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Unformatted text preview: Lecture 1 Introduction What is an Algorithm ? • An algorithm is a computational procedure that takes some value, or a set of values, as input and produces some values, or a set of values, as output . • So, it is a sequence of computational steps that transform the input into the output. • Correction: sequence > combination Sequential and Parallel • In sequential computation , an algorithm is a sequence of computational steps. • However, it is not true in parallel computation . • In this course, we study only algorithms in sequential computation. Algorithms for Sorting . ' ' ' such that sequence input of } ' ,..., ' , ' { n permutatio A : Output }. ,..., , { numbers of sequence A : Input 2 1 2 1 2 1 n n n a a a a a a a a a n ≤ ≤ ≤ Insertion Sort, Merge Sort 6. 5, 4, 3, 2, 1, : Output 3. 1, 6, 4, 2, 5, : Input e.g., Efficiency • Running time from receiving the input to producing the output. ) log ( ) ( 2 n n O n O Insert Sort Merge Sort Running time . for ) ( ) ( such that and constants exist there means )) ( ( ) ( n n n cg n f n c n g O n f ≥ ≤ ≤ = function! the of growth the is about care really what we Therefore, . log large, ly sufficient is When bigger? is who , log and 2 2 1 2 2 1 n n c n c n n n c n c key i A i i i A i A key i A i j i j A key A length j ← + ← ← + ← ← ← ] 1 [ 1 ] [ ] 1 [ do ] [ and while 1 ] [ do ] [ to 2 for Insertion Sort A array input for. end ; ] 1 [ while; end ; 1 ]; [ ] 1 [ begin do ] [ and while ; 1 ]; [ begin do ] [ to 2 for key i A i i i A i A key i A i j i j A key A length j ← + ← ← + ← ← ← 3...
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This note was uploaded on 11/03/2010 for the course COMPUTER S CS 6363 taught by Professor Dingzhudu during the Fall '10 term at University of Texas at Dallas, Richardson.
 Fall '10
 DingzhuDu
 Algorithms

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