13
Trees Linear Vs non-linear data structures Types of binary trees Binary tree traversals Representations of a binary tree Binary tree ADT Binary search tree EECS 268 Programming II 1 Overview We have discussed linear data structures arrays, linked lists, stacks, queues Some other data structures we will consider trees, tables, graphs, hash-tables Trees are extremely useful and suitable for a wide range of applications sorting, searching, expression evaluation, data set representation especially well suited to recursive algorithm implementation EECS 268 Programming II 2 Terminology A Tree T is a set of n >= 0 elements: if n == 0, T is an empty tree if n > 0 then there exists some element called r T called the root of T such that T - {r} can be partitioned into zero or more disjoint sets T 1 ,T 2 , ... where each subset forms a tree Trees are composed of nodes and edges Trees are hierarchical parent-child relationship between two nodes ancestor-descendant relationships among nodes Subtree of a tree: Any node and its descendants 3 EECS 268 Programming II Terminology 4 Figure 10-1 A general tree Figure 10-2 A subtree of the tree in Figure 10-1 EECS 268 Programming II

Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

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Page 1: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Tre

es

Lin

ea

r V

s n

on

-lin

ea

r d

ata

str

uct

ure

s

Typ

es

of

bin

ary

tre

es

Bin

ary

tre

e t

rave

rsa

ls

Re

pre

sen

tati

on

s o

f a

bin

ary

tre

e

Bin

ary

tre

e A

DT

Bin

ary

se

arc

h t

ree

EE

CS

26

8 P

rogra

mm

ing I

I 1

Ove

rvie

w

We

ha

ve d

iscu

sse

d l

ine

ar

da

ta s

tru

ctu

res

arr

ays

, li

nke

d lis

ts,

sta

cks,

qu

eu

es

So

me

oth

er

da

ta s

tru

ctu

res

we

wil

l co

nsi

de

r

tre

es,

ta

ble

s, g

rap

hs,

ha

sh-t

ab

les

Tre

es

are

ext

rem

ely

use

ful a

nd

su

ita

ble

fo

r a

wid

e

ran

ge

of

ap

pli

cati

on

s

sort

ing

, se

arc

hin

g,

exp

ress

ion

eva

lua

tio

n,

da

ta s

et

rep

rese

nta

tio

n

esp

eci

all

y w

ell

su

ite

d t

o r

ecu

rsiv

e a

lgo

rith

m

imp

lem

en

tati

on

E

EC

S 2

68 P

rogra

mm

ing I

I 2

Term

ino

log

y

A T

ree

T i

s a

se

t o

f n

>=

0 e

lem

en

ts:

if n

==

0,

T is

an

em

pty

tre

e

if n

> 0

th

en

th

ere

exi

sts

som

e e

lem

en

t ca

lle

d r

T

ca

lle

d t

he

ro

ot

of

T s

uch

th

at

T -

{r}

ca

n b

e p

art

itio

ne

d

into

ze

ro o

r m

ore

dis

join

t se

ts T

1 ,T

2 ,

...

wh

ere

ea

ch

sub

set

form

s a

tre

e

Tre

es

are

co

mp

ose

d o

f n

od

es

an

d e

dg

es

Tre

es

are

hie

rarc

hic

al

pa

ren

t-ch

ild

re

lati

on

ship

be

twe

en

tw

o n

od

es

an

cest

or-

de

sce

nd

an

t re

lati

on

ship

s a

mo

ng

no

de

s

Su

btr

ee

of

a t

ree

: A

ny

no

de

an

d i

ts d

esc

en

da

nts

3

EE

CS

26

8 P

rogra

mm

ing I

I

Term

ino

log

y

4

Fig

ure

10

-1 A

ge

ne

ral t

ree

F

igu

re 1

0-2

A s

ub

tre

e o

f th

e tre

e in

Fig

ure

10

-1

EE

CS

268 P

rogra

mm

ing I

I

Page 2: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Term

ino

log

y

Pa

ren

t o

f n

od

e n

Th

e n

od

e d

ire

ctly

ab

ove

no

de

n i

n t

he

tre

e

Ch

ild

of

no

de

n

A n

od

e d

ire

ctly

be

low

no

de

n i

n t

he

tre

e

Ro

ot

Th

e o

nly

no

de

in

th

e t

ree

wit

h n

o p

are

nt

Su

btr

ee

of

no

de

n

A t

ree

th

at

con

sist

s o

f a

ch

ild

(if

an

y)

of

no

de

n

5

EE

CS

26

8 P

rogra

mm

ing I

I

Term

ino

log

y

Lea

f

A n

od

e w

ith

no

ch

ild

ren

Sib

lin

gs

No

de

s w

ith

a c

om

mo

n p

are

nt

An

cest

or

of

no

de

n

A n

od

e o

n t

he

pa

th f

rom

th

e r

oo

t to

n

De

sce

nd

an

t o

f n

od

e n

A n

od

e o

n a

pa

th f

rom

n t

o a

le

af

6

EE

CS

268 P

rogra

mm

ing I

I

A B

ina

ry T

ree

A b

ina

ry t

ree

is a

se

t T

of

no

de

s su

ch t

ha

t

T i

s e

mp

ty,

or

T i

s p

art

itio

ne

d i

nto

th

ree

dis

join

t su

bse

ts:

