05 binarysearch complexity

8/10/2019 05 Binarysearch Complexity

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CSE 143

Lecture 5

Binary search; complexity

reading: 13.1 - 13.2

slides created by Marty Stepp and Hlne Martin

http:!!""".cs."ashington.ed#!1$3!
http://www.cs.washington.edu/143/http://www.cs.washington.edu/143/


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2

Sequential search

%sequential search: &ocates a target 'al#e in anarray ! list by examining each element (rom startto (inish. )sed in indexOf.

* Ho" many elements "ill it need to examine+

* ,xample: Searching the array belo" (or the 'al#e 42:

* otice that the array is sorted. o#ld "e ta/e

ad'antage o( this+

index

0 1 2 3 $ 4 5 10

11

12

13

1$

1

1

'al#e -$ 2 10 1 20 22 2 30 3 $2 0 4 4 52 103

i


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3

Binary search (13.1)

%binary search: &ocates a target 'al#e in asorted array ! list by s#ccessi'elyeliminating hal( o( the array (romconsideration.

* Ho" many elements "ill it need to examine+

* ,xample: Searching the array belo" (or the 'al#e 42:

index

0 1 2 3 $ 4 5 10

11

12

13

1$

1

1

'al#e -$ 2 10 1 20 22 2 30 3 $2 0 4 4 52 103

min mid max


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4

Arrays.binarySearch

// searches an entire sorted array for a given value

// returns its index if found; a negative number if not found

// Precondition: array is sorted

Arrays.binarySearch(array, value)

// searches given portion of a sorted array for a given value

// examines minIndex (inclusive through maxIndex (exclusive

// returns its index if found; a negative number if not found// Precondition: array is sorted

Arrays.binarySearch(array, minIne!, ma!Ine!, value)

%6he binarySearchmethod in the Arraysclass searchesan array 'ery e((iciently i( the array is sorted.

* 7o# can search the entire array8 or 9#st a range o(indexes#se(#l (or #n(illed arrays s#ch as the one inArrayIntList


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5

"sin#binarySearch

// index ! " # $ % & ' ) * "! "" "# "$ "% "&

int[] a = {-4, 2, , !, "#, "!, 2#, 2$, %&, %', 42, #&, #', '$, $#, !2

int index =Arrays.binarySearch(a, &, "', %#) // index" is "!

int index2 =Arrays.binarySearch(a, &, "', #") // index# is +

*binarySearchret#rns the index "here the 'al#e is

(o#nd%i( the 'al#e is not (o#nd8 binarySearchret#rns:

-(inserti+n+int ")

% "here inserti+n+intis the index "here the element wouldha'e been8 i( it had been in the array in sorted order.

% 6o insert the 'al#e into the array8 negate inserti+n+int= 1

int index,oInsert#" - +(index# "; // '

i i i


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$untime E%%iciency(13.2)

%Ho" m#ch better is binary search than se>#entialsearch+

%e%%iciency: ? meas#re o( the #se o( comp#ting reso#rcesby code.

* can be relati'e to speed time


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E%%iciency e!am&les

statement1statement2statement3

f+r (int i = " i = / i) {

statement4

f+r (int i = " i = / i) {

statement5 statement' statement

3

3

$ = 3


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E%%iciency e!am&les 2

f+r (int i = " i = / i) { f+r (int 0 = " 0 = / 0) {

statement1

f+r (int i = " i = / i) {

statement2 statement3 statement4

statement5

%Ho" many statements "ill exec#te i( 10+ C( 1000+

2= $

2

$


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l#*rithm #r*+th rates(13.2)

%De meas#re r#ntime in proportion to the inp#t datasiEe8 .

* #r*+th rate: hange in r#ntime as changes.

%Say an algorithm r#ns ,.4-3 25-2 /- 1

statements.* onsider the r#ntime "hen is extremely large.

* De ignore constants li/e 2 beca#se they are tiny next to.

* 6he highest-order term 3< dominates the o'erall r#ntime.

* De say that this algorithm r#ns on the order o( 3.

* or 0(-3)(or short Bi#0ho( c#bed#adr#ples 1 min $2sec

c#bic F3< m#ltiplies by 4 min

... ... ... ...


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C*m&le!ity classes

From http://recursive-design.com/blog/2010/12/07/comp-sci-101-big-o-notation/- post about a Google interview
http://recursive-design.com/blog/2010/12/07/comp-sci-101-big-o-notation/http://recursive-design.com/blog/2010/12/07/comp-sci-101-big-o-notation/


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Sequential search

%Dhat is its complexity class+

1b3ic int indexOf(int a3e) {

f+r (int i = & i si5e i) {

if (e3e6ent7ata[i] == a3e) {

retrn i

retrn -" 88 n+t f+nd

%Fn a'erage8 only !2 elements are 'isited

* 1!2 is a constant that can be ignored

index

0 1 2 3 $ 4 5 10

11

12

13

1$

1

1

'al#e

-$

2 10

1

20

22

2

30

3

$2

0

4

4

52

103


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C*llecti*n e%%iciency

eth* rrayList

add

add(index,

value)

indexOf

9et

re6+eset

si5e

%,((iciency o( o#r ArrayIntListor @a'aAsArrayList:eth* rrayLi

st

add F1

05 binarysearch complexity

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