Download Asymptotic Algorithm Analysis: Terms and Notations and more Quizzes Computer Science in PDF only on Docsity!
Asymptotic Algorithm Analysis
An attempt to estimate the resource consumption of an algorithm, you ignore constant factors, this is only reasonable hen working with large numbers of n. With n < 10 this is generally not a reasonable method of analysis. TERM 2
instance
DEFINITION 2 specific selection of values for the parameters of the problem TERM 3
algorithm
DEFINITION 3 method or process followed to solve a problem1. must be correct2. composed of a series of concrete steps, meaning it is completely understood3.no ambiguity with step order or selection4. Finite number of steps5. it must terminate TERM 4
Program
DEFINITION 4 Instantiation of a algorithm in a programming language TERM 5
Run Time
DEFINITION 5 affected by speed of computer's CPU, bus, and peripheral hardware, and competition for resources from other users or the network.
T(n)
the approximated runtime for an algorithm TERM 7
Constant Running time
DEFINITION 7 n, the size of the input, has no effect on the running time so it would simply cost a constant value c. An assignment statement is a good example. TERM 8
Growth Rate
DEFINITION 8 the rate of which the cost of an algorithm grows as the size of the inputs grows. As a basic rule for n > 5 growth rates from worst to best:n! exponential growth rate2^n exponential growth raten^2 quadratic growth ratenlogna*n, where a < 30? Linear growth rate TERM 9
Rates, best order
DEFINITION 9 loglognlognnnlognn^2n^32^n TERM 10
Cases of Interest
DEFINITION 10 Best CaseAverage CaseWorst caseWe usually focus on worst case, but otherwise average-case. We almost never focus on best case scenarios.
Run time for if..then..else
Worst Case: greatest cost of the clausesAverage Case: same as worst, greatest cost of clausesthis is if the probability of the clauses being run are the same. Otherwise use the amortized analysis. TERM 17
Run Time for Switch
DEFINITION 17 Worst Case: Cost of most expensive branch TERM 18
Run time for recursive
DEFINITION 18 Calculate how many times the function will be called then add 1?