a s

ing

le n

od

e r

, th

e r

oo

t

two

po

ssib

ly e

mp

ty s

ets

th

at

are

bin

ary

tre

es,

ca

lle

d

the

le

ft s

ub

tre

e o

f r

an

d t

he

rig

ht

sub

tre

e o

f r

Bin

ary

tre

es

are

ord

ere

d

Th

ese

tre

es

are

no

t e

qu

al

7

EE

CS

26

8 P

rogra

mm

ing I

I

A

B

B

A

R

L

A G

en

era

l Tr

ee

& A

Bin

ary

Tre

e

8

EE

CS

268 P

rogra

mm

ing I

I

Page 3: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Mo

re B

ina

ry T

ree

s

9

Fig

ure

10

-4 B

ina

ry tre

es th

at re

pre

se

nt a

lge

bra

ic e

xp

ressio

ns

A B

ina

ry S

ea

rch

Tre

e

A b

ina

ry s

ea

rch

tre

e is

a

bin

ary

tre

e t

ha

t h

as

the

fo

llo

win

g p

rop

ert

ies

for

ea

ch n

od

e n

sub

tre

e T

L

sub

tre

e T

R

bo

th T

L a

nd

TR

are

bin

ary

se

arc

h t

ree

s

10

EE

CS

268 P

rogra

mm

ing I

I

Th

e H

eig

ht

of

Tre

es

He

igh

t o

f a

tre

e

Nu

mb

er

of

no

de

s a

lon

g t

he

lon

ge

st p

ath

fro

m t

he

ro

ot

to a

le

af

H

eig

ht

3

He

igh

t 5

H

eig

ht

7

11

Fig

ure

10

-6

Bin

ary

tre

es w

ith

the

sa

me

no

de

s b

ut

diffe

rent h

eig

hts

Th

e H

eig

ht

of

Tre

es

Leve

l o

f a

no

de

n i

n a

tre

e T

If n

is

the

ro

ot

of

T, i

t is

at

leve

l 1

If n

is

no

t th

e r

oo

t o

f T,

its

le

vel is

1 g

rea

ter

tha

n

the

le

vel o

f it

s p

are

nt

He

igh

t o

f a

tre

e T

de

fin

ed

in

te

rms

of

the

le

vels

of

its

no

de

s

If T

is

em

pty

, it

s h

eig

ht

is 0

If T

is

no

t e

mp

ty,

its

he

igh

t is

eq

ua

l to

th

e

ma

xim

um

le

vel o

f it

s n

od

es

12

EE

CS

268 P

rogra

mm

ing I

I

Page 4: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Th

e H

eig

ht

of

Tre

es

A r

ecu

rsiv

e d

efi

nit

ion

of

he

igh

t

If T

is

em

pty

, it

s h

eig

ht

is 0

If T

is

no

t e

mp

ty,

h

eig

ht(

T)

= 1

+ m

ax{

he

igh

t(T

L),

he

igh

t(T

R)}

r

/

\

T

L

TR

13

EE

CS

26

8 P

rogra

mm

ing I

I

Fu

ll B

ina

ry T

ree

s

A b

ina

ry t

ree

of

he

igh

t h

is

fu

ll i

f

No

de

s a

t le

vels

< h

ha

ve

two

ch

ild

ren

ea

ch

Re

curs

ive

de

fin

itio

n

If T

is

em

pty

, T

is

a f

ull

b

ina

ry t

ree

of

he

igh

t 0

If T

is

no

t e

mp

ty a

nd

ha

s h

eig

ht

h >

0,

T is

a f

ull

sub

tre

es

are

bo

th f

ull

b

ina

ry t

ree

s o

f h

eig

ht

h

1

14

Fig

ure

10

-7

A fu

ll b

ina

ry tre

e o

f h

eig

ht 3

Co

mp

lete

Bin

ary

Tre

es

A b

ina

ry t

ree

of

he

igh

t h

is

com

ple

te i

f

It i

s fu

ll t

o le

vel

h

1,

an

d

Leve

l h

is

fill

ed

fro

m l

eft

to

rig

ht

15

EE

CS

26

8 P

rogra

mm

ing I

I

Co

mp

lete

Bin

ary

Tre

es

An

oth

er

de

fin

itio

n:

A b

ina

ry t

ree

of

he

igh

t h

is

com

ple

te i

f

All

no

de

s a

t le

vels

<=

h

2 h

ave

tw

o c

hil

dre

n

ea

ch,

an

d

Wh

en

a n

od

e a

t le

vel h

1

ha

s ch

ild

ren

, a

ll n

od

es

to i

ts l

eft

at

the

sa

me

le

vel

ha

ve t

wo

ch

ild

ren

ea

ch,

an

d

Wh

en

a n

od

e a

t le

vel h

1

ha

s o

ne

ch

ild

, it

is

a

left

ch

ild

16

EE

CS

268 P

rogra

mm

ing I

I

Page 5: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Ba

lan

ced

Bin

ary

Tre

es

A b

ina

ry t

ree

is b

ala

nce

d i

f th

e h

eig

hts

of

an

y

Co

mp

lete

bin

ary

tre

es

are

ba

lan

ced

Fu

ll b

ina

ry t

ree

s a

re c

om

ple

te a

nd

ba

lan

ced

17

EE

CS

26

8 P

rogra

mm

ing I

I

Tra

vers

als

of

a B

ina

ry T

ree

A t

rave

rsa

l v

isit

s e

ach

no

de

in

a t

ree

to

do

so

me

thin

g w

ith

or

to t

he

no

de

du

rin

g a

vis

it

for

exa

mp

le,

dis

pla

y t

he

da

ta in

th

e n

od

e

Ge

ne

ral

form

of

a r

ecu

rsiv

e t

rave

rsa

l a

lgo

rith

m

traverse (in binTree:BinaryTree)

if (binTree is not empty)

{ traverse(Left subtree of

root)

traverse(Right subtree of

root)

