Red&BlackTree

AnwarMamat

BST

BalancedBSTUnbalancedBST

Search:O(Logn) Search:O(n)

BalancedBinarySearchTree

• Red&BlackTree• AVLTree• 2-3Tree• B-tree

Red&BlackTree

• ABSTsuchthat:• Treeedgeshavecolor:RedorBlack• Nonodehastworededgesconnectedtoit.• Everypathfromroottonulllinkhasthesamenumberofblacklinks.• Redlinksleanleft.• NewnodeedgeisRed

Search:red-blackBSTs

• Observation.SearchisthesameasforelementaryBST(ignorecolor).

Red-blackBSTrepresentation

Elementaryred-blackBSToperations• Leftrotation.Orienta(temporarily)right-leaningredlinktoleanleft.

rotateEleft(before) rotateEleft(after)

Elementaryred-blackBSToperationscont.• Leftrotation.Orienta(temporarily)right-leaningredlinktoleanleft.

Elementaryred-blackBSToperationscont.• Rightrotation:Orientaleft-leaningredlinkto(temporarily)leanright.

rotateEleft(before) rotateEleft(after)

Elementaryred-blackBSToperationscont.• Rightrotation:Orientaleft-leaningredlinkto(temporarily)leanright.

Elementaryred-blackBSToperationscont.• Colorflip.

Colorflip(before) Colorflip (after)

Elementaryred-blackBSToperationscont.• Colorflip.

InsertioninaLLRBtree

• Rightchildred,leftchildblack:rotateleft.• Leftchild,left-left grandchildred:rotateright.• Bothchildrenred:flipcolors.

InsertioninaLLRBtree:Javaimplementation

R&BExample:Insertion

MInsert:M,D

D

R&BExample:Insertion

MInsert:M,X

X

RotateLeft

R&BExample:Insertion

Insert:M,X M

X

RotateLeft

R&BExample:Insertion

Insert:M,D,X

D

M

XD

M

X

Flip Color

R&BExample:Insertion

Insert:M,D,B

D

M

B

B

D

MFlip Color

RotateRight

R&BExample:Insertion

Insert:M,D,B

B

D

MFlip Color

B

D

M

R&BExample:Insertion

M,D,BInsertH

B

D

M

B

D

M

H

R&BExample:Insertion

M,D,B,HInsertS

B

D

M

H

B

D

M

H S

Colorflip

R&BExample:InsertionM,D,B,HInsertS

B

D

M

H S

Colorflip

B

D

M

H S

RotateLeft

R&BExample:InsertionM,D,B,HInsertS

B

D

M

H S

RotateLeft

B

D

M

H

S

R&BExample:InsertionM,D,B,H,SInsertE,K

B

D

M

H

S

B

D

M

H

S

E K

R&BExample:InsertionM,D,B,H,SInsertE,K

B

D

M

H

S

E K

B

D

M

H

S

E K

Color flip

RotateLeft

R&BExample:InsertionM,D,B,H,SInsertE,K

B

D

M

H

S

E D

B

D

M

HS

E

K

Rotateleft

R&BExample:InsertionM,D,B,H,SInsertE,K

B

D

M

HS

E

K

RotateRight

B

D M

H

SE K

R&BExample:InsertionM,D,B,H,S,E,K

B

D M

H

SE K B

D M

H

SE K

Color flip