Red-black tree visualization - University of Cambridge · Andrej Ivaskovic (University of...

Red-black tree visualization

Andrej Ivaskovic

University of Cambridge

February 8, 2015

Andrej Ivaskovic (University of Cambridge) Red-black tree visualization February 8, 2015 1 / 1

Inserting A

There are no non-empty nodes in the tree yet!


Inserting A

A

Add a new node: make it red [A].


Inserting A

A

Everything is consistent =⇒ no important updates!


Inserting A

A

Remember that the root must be black!


Inserting A

A

And we are done!


Inserting L

A

Compare [L] and A.


Inserting L

A

L

Add a new node: make it red [L].


Inserting L

A

L



Inserting L

A

L

And we are done!


Inserting G

A

L

Compare [G] and A.


Inserting G

A

L

Compare [G] and L.


Inserting G

A

L

G

Add a new node: make it red [G].


Inserting G

A

L

G

G and L violate the red-black rule!


Inserting G

A

L

G

G’s uncle is -.First perform a rotation. . .


Inserting G

A

G

L

Now perform yet another rotation. . .


Inserting G

G

A L

Make sure all colours are consistent!


Inserting G

G

A L



Inserting G

G

A L

And we are done!


Inserting O

G

A L

Compare [O] and G.


Inserting O

G

A L

Compare [O] and L.


Inserting O

G

A L

O

Add a new node: make it red [O].


Inserting O

G

A L

O

O and L violate the red-black rule!


Inserting O

G

A L

O

O’s uncle is A.Simple colour substitution will suffice.


Inserting O

G

A L

O

Now consider the grandparent node. . .


Inserting O

G

A L

O



Inserting O

G

A L

O

And we are done!


Inserting R

G

A L

O

Compare [R] and G.


Inserting R

G

A L

O

Compare [R] and L.


Inserting R

G

A L

O

Compare [R] and O.


Inserting R

G

A L

O

R

Add a new node: make it red [R].


Inserting R

G

A L

O

R

R and O violate the red-black rule!


Inserting R

G

A L

O

R

R’s uncle is -.First perform a rotation. . .


Inserting R

G

A O

L R



Inserting R

G

A O

L R

And we are done!


Inserting I

G

A O

L R

Compare [I] and G.


Inserting I

G

A O

L R

Compare [I] and O.


Inserting I

G

A O

L R

Compare [I] and L.


Inserting I

G

A O

L

I

R

Add a new node: make it red [I].


Inserting I

G

A O

L

I

R

I and L violate the red-black rule!


Inserting I

G

A O

L

I

R

I’s uncle is R.Simple colour substitution will suffice.


Inserting I

G

A O

L

I

R



Inserting I

G

A O

L

I

R

And we are done!


Inserting T

G

A O

L

I

R

Compare [T] and G.


Inserting T

G

A O

L

I

R

Compare [T] and O.


Inserting T

G

A O

L

I

R

Compare [T] and R.


Inserting T

G

A O

L

I

R

T

Add a new node: make it red [T].


Inserting T

G

A O

L

I

R

T



Inserting T

G

A O

L

I

R

T

And we are done!


Inserting H

G

A O

L

I

R

T

Compare [H] and G.


Inserting H

G

A O

L

I

R

T

Compare [H] and O.


Inserting H

G

A O

L

I

R

T

Compare [H] and L.


Inserting H

G

A O

L

I

R

T

Compare [H] and I.


Inserting H

G

A O

L

I

H

R

T

Add a new node: make it red [H].


Inserting H

G

A O

L

I

H

R

T

H and I violate the red-black rule!


Inserting H

G

A O

L

I

H

R

T

H’s uncle is -.First perform a rotation. . .


Inserting H

G

A O

I

H L

R

T



Inserting H

G

A O

I

H L

R

T

And we are done!


Inserting M

G

A O

I

H L

R

T

Compare [M] and G.


Inserting M

G

A O

I

H L

R

T

Compare [M] and O.


Inserting M

G

A O

I

H L

R

T

Compare [M] and I.


Inserting M

G

A O

I

H L

R

T

Compare [M] and L.


Inserting M

G

A O

I

H L

M

R

T

Add a new node: make it red [M].


Inserting M

G

A O

I

H L

M

R

T

M and L violate the red-black rule!


