cs2114 lecture06 algorithmefficiency 2015f

7/24/2019 CS2114 Lecture06 AlgorithmEfficiency 2015F

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The Efficiency of Algorithms

Chapter 4

2015 Pearson Education, Inc., UpperSaddle River, NJ. All rights reserved.

Data Structures and Abstractions with Java, 4e

Frank Carrano


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Why Efficient Code?

Computers are faster, have larger

memories!So why worry about efficient code?

And how do we measure efficiency?



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Example

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Example

Java code for the three algorithms



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What is best?

An algorithm has both time and space

constraints that is complexity

!Time complexity

!

Space complexity

This study is called analysis of

algorithms



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Counting Basic Operations

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FIGURE 4-3 The number of basic operations required by thealgorithms in Figure 4-1 as a function of n



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FIGURE 4-4 Typical growth-rate functions evaluatedat increasing values of n



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Best, Worst,

and Average Cases

For some algorithms, execution time

depends only on size of data set

Other algorithms depend on the natureof the data itself

!Here we seek to know best case, worst

case, average case



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Big Oh Notation

A function f(n) is of order at most g(n)

That is, f(n) is O(g(n))if

!A positive real number c and positive

integer N exist

!

Such that f(n) "c xg(n) for all n #N

!That is, c xg(n) is an upper bound on f(n)

when n is sufficiently large



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Picturing Efficiency

FIGURE 4-6 An O(n) algorithm



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FIGURE 4-7 An O(n2) algorithm 2015 Pearson Education, Inc., UpperSaddle River, NJ. All rights reserved.


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FIGURE 4-8 Another O(n2) algorithm 2015 Pearson Education, Inc., UpperSaddle River, NJ. All rights reserved.


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FIGURE 4-9 The effect of doubling the problemsize on an algorithms time requirement



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FIGURE 4-10 The time required to process one million itemsby algorithms of various orders at the rate of one million

operations per second



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Efficiency of

Implementations of ADT Bag

FIGURE 4-11 The time efficiencies of the ADT bagoperations for two implementations, |

expressed in Big Oh notation



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End

Chapter 4



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cs2114 lecture06 algorithmefficiency 2015f

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