}

18

EE

CS

268 P

rogra

mm

ing I

I

Tra

vers

als

of

a B

ina

ry T

ree

Pre

ord

er

tra

vers

al

Vis

it r

oo

t b

efo

re v

isit

ing

its

su

btr

ee

s

i. e

. B

efo

re t

he

re

curs

ive

ca

lls

Ino

rde

r tr

ave

rsa

l

Vis

it r

oo

t b

etw

ee

n v

isit

ing

its

su

btr

ee

s

i. e

. B

etw

ee

n t

he

re

curs

ive

ca

lls

Po

sto

rde

r tr

ave

rsa

l

Vis

it r

oo

t a

fte

r v

isit

ing

its

su

btr

ee

s

i. e

. A

fte

r th

e r

ecu

rsiv

e c

all

s

19

EE

CS

26

8 P

rogra

mm

ing I

I

Tra

vers

als

of

a B

ina

ry T

ree

20

Fig

ure

10-1

0

Tra

ve

rsa

ls o

f a

bin

ary

tre

e: (a

) p

reo

rde

r; (

b)

ino

rde

r; (

c)

po

sto

rder

EE

CS

268 P

rogra

mm

ing I

I

Page 6: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Tra

vers

als

of

a B

ina

ry T

ree

A t

rave

rsa

l o

pe

rati

on

ca

n c

all

a f

un

ctio

n t

o

pe

rfo

rm a

ta

sk o

n e

ach

ite

m i

n t

he

tre

e

the

cli

en

t d

efi

ne

s a

nd

pa

sse

s th

is f

un

ctio

n a

s a

n

arg

um

en

t to

th

e t

rave

rsa

l o

pe

rati

on

Tre

e t

rave

rsa

l o

rde

rs c

orr

esp

on

d t

o a

lge

bra

ic

exp

ress

ion

s

infi

x, p

refi

x, a

nd

po

stfi

x

21

EE

CS

26

8 P

rogra

mm

ing I

I

Th

e A

DT

Bin

ary

Tre

e

+cr

ea

teB

ina

ryTr

ee

()

+cr

ea

teB

ina

ryTr

ee

(in

ro

otI

tem

: Tr

ee

Ite

mTy

pe

)

+cr

ea

teB

ina

ryTr

ee

(in

ro

otI

tem

: Tr

ee

Ite

mTy

pe

,

in

ou

t le

ftTr

ee

: B

ina

ryTr

ee

,

ino

ut

rig

htT

ree

: B

ina

ryTr

ee

)

+d

est

roy

Bin

ary

Tre

e()

+is

Em

pty

():

bo

ole

an

{q

ue

ry}

+g

etR

oo

tDa

ta()

: Tr

ee

Ite

mTy

pe

thro

w T

ree

Exc

ep

tio

n

+se

tRo

otD

ata

(in

ne

wIt

em

: Tr

ee

Ite

mTy

pe

)

th

row

Tre

eE

xce

pti

on

+a

tta

chLe

ft(i

n n

ew

Ite

m:

Tre

eIt

em

Typ

e)

thro

w T

ree

Exc

ep

tio

n

+a

tta

chR

igh

t(in

ne

wIt

em

: Tr

ee

Ite

mTy

pe

)

th

row

Tre

eE

xce

pti

on

+a

tta

chLe

ftS

ub

tre

e(i

no

ut

left

Tre

e:

Bin

ary

Tre

e)

t

hro

w T

ree

Exc

ep

tio

n

+a

tta

chR

igh

tSu

btr

ee

(in

ou

t ri

gh

tTre

e:

Bin

ary

Tre

e)

thro

w T

ree

Exc

ep

tio

n

+d

eta

chLe

ftS

ub

tre

e(o

ut

left

Tre

e:

Bin

ary

Tre

e)

t

hro

w T

ree

Exc

ep

tio

n

+d

eta

chR

igh

tSu

btr

ee

(ou

t ri

gh

tTre

e:

Bin

ary

Tre

e)

t

hro

w T

ree

Exc

ep

tio

n

+g

etL

eft

Su

btr

ee

():

Bin

ary

Tre

e

+g

etR

igh

tSu

btr

ee

():

Bin

ary

Tre

e

+p

reo

rde

rTra

vers

e(i

n v

isit

:Fu

nct

ion

Typ

e)

+in

ord

erT

rave

rse

(in

vis

it:F

un

ctio

nTy

pe

)

+p

ost

ord

erT

rave

rse

(in

vis

it:F

un

ctio

nTy

pe

) E

EC

S 2

68 P

rogra

mm

ing I

I 22

Th

e A

DT

Bin

ary

Tre

e

Bu

ild

ing

th

e A

DT

bin

ary

tre

e i

n F

ig.

10

-6b

tree2.attachLeftSubtree(tree1)

tree3.attachLeftSubtree(tree2)

23

Po

ssib

le R

ep

rese

nta

tio

ns

of

a

Bin

ary

Tre

e

An

arr

ay

-ba

sed

re

pre

sen

tati

on

Use

s a

n a

rra

y o

f tr

ee

no

de

s

Re

qu

ire

s th

e c

rea

tio

n o

f a

fre

e l

ist

tha

t ke

ep

s tr

ack

of

ava

ila

ble

no

de

s

on

ly s

uit

ab

le f

or

com

ple

te b

ina

ry t

ree

s

A p

oin

ter-

ba

sed

re

pre

sen

tati

on

No

de

s h

ave

tw

o p

oin

ters

th

at

lin

k t

he

no

de

s in

th

e

tre

e

24

EE

CS

268 P

rogra

mm

ing I

I

Page 7: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Arr

ay

Ba

sed

Bin

ary

Tre

e

Giv

en

a c

om

ple

te b

ina

ry t

ree

T w

ith

n n

od

es,

T c

an

be

re

pre

sen

ted

usi

ng

an

arr

ay

A[0

:n1

] su

ch t

ha

t ro

ot

of

T i

s in

A[0

]

for

no

de

A[i

], i

ts le

ft c

hil

d is

at

A[2

i+1

] a

nd

its

rig

ht

chil

d a

t A

[2i+

2]