Inserting M

G

A O

I

H L

M

R

T

M’s uncle is H.Simple colour substitution will suffice.


Inserting M

G

A O

I

H L

M

R

T



Inserting M

G

A O

I

H L

M

R

T

I and O violate the red-black rule!


Inserting M

G

A O

I

H L

M

R

T

I’s uncle is A.First perform a rotation. . .


Inserting M

G

A I

H O

L

M

R

T



Inserting M

I

G

A H

O

L

M

R

T



Inserting M

I

G

A H

O

L

M

R

T

And we are done!


Inserting S

I

G

A H

O

L

M

R

T

Compare [S] and I.


Inserting S

I

G

A H

O

L

M

R

T

Compare [S] and O.


Inserting S

I

G

A H

O

L

M

R

T

Compare [S] and R.


Inserting S

I

G

A H

O

L

M

R

T

Compare [S] and T.


Inserting S

I

G

A H

O

L

M

R

T

S

Add a new node: make it red [S].


Inserting S

I

G

A H

O

L

M

R

T

S

S and T violate the red-black rule!


Inserting S

I

G

A H

O

L

M

R

T

S

S’s uncle is -.First perform a rotation. . .


Inserting S

I

G

A H

O

L

M

R

S

T



Inserting S

I

G

A H

O

L

M

S

R T



Inserting S

I

G

A H

O

L

M

S

R T

And we are done!


Inserting C

I

G

A H

O

L

M

S

R T

Compare [C] and I.


Inserting C

I

G

A H

O

L

M

S

R T

Compare [C] and G.


Inserting C

I

G

A H

O

L

M

S

R T

Compare [C] and A.


Inserting C

I

G

A

C

H

O

L

M

S

R T

Add a new node: make it red [C].


Inserting C

I

G

A

C

H

O

L

M

S

R T



Inserting C

I

G

A

C

H

O

L

M

S

R T

And we are done!


Inserting A

I

G

A

C

H

O

L

M

S

R T

Compare [A] and I.


Inserting A

I

G

A

C

H

O

L

M

S

R T

Compare [A] and G.


Inserting A

I

G

A

C

H

O

L

M

S

R T

Compare [A] and A.


Inserting A

I

G

A

C

H

O

L

M

S

R T

No new node is added: duplicate key!


Inserting M

I

G

A

C

H

O

L

M

S

R T

Compare [M] and I.


Inserting M

I

G

A

C

H

O

L

M

S

R T

Compare [M] and O.


Inserting M

I

G

A

C

H

O

L

M

S

R T

Compare [M] and L.


Inserting M

I

G

A

C

H

O

L

M

S

R T

Compare [M] and M.


Inserting M

I

G

A

C

H

O

L

M

S

R T



Inserting B

I

G

A

C

H

O

L

M

S

R T

Compare [B] and I.


Inserting B

I

G

A

C

H

O

L

M

S

R T

Compare [B] and G.


Inserting B

I

G

A

C

H

O

L

M

S

R T

Compare [B] and A.


Inserting B

I

G

A

C

H

O

L

M

S

R T

Compare [B] and C.


Inserting B

I

G

A

C

B

H

O

L

M

S

R T

Add a new node: make it red [B].


Inserting B

I

G

A

C

B

H

O

L

M

S

R T

B and C violate the red-black rule!


Inserting B

I

G

A

C

B

H

O

L

M

S

R T

B’s uncle is -.First perform a rotation. . .


Inserting B

I

G

A

B

C

H

O

L

M

S

R T



Inserting B

I

G

B

A C

H

O

L

M

S

R T



Inserting B

I

G

B

A C

H

O

L

M

S

R T

And we are done!


Inserting R

I

G

B

A C

H

O

L

M

S

R T

Compare [R] and I.


Inserting R

I

G

B

A C

H

O

L

M

S

R T

Compare [R] and O.


Inserting R

I

G

B

A C

H

O

L

M

S

R T

Compare [R] and S.


Inserting R

I

G

B

A C

H

O

L

M

S

R T

Compare [R] and R.


Inserting R

I

G

B

A C

H

O

L

M

S

R T



Inserting I

I

G

B

A C

H

O

L

M

S

R T

Compare [I] and I.


