DATA STRUCALGORITHMS COP 3530
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This 5 page Class Notes was uploaded by Hans Farrell PhD on Friday September 18, 2015. The Class Notes belongs to COP 3530 at University of Florida taught by Staff in Fall. Since its upload, it has received 44 views. For similar materials see /class/206695/cop-3530-university-of-florida in Computer Programming at University of Florida.
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Date Created: 09/18/15
H Insertion SoIt H for int i 1 ilt aength i I insert ai into a0i1 intt ai forji1jgt0ampamptltajj WHwi aj1t Complexity ASpaceMemory ATime Count a particular operation Count number of steps Asymptotic complexity Comparison Count for int i 1 ilt aength i I insert ai into a0i1 intt ai intj forji1jgt0ampamptltajj WHwi aj 1 t Comparison Count APiCk an instance characteristic n n aength for insertion sort ADetermine count as a function of this instance characteristic Comparison Count forji1jgt0ampamptltaiijquot ai1aii How many comparisons are made Comparison Count for0i1j gtoampamptltani ai1 3U number of compares depends on as and t as well as on i Comparison Count Worstcase count maximum count Bestcase count minimum count Average count WorstCase Comparison Count for0i1jgt0ampamptltaiJ ai1aii a 1 2 3 4 and t 0 gt 4 compares a 123 i and t 0 gt i compares WorstCase Comparison Count for int i 1 i lt n i forji1j gt0ampamptltaij ai1 ai total compares 1 2 3 n1 n1n2 Step Count A step is an amount of computing that does not depend on the instance characteristic n 10 adds 100 subtracts 1000 multiplies can all be counted as a single step n adds cannot be counted as 1 step Step Count I a for int i 1 ilt aength i I insert ai into a0i1 forji1jgt0ampamptltajj aii1iaLii aj1t S ooo Step Count se isn t always 0 or 1 X MyMathsuma n where n is the instance characteristic has a se count of n Step Count se steps for int i 1 ilt alength i 1 I insert ai into a0i1 0 intt ai 1 intj 0 forji1jgt0ampamptltajj 1 I1 ali1lalil 1 i aj 1 t 1 0 Step Count for int i 1 ilt alength i 2i 3 step count for for int i 1 ilt alength i is n step count for body of for loop is 2123 n1 3n1 n1n 3n1 n1n3 Asymptotic Complexity of Insertion SoIt A 0n1 AWhat does this mean Complexity of InseItion Sort ATime or number of operations does not exceed cn2 on any input of size n n suitably large AActually the worstcase time is Thetan1 and the bestcase is Thetan ASO the worstcase time is expected to quadruple each time n is doubled Complexity of Insertion Sort Practical Complexities A IS omz too much time 109 instructionssecond A Is the algorithm practical n n nlogn ii i iii iiriiiiii ii i iiiii 1000 iUiTiii iiiiiiii i iiiii iTiTiii39i 10 ii i iiiii Iiiii39i39iiiii iTiTiii39i Faster Computer Vs Better Impractical CompleX1t1es Algorithm 109 instructionssecond Algorithmic improvement more useful than hardware improvement Eg 2quot to h3
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