if i

t e

xist

s

Co

mp

lete

ne

ss o

f th

e t

ree

is

imp

ort

an

t b

eca

use

it

min

imiz

es

the

siz

e o

f th

e a

rra

y r

eq

uir

ed

No

te t

ha

t p

are

nt

of

no

de

A[i

] is

at

A[(

i1)/

2]

for

n >

1,

A[i

] is

a le

af

no

de

iff

n <

= 2

i

Ba

lan

ced

re

qu

ire

me

nt

ma

kes

an

arr

ay

re

pre

sen

tati

on

u

nsu

ita

ble

fo

r b

ina

ry s

ea

rch

tre

e im

ple

me

nta

tio

n

EE

CS

26

8 P

rogra

mm

ing I

I 25

Arr

ay

Ba

sed

Bin

ary

Tre

e

Co

mp

lete

tre

e f

its

in m

inim

um

siz

e a

rra

y

spa

ce e

ffic

ien

t

No

de

s d

o n

ot

ne

ed

ch

ild

or

pa

ren

t p

oin

ters

in

de

x o

f th

ese

ca

n b

e c

alc

ula

ted

fro

m t

he

in

de

x o

f th

e

curr

en

t n

od

e

EECS 268 Programming II

26

A

B

C

D

E

F

G

H

I J

A B C D E F G H I J

Arr

ay

Ba

sed

Bin

ary

Tre

e

Ad

van

tag

es

spa

ce s

av

ing

th

rou

gh

dir

ect

co

mp

uta

tio

n o

f ch

ild

an

d

pa

ren

t in

dic

es

rath

er

tha

n p

oin

ters

O(1

) a

cce

ss t

ime

th

rou

gh

dir

ect

co

mp

uta

tio

n

po

inte

rs a

re a

lso

O(1

) a

cce

ss b

ut

wit

h la

rge

r K

Dis

ad

van

tag

es

on

ly u

sefu

l w

he

n t

ree

is

com

ple

te

or,

co

mp

lete

en

ou

gh

th

at

un

use

d c

ell

s d

o n

ot

wa

ste

mu

ch m

em

ory

spa

rse

tre

e r

ep

rese

nta

tio

n i

s to

o m

em

ory

inte

nsi

ve

If a

co

mp

lete

tre

e i

s o

f h

eig

ht

h,

it r

eq

uir

es

an

arr

ay

of

size

2h-1

a

ske

we

d B

ST

of

10

no

de

s is

of

he

igh

t 1

0,

req

uir

ing

an

a

rra

y o

f si

ze 2

10-1

= 1

02

3

EE

CS

26

8 P

rogra

mm

ing I

I 27

Po

inte

r-b

ase

d A

DT

Bin

ary

Tre

e

28

Fig

ure

10

-14

A

po

inte

r-ba

se

d im

ple

me

nta

tio

n o

f a

bin

ary

tre

e

EE

CS

268 P

rogra

mm

ing I

I

Page 8: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Po

inte

r-b

ase

d A

DT

Bin

ary

Tre

e

TreeException

an

d TreeNode

cla

sse

s

BinaryTree

cla

ss

Se

vera

l co

nst

ruct

ors

, in

clu

din

g a

Pro

tect

ed

co

nst

ruct

or

wh

ose

arg

um

en

t is

a p

oin

ter

to a

roo

t n

od

e;

pro

hib

its

clie

nt

acc

ess

Co

py

co

nst

ruct

or

tha

t ca

lls

a p

riva

te f

un

ctio

n t

o c

op

y

ea

ch n

od

e d

uri

ng

a t

rave

rsa

l o

f th

e t

ree

De

stru

cto

r

29

EE

CS

26

8 P

rogra

mm

ing I

I

Bin

ary

Tre

e A

DT

T

ree

No

de

.h

// T

reeN

ode.h

typedef str

ing T

reeItem

Type

;

// n

ode

in the tre

e

cla

ss T

reeN

ode

{

pri

vate

:

T

reeN

ode

() {

};

T

reeN

ode

(const T

reeItem

Type

& n

odeItem

, T

reeN

ode

*le

ft =

NU

LL,

T

reeN

od

e *

rig

ht =

NU

LL

): ite

m(n

od

eIte

m),

le

ftC

hild

Ptr

(left),

rig

htC

hild

Ptr

(rig

ht)

{}

T

reeItem

Type

ite

m; // d

ata

po

rtio

n

T

reeN

ode

*le

ftC

hild

Ptr

; // poin

ter

to left c

hild

T

reeN

ode

*righ

tChild

Ptr

; // p

oin

ter

to r

igh

t ch

ild

fr

iend c

lass B

inary

Tre

e; // fr

ien

d c

lass

};

EE

CS

268 P

rogra

mm

ing I

I 30

Bin

ary

Tre

e A

DT

T

ree

Exc

ep

tio

n.h

// T

ree

Exce

ption.h

#in

clu

de <

std

exce

pt>

#in

clu

de <

str

ing>

usin

g n

am

espace s

td;

Cla

ss T

ree

Exce

ptio

n :

pu

blic

lo

gic

_e

rro

r {

pub

lic:

T

ree

Exce

ption

(co

nst

lo

gic

_err

or(

message

.c_str

())

{}

};

EE

CS

26

8 P

rogra

mm

ing I

I 31

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.h

//B

eg

in B

ina

ryT

ree.h

#in

clu

de

"T

reeE

xce

ptio

n.h

"

#in

clu

de "

Tre

eN

ode.h

"

// T

his

fu

nctio

n p

oin

ter

is u

sed

by t

he c

lien

t

// to

cu

sto

miz

e w

hat

hap

pe

ns w

hen

a n

ode

is v

isite

d

typ

ed

ef

vo

id (

*Fu

nctio

nT

yp

e)(

Tre

eIt

em

Typ

e&

anIt

em

);

cla

ss B

ina

ryT

ree {

pub

lic:

// c

onstr

ucto

rs a

nd

destr

ucto

r:

