Red-Black Tree Example - University of Cambridge · Red-Black Tree Example James Clarke University...

Red-Black Tree Example

James Clarke

University of Cambridge

February 7, 2015

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 1 / 144

Inserting ‘A’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 2 / 144

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Inserting ‘L’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 5 / 144

Inserting ‘G’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 7 / 144

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Inserting ‘O’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 10 / 144

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Inserting ‘R’

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Inserting ‘I’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 20 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 22 / 144

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Inserting ‘T’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 25 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 26 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 27 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 28 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 29 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 30 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 31 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 32 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 34 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 35 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 36 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 39 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 40 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 41 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 42 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 43 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 46 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 47 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 48 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 49 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 51 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 52 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 53 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 54 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 55 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 56 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 57 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 58 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 59 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 60 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 61 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 62 / 144

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Inserting ‘B’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 65 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 66 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 67 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 68 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 69 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 71 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 72 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 73 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 74 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 75 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 76 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 77 / 144

Inserting ‘I’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 78 / 144

Inserting ‘I’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 79 / 144

Inserting ‘I’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 80 / 144

Inserting ‘I’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 81 / 144

Inserting ‘I’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 82 / 144

Inserting ‘I’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 83 / 144

Inserting ‘D’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 84 / 144

Inserting ‘D’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 85 / 144

Inserting ‘D’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 86 / 144

Inserting ‘D’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 87 / 144

Inserting ‘D’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 88 / 144

Inserting ‘G’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 89 / 144

Inserting ‘G’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 90 / 144

Inserting ‘G’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 91 / 144

Inserting ‘G’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 92 / 144

Inserting ‘E’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 93 / 144

Inserting ‘E’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 94 / 144

Inserting ‘E’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 95 / 144

Inserting ‘E’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 96 / 144

Inserting ‘E’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 97 / 144

Inserting ‘E’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 98 / 144

Inserting ‘E’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 99 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 100 / 144

Inserting ‘J’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 101 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 102 / 144

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 103 / 144

Inserting ‘J’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 104 / 144

Inserting ‘J’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 105 / 144

Inserting ‘J’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 106 / 144

Inserting ‘J’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 107 / 144

Inserting ‘R’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 108 / 144

Inserting ‘R’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 109 / 144

Inserting ‘R’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 110 / 144

Inserting ‘R’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 111 / 144

Inserting ‘R’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 112 / 144

Inserting ‘R’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 113 / 144

Inserting ‘R’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 114 / 144

Inserting ‘T’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 115 / 144

Inserting ‘T’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 116 / 144

Inserting ‘T’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 117 / 144

Inserting ‘T’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 118 / 144

Inserting ‘T’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 119 / 144

Inserting ‘C’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 120 / 144

Inserting ‘C’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 