Inserting I

I

G

B

A C

H

O

L

M

S

R T



Inserting D

I

G

B

A C

H

O

L

M

S

R T

Compare [D] and I.


Inserting D

I

G

B

A C

H

O

L

M

S

R T

Compare [D] and G.


Inserting D

I

G

B

A C

H

O

L

M

S

R T

Compare [D] and B.


Inserting D

I

G

B

A C

H

O

L

M

S

R T

Compare [D] and C.


Inserting D

I

G

B

A C

D

H

O

L

M

S

R T

Add a new node: make it red [D].


Inserting D

I

G

B

A C

D

H

O

L

M

S

R T

D and C violate the red-black rule!


Inserting D

I

G

B

A C

D

H

O

L

M

S

R T

D’s uncle is A.Simple colour substitution will suffice.


Inserting D

I

G

B

A C

D

H

O

L

M

S

R T



Inserting D

I

G

B

A C

D

H

O

L

M

S

R T

B and G violate the red-black rule!


Inserting D

I

G

B

A C

D

H

O

L

M

S

R T

B’s uncle is O.Simple colour substitution will suffice.


Inserting D

I

G

B

A C

D

H

O

L

M

S

R T



Inserting D

I

G

B

A C

D

H

O

L

M

S

R T

And we are done!


Inserting G

I

G

B

A C

D

H

O

L

M

S

R T

Compare [G] and I.


Inserting G

I

G

B

A C

D

H

O

L

M

S

R T

Compare [G] and G.


Inserting G

I

G

B

A C

D

H

O

L

M

S

R T



Inserting E

I

G

B

A C

D

H

O

L

M

S

R T

Compare [E] and I.


Inserting E

I

G

B

A C

D

H

O

L

M

S

R T

Compare [E] and G.


Inserting E

I

G

B

A C

D

H

O

L

M

S

R T

Compare [E] and B.


Inserting E

I

G

B

A C

D

H

O

L

M

S

R T

Compare [E] and C.


Inserting E

I

G

B

A C

D

H

O

L

M

S

R T

Compare [E] and D.


Inserting E

I

G

B

A C

D

E

H

O

L

M

S

R T

Add a new node: make it red [E].


Inserting E

I

G

B

A C

D

E

H

O

L

M

S

R T

E and D violate the red-black rule!


Inserting E

I

G

B

A C

D

E

H

O

L

M

S

R T

E’s uncle is -.First perform a rotation. . .


Inserting E

I

G

B

A D

C E

H

O

L

M

S

R T



Inserting E

I

G

B

A D

C E

H

O

L

M

S

R T

And we are done!


Inserting A

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [A] and I.


Inserting A

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [A] and G.


Inserting A

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [A] and B.


Inserting A

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [A] and A.


Inserting A

I

G

B

A D

C E

H

O

L

M

S

R T



Inserting I

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [I] and I.


Inserting I

I

G

B

A D

C E

H

O

L

M

S

R T



Searching for A

I

G

B

A D

C E

H

O

L

M

S

R T

We wish to find a node with key A.


Searching for A

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [A] with I.


Searching for A

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [A] with G.


Searching for A

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [A] with B.


Searching for A

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [A] with A.


Searching for A

I

G

B

A D

C E

H

O

L

M

S

R T

We found a node with this key!


Searching for Z

I

G

B

A D

C E

H

O

L

M

S

R T

We wish to find a node with key Z.


Searching for Z

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [Z] with I.


Searching for Z

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [Z] with O.


Searching for Z

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [Z] with S.


Searching for Z

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [Z] with T.


Searching for Z

I

G

B

A D

C E

H

O

L

M

S

R T

There is no such node!


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

We wish to find the predecessor of the node with key M. We first have to find thenode whose key is M.


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [M] with I.


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [M] with O.


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [M] with L.


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

Compare [M] with M.


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

Now we can find the predecessor!


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

M has no left child, so we have to go up.


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

M’s parent is L, which is less than M =⇒ the predecessor is L.


Predecessor of M

I

G

B

A D

C E

H

O

L

M

S

R T

M’s predecessor is L.


Red-black tree visualization - University of Cambridge · Andrej Ivaskovic (University of...

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Transcript of Red-black tree visualization - University of Cambridge · Andrej Ivaskovic (University of...