Bin

ary

Tre

e()

;

Bin

ary

Tre

e(c

onst

Tre

eIt

em

Typ

e&

ro

otI

tem

);

Bin

ary

Tre

e(c

onst

Tre

eIt

em

Type&

rootI

tem

, B

inary

Tre

e&

left

Tre

e,

Bin

ary

Tre

e&

rig

htT

ree);

Bin

ary

Tre

e(c

onst

Bin

ary

Tre

e&

tre

e);

virtu

al ~

Bin

ary

Tre

e()

;

E

EC

S 2

68 P

rogra

mm

ing I

I 32

Page 9: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.h

// b

inary

tre

e o

pe

ratio

ns:

virtu

al bool is

Em

pty

() c

onst;

virtu

al T

reeIt

em

Typ

e g

etR

ootD

ata

() c

onst

t

hro

w(T

reeE

xce

ptio

n);

virtu

al void

setR

ootD

ata

(const T

reeIt

em

Type&

new

Item

) th

row

(T

reeE

xception);

virtu

al vo

id a

tta

chL

eft

(co

nst T

reeIt

em

Typ

e&

new

Ite

m)

th

row

(Tre

eE

xce

ptio

n);

virtu

al vo

id a

tta

chR

ight(

co

nst T

reeIt

em

Typ

e&

new

Ite

m)

th

row

(Tre

eE

xce

ptio

n);

virtu

al vo

id a

tta

chL

eft

Sub

tree(B

ina

ryT

ree&

left

Tre

e)

th

row

(Tre

eE

xce

ptio

n);

virtu

al vo

id a

tta

chR

ightS

ubtr

ee(B

ina

ryT

ree&

rig

htT

ree)

t

hro

w(T

reeE

xce

ptio

n);

virtu

al vo

id d

eta

chL

eft

Sub

tree(B

ina

ryT

ree&

left

Tre

e)

th

row

(Tre

eE

xce

ptio

n);

virtu

al vo

id d

eta

chR

ightS

ubtr

ee(B

ina

ryT

ree&

rig

htT

ree)

th

row

(Tre

eE

xce

ptio

n);

virtu

al B

ina

ryT

ree g

etL

eft

Sub

tree()

co

nst;

virtu

al B

inary

Tre

e g

etR

ightS

ubtr

ee()

const;

virtu

al vo

id p

reo

rde

rTra

vers

e(F

unctio

nT

yp

e v

isit);

virtu

al vo

id ino

rde

rTra

vers

e(F

unctio

nT

yp

e v

isit);

virtu

al vo

id p

osto

rde

rTra

vers

e(F

unctio

nT

yp

e v

isit);

E

EC

S 2

68 P

rogra

mm

ing I

I 33

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.h

// o

verloa

de

d a

ssig

nm

ent

ope

rato

r:

virtu

al B

ina

ryT

ree&

ope

rato

r=(c

onst

Bin

ary

Tre

e&

rh

s);

pro

tecte

d:

Bin

ary

Tre

e(T

reeN

od

e *

nod

eP

tr);

//

con

str

ucto

r

// C

op

ies t

he t

ree r

oote

d a

t tr

eeP

tr into

a t

ree r

oote

d

// a

t n

ew

Tre

eP

tr.

Th

row

s T

reeE

xce

ptio

n if

a c

opy o

f th

e

// tre

e c

ann

ot

be a

lloca

ted

.

void

copyT

ree(T

reeN

ode *

tre

eP

tr, T

reeN

ode*

& n

ew

Tre

eP

tr)

const

th

row

(Tre

eE

xce

ptio

n);

;

// D

ea

lloca

te m

em

ory

fo

r a

tre

e.

v

oid

destr

oyT

ree(T

reeN

od

e *

&tr

eeP

tr);

// T

he n

ext

two f

unctions r

etr

ieve a

nd s

et

the v

alu

e

// o

f th

e p

rivate

data

me

mbe

r ro

ot.

T

reeN

od

e *

rootP

tr(

) co

nst;

vo

id s

etR

oo

tPtr

(Tre

eN

od

e *

new

Ro

ot)

;

EE

CS

268 P

rogra

mm

ing I

I 34

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.h

// T

he n

ext

two

fu

nctio

ns r

etr

ieve

an

d s

et

the v

alu

es

// o

f th

e le

ft a

nd

rig

ht

ch

ild p

oin

ters

of

a t

ree n

od

e.

void

getC

hild

Ptr

s(T

reeN

ode *

nodeP

tr, T

reeN

ode *

&le

ftC

hild

Ptr

,

T

reeN

od

e *

&righ

tChild

Ptr

) co

nst;

vo

id s

etC

hild

Ptr

s(T

reeN

od

e *

nod

eP

tr, T

reeN

od

e *

left

Child

Ptr

,

T

reeN

od

e *

righ

tChild

Ptr

);

vo

id p

reord

er(

Tre

eN

od

e *

tre

eP

tr, F

unctio

nT

yp

e v

isit);

vo

id ino

rde

r(T

reeN

od

e *

tre

eP

tr, F

unctio

nT

yp

e v

isit);

vo

id p

osto

rde

r(T

reeN

od

e *

tre

eP

tr,

Fu

nctio

nT

yp

e v

isit);

priva

te:

T

reeN

od

e *

roo

t; /

/ p

oin

ter

to r

oot

of

tre

e

}; // e

nd

cla

ss

// E

nd

of

hea

de

r file

. B

ina

ryT

ree.h

EE

CS

26

8 P

rogra

mm

ing I

I 35

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

// Im

ple

me

nta

tion

file

Bin

ary

Tre

e.c

pp f

or

the A

DT

bin

ary

tr

ee.

