lec-2 of data stc

8/9/2019 Lec-2 of data stc

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Questions that will be answered

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What is a good or "efficient" program?

How to measure the efficiency of a program?

How to analyse a simple program?

How to compare different programs?

What is the big! notation?

What is the impact of input on program performance?

What are the standard program analysis techniues?

#o we need fast machines or fast algorithms?


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Which is better?

$/31

The running time of a program.

%rogram easy to understand?

%rogram easy to code and debug?

%rogram ma&ing efficient use of resources?

%rogram running as fast as possible?

Ways of measuring efficiency:

how long it ta&eshow much memory it uses


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Measuring Efciency

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Want to achieve platform-independence

'se an abstract machine that usesstepsof time and units

of memory( instead of seconds or bytes

each elementary operation ta&es 1 step

each elementary instance occupies 1 unit of memory


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5/13

Analysis o Sum

*/31

1+, #escribe the si-e of the input in terms of one or more

parameters.

nput to Sumis an array of 0 integers( so si-e is 0+

$+, hen( count how many steps are used for an input of that si-e. 2 step is an elementary operation such as

( 4( 5( 26i7

2 8imple 9:ample


6/13

Analysis o Sum(!

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// Input: int A[N], array of N integers

// Output: Sum of all numbers in array A

int Sum(int A[], int N {

int s=!

for (int i=! i" N! i##)

s = s # A[i]!

return s!

$

1

$ 3 )

*; aluate each le>el of

nesting as needed.

int %,&!

for (%=! %"N! %##) for (&=N! &'! &)

sum #= %!

8tart with outer loop.

How many iterations? 0

How much time per iteration? 0eed to e>aluate inner loop

nner loop uses !C0, time

otal time is 0 F !C0, 5 !C0F0, 5 !C0$,

8tandard 2nalysis echniues

%!#'A 'E9


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Se+uence o Statements

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Ior a seuence of statements( compute their comple:ity functions

indi>idually and add them up

for (%=! % " N! %##)

for (& =! & " %! #) sum = sum # %&!

for (l=! l " N! l##)

sum = sum l!

printf(*sum is no+ f*, sum)!

!C0$,

!C0,

!C1,

otal cost is !C0$, !C0, !C1, 5 !C0$,

8'D 'E9

8tandard 2nalysis echniues

lec-2 of data stc

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