1 An algorithm is a nite set of...

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