#in

clu

de

"B

ina

ryT

ree.h

"

//

he

ad

er

file

#in

clu

de

<cstd

de

f>

//

de

finitio

n o

f N

UL

L

#in

clu

de

<ca

ssert

>

//

for

assert

()

Bin

ary

Tre

e::

Bin

ary

Tre

e()

: r

oo

t(N

UL

L)

{ }

Bin

ary

Tre

e::

Bin

ary

Tre

e(c

on

st

Tre

eIt

em

Typ

e&

ro

otI

tem

) {

root

= n

ew

Tre

eN

od

e(r

ootI

tem

, N

UL

L,

NU

LL);

assert

(ro

ot

!= N

ULL);

} Bin

ary

Tre

e::

Bin

ary

Tre

e(c

on

st

Tre

eIt

em

Typ

e&

ro

otI

tem

,

B

ina

ryT

ree&

left

Tre

e,

Bin

ary

Tre

e&

rig

htT

ree)

{

root

= n

ew

Tre

eN

od

e(r

ootI

tem

, N

UL

L,

NU

LL);

assert

(ro

ot

!= N

ULL);

att

achL

eft

Sub

tree

(left

Tre

e);

att

achR

ightS

ubtr

ee(r

igh

tTre

e);

} E

EC

S 2

68 P

rogra

mm

ing I

I 36

Page 10: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

Bin

ary

Tre

e::

Bin

ary

Tre

e(c

on

st

Bin

ary

Tre

e&

tre

e)

{

co

pyT

ree(t

ree.r

oot,

ro

ot)

;

} Bin

ary

Tre

e::

Bin

ary

Tre

e(T

reeN

ode *

nodeP

tr):

root(

nodeP

tr)

{ }

Bin

ary

Tre

e::

~B

ina

ryT

ree()

{

destr

oyT

ree(r

oot)

;

}

bool B

ina

ryT

ree::

isE

mpty

() c

onst

{

retu

rn (

root

==

NU

LL);

}

Tre

eIt

em

Typ

e B

ina

ryT

ree::

getR

ootD

ata

() c

onst

{

if (

isE

mpty

())

thro

w T

reeE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Em

pty

tre

e")

;

retu

rn r

oot>

ite

m;

}

EE

CS

26

8 P

rogra

mm

ing I

I 37

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

vo

id B

ina

ryT

ree::

se

tRoo

tData

(co

nst

Tre

eIt

em

Typ

e&

new

Ite

m)

{

if (

!isE

mpty

())

{

root>

ite

m =

new

Ite

m;

} e

lse

{

root

= n

ew

Tre

eN

ode(n

ew

Item

, N

ULL,

NU

LL);

if (

roo

t =

= N

ULL

)

th

row

Tre

eE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Can

no

t a

lloca

te m

em

ory

");

}

} vo

id B

ina

ryT

ree::

att

achL

eft

(co

nst T

reeIt

em

Typ

e&

new

Ite

m)

{

if (

isE

mpty

())

{

thro

w T

reeE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Em

pty

tre

e")

;

} e

lse

if

(ro

ot>

left

Child

Ptr

!=

NU

LL)

{

thro

w T

reeE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Can

no

t o

verw

rite

left

su

btr

ee")

;

} els

e {

//

Assert

ion:

nonem

pty

tre

e;

no left

ch

ild

root>

left

Child

Ptr

= n

ew

Tre

eN

od

e(n

ew

Ite

m,

NU

LL,

NU

LL);

if (

roo

t>le

ftC

hild

Ptr

==

NU

LL)

th

row

Tre

eE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Can

no

t a

lloca

te m

em

ory

");

}

} E

EC

S 2

68 P

rogra

mm

ing I

I 38

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

vo

id B

ina

ryT

ree::

att

achR

ight(

co

nst

Tre

eIt

em

Typ

e&

new

Ite

m)

{

if (

isE

mpty

())

thro

w T

reeE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Em

pty

tre

e")

;

els

e if

(ro

ot>

righ

tChild

Ptr

!=

NU

LL)

thro

w T

reeE

xception("

Tre

eE

xception:

Cannot

overw

rite

rig

ht

subtr

ee")

;

els

e {

// A

ssert

ion:

non

em

pty

tre

e;

no r

ight

ch

ild

root>

righ

tChild

Ptr

= n

ew

Tre

eN

od

e(n

ew

Ite

m,

NU

LL,

NU

LL);

if (

roo

t>righ

tChild

Ptr

==

NU

LL)

th

row

Tre

eE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Can

no

t a

lloca

te m

em

ory

");

}

} vo

id B

ina

ryT

ree::

att

achL

eft

Sub

tree(B

ina

ryT

ree&

left

Tre

e)

{

if (

isE

mpty

())

thro

w T

reeE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Em

pty

tre

e")

;

els

e if

(ro

ot>

left

Child

Ptr

!=

NU

LL)

thro

w T

reeE

xception("

Tre

eE

xception:

Cannot

overw

rite

left

subtr

ee")

;

els

e {

//

Assert

ion:

non

em

pty

tre

e;

no le

ft c

hild

root>

left

Child

Ptr

= left

Tre

e.r

oot;

left

Tre

e.r

oot

= N

ULL

;

}

} E

EC

S 2

68 P

rogra

mm

ing I

I 39

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

vo

id B

ina

ryT

ree::

att

achR

ightS

ubtr

ee(B

ina

ryT

ree&

rig

htT

ree)

{

if (

isE

mpty

())

thro

w T

reeE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Em

pty

tre

e")

;

els

e if

(ro

ot>

rightC

hild

Ptr

!=

NU

LL)

thro

w T

reeE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Can

no

t o

verw

rite

rig

ht

su

btr

ee")

;

els

e {

// A

ssert

ion:

non

em

pty

tre

e;

no

rig

ht

ch

ild

root>

righ

tChild

Ptr

= r

igh

tTre

e.r

oot;

righ

tTre

e.r

oot

= N

UL

L;

}

} vo

id B

ina

ryT

ree::

deta

chL

eft

Sub

tree(B

ina

ryT

ree&

left

Tre

e)

{

if (

isE

mpty

())

thro

w T

reeE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Em

pty

tre

e")

;

els

e {

left

Tre

e =

Bin

ary

Tre

e(r

oot>

left

Child

Ptr

); /

/ co

nstr

ucto

r ta

kin

g n

ode

* n

ot

tre

e *

root>

left

Child

Ptr

= N

ULL

;

}

} E

EC

S 2

68 P

rogra

mm

ing I

I 40

Page 11: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

void

Bin

ary

Tre

e::deta

chR

igh

tSubtr

ee

(Bin

ary

Tre

e&

rig

htT

ree

) {

if (

isE

mpty

())

th

row

Tre

eE

xce

ption

("T

reeE

xce

ption

: E

mpty

tre

e")

;

els

e {

righ

tTre

e =

Bin

ary

Tre

e(r

oot>

rightC

hild

Ptr

); // node *

to tre

e

co

nvers

ion

ro

ot>

rightC

hild

Ptr

= N

ULL; // this

tre

e n

o longe

r hold

s that su

btr

ee

}

}

Bin

ary

Tre

e B

inary

Tre

e::getL

eftS

ubtr

ee()

co

nst {

T

reeN

ode

*su

bT

reeP

tr;

if (

isE

mpty

())

re

turn

Bin

ary

Tre

e()

;

els

e {

co

pyT

ree

(root>

leftC

hild

Ptr, su

bT

reeP

tr);

re

turn

Bin

ary

Tre

e(s

ubT

reeP

tr);

}

} E

EC

S 2

68 P

rogra

mm

ing I

I 41

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

Bin

ary

Tre

e B

ina

ryT

ree::

righ

tSub

tree()

co

nst

{

T

reeN

od

e *

su

bT

reeP

tr;

if (

isE

mpty

())

retu

rn B

inary

Tre

e()

;

els

e {

co

pyT

ree(r

oot>

righ

tChild

Ptr

, su

bT

reeP

tr);

retu

rn B

ina

ryT

ree(s

ubT

reeP

tr);

}

}

vo

id B

ina

ryT

ree::

pre

ord

erT

ravers

e(F

unctio

nT

yp

e v

isit)

{

pre

ord

er(

roo

t, v

isit);

//

pre

ord

er

writt

en w

ith

re

spe

ct

to a

tre

e p

tr

}

void

Bin

ary

Tre

e::

inord

erT

ravers

e(F

unctionT

yp

e v

isit)

{

ino

rde

r(ro

ot,

vis

it);

}

EE

CS

268 P

rogra

mm

ing I

I 42

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

void

Bin

ary

Tre

e::posto

rderT

ravers

e(F

unctionT

ype

vis

it)

{

posto

rder(

root, v

isit);

} Bin

ary

Tre

e&

Bin

ary

Tre

e::opera

tor=

(const B

inary

Tre

e&

rhs)

{

if (

this

!=

&rh

s)

{

destr

oyT

ree(r

oot)

; // deallo

cate

lefth

an

d s

ide

co

pyT

ree

(rhs.r

oot, r

oot)

; // co

py r

igh

tha

nd

sid

e

}

re

turn

*th

is;

} void

Bin

ary

Tre

e::destr

oyT

ree

(Tre

eN

ode *

& tre

eP

tr)

{

if (

treeP

tr !=

NU

LL)

{

destr

oyT

ree(t

reeP

tr>

leftC

hild

Ptr

);

destr

oyT

ree(t

reeP

tr>

rightC

hild

Ptr

);

dele

te tre

eP

tr; // posto

rder

travers

al

tr

eeP

tr =

NU

LL;

}

} E

EC

S 2

68 P

rogra

mm

ing I

I 43

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

vo

id B

ina

ryT

ree::

co

pyT

ree(T

reeN

od

e *

tre

eP

tr, T

reeN

od

e *

& n

ew

Tre

eP

tr)

co

nst

{

//

pre

ord

er

tra

vers

al

if (

tre

eP

tr !=

NU

LL)

{

// c

opy n

od

e

new

Tre

eP

tr =

new

Tre

eN

od

e(t

reeP

tr>

ite

m,

NU

LL,

NU

LL);

if (

new

Tre

eP

tr =

= N

UL

L)

th

row

Tre

eE

xce

ptio

n("

Tre

eE

xce

ptio

n:

Can

no

t a

lloca

te m

em

ory

");

co

pyT

ree(t

reeP

tr>

left

Child

Ptr

, n

ew

Tre

eP

tr>

left

Child

Ptr

);

copyT

ree(t

reeP

tr>

rightC

hild

Ptr

, new

Tre

eP

tr>

rightC

hild

Ptr

);

} e

lse

new

Tre

eP

tr =

NU

LL;

//

cop

y e

mpty

tre

e

} Tre

eN

od

e *

Bin

ary

Tre

e::

rootP

tr()

co

nst

{

re

turn

ro

ot;

}

EE

CS

268 P

rogra

mm

ing I

I 44

Page 12: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

void

Bin

ary

Tre

e::se

tRootP

tr(T

reeN

ode *

new

Ro

ot)

{

ro

ot =

new

Ro

ot;

} void

Bin

ary

Tre

e::getC

hild

Ptr

s(T

reeN

ode *

node

Ptr

, T

reeN

ode

*&

leftP

tr,

T

reeN

ode

*&

rig

htP

tr)

co

nst {

le

ftP

tr =

node

Ptr

>le

ftC

hild

Ptr

;

righ

tPtr

= n

ode

Ptr

>righ

tChild

Ptr

;

} void

Bin

ary

Tre

e::se

tChild

Ptr

s(T

reeN

ode

*node

Ptr

, T

reeN

ode

*le

ftP

tr,

T

reeN

ode

*righ

tPtr

) {

node

Ptr

>le

ftC

hild

Ptr

= leftP

tr;

nodeP

tr>

rightC

hild

Ptr

= r

ightP

tr;

}

EE

CS

26

8 P

rogra

mm

ing I

I 45

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

void

Bin

ary

Tre

e::pre

ord

er(

Tre

eN

ode

*tr

ee

Ptr

, F

un

ction

Typ

e v

isit)

{

if (

treeP

tr !=

NU

LL)

{

vis

it(t

reeP

tr>

item

);

pre

ord

er(

treeP

tr>

leftC

hild

Ptr

, vis

it);

pre

ord

er(

treeP

tr>

rig

htC

hild

Ptr

, vis

it);

}

} void

Bin

ary

Tre

e::in

ord

er(

Tre

eN

ode

*tr

eeP

tr, F

unctionType

vis

it)

{

if (

treeP

tr !=

NU

LL)

{

in

ord

er(

treeP

tr>

leftC

hild

Ptr

, vis

it);

vis

it(t

reeP

tr>

item

);

in

ord

er(

treeP

tr>

rig

htC

hild

Ptr

, vis

it);

}

}

EE

CS

268 P

rogra

mm

ing I

I 46

Bin

ary

Tre

e A

DT

B

ina

ryTr

ee

.cp

p

void

Bin

ary

Tre

e::posto

rder(

Tre

eN

ode

*tr

eeP

tr, F

unctionType

vis

it)

{

if (

treeP

tr !=

NU

LL)

{

posto

rder(

treeP

tr>

leftC

hild

Ptr

, vis

it);

posto

rder(

treeP

tr>

rightC

hild

Ptr

, vis

it);

vis

it(t

reeP

tr>

item

);

}

} // E

nd o

f im

ple

menta

tion file

.

EE

CS

26

8 P

rogra

mm

ing I

I 47

Bin

ary

Tre

e A

DT

C

lie

nt

Co

de

// E

xa

mple

clie

nt

co

de

#in

clu

de <

iostr

eam

>

#in

clu

de

"B

ina

ryT

ree.h

"

usin

g n

am

espace s

td;

vo

id d

isp

lay(T

reeIt

em

Typ

e&

anIt

em

);

int

ma

in()

{ B

ina

ryT

ree t

ree1

, tr

ee2

, le

ft;

// tr

ee w

ith

only

a r

oo

t 7

0

B

ina

ryT

ree t

ree3

(70

);

/

/ build

th

e t

ree in F

igure

10

-10

tre

e1

.setR

ootD

ata

(40);

tre

e1

.att

achL

eft

(30);

tre

e1

.att

achR

ight(

50);

E

EC

S 2

68 P

rogra

mm

ing I

I 48

tre

e2

.setR

ootD

ata

(20);

tre

e2

.att

achL

eft

(10);

tre

e2

.att

achR

ightS

ubtr

ee(t

ree

1);

/

/ tr

ee in

Fig

10-1

0

B

ina

ryT

ree b

inT

ree(6

0,

tre

e2

, tr

ee3

);

b

inT

ree.in

ord

erT

ravers

e(d

isp

lay);

b

inT

ree.g

etL

eft

Subtr

ee()

.inord

erT

ravers

e

(dis

pla

y);

b

inT

ree.d

eta

chL

eft

Sub

tree(left

);

left

.in

ord

erT

ravers

e(d

isp

lay);

b

inT

ree.in

ord

erT

ravers

e(d

isp

lay);

r

etu

rn 0

;

} // e

nd

ma

in

Page 13: Overview Terminologykulkarni/teaching/EECS268/slides/chap10-part1.ha… · Terminology Parent of node n ±The node directly above node n in the tree Child of node n ±A node directly

Po

inte

r-b

ase

d A

DT

Bin

ary

Tre

e:

Tre

e T

rave

rsa

ls

BinaryTree

cla

ss (

con

tin

ue

d)

Pu

bli

c m

eth

od

s fo

r tr

ave

rsa

ls s

o t

ha

t vis

itin

g a

no

de

re

ma

ins

void inorderTraverse(FunctionType visit);

typedef void (*FunctionType)(TreeItemType&

item);

Pro

tect

ed

me

tho

ds,

su

ch a

s inorder

, th

at

en

ab

le t

he

re

curs

ion

void inorder(TreeNode *treeptr,

FunctionType visit);

inorderTraverse

ca

lls inorder

, p

ass

ing

it

a n

od

e

po

inte

r a

nd

th

e c

lie

nt-

de

fin

ed

fu

nct

ion

visit

49

EE

CS

26

8 P

rogra

mm

ing I

I

Re

curs

ive

In

ord

er

Tra

vers

al

50

EE

CS

268 P

rogra

mm

ing I

I

No

nre

curs

ive

In

ord

er

Tra

vers

al

An

ite

rati

ve m

eth

od

an

d a

n e

xpli

cit

sta

ck

can

mim

ic t

he

act

ion

s

of

a r

etu

rn f

rom

a

recu

rsiv

e c

all

to

inorder

51

Fig

ure

10

-16

Tra

ve

rsin

g (

a)

the

le

ft a

nd

(b

) th

e r

igh

t su

btr

ee

s o

f 2

0

Co

py

ing

a B

ina

ry T

ree

To c

op

y a

tre

e

tra

vers

e i

t in

pre

ord

er

inse

rt e

ach

ite

m v

isit

ed

in

to a

ne

w t

ree

use

in

co

py

co

nst

ruct

or

To d

ea

llo

cate

a t

ree

tr

ave

rse

in

po

sto

rde

r

de

lete

ea

ch n

od

e v

isit

ed

de

all

oca

tio

n

sub

tre

es

use

in

de

stru

cto

r EE

CS

268 P

rogra

mm

ing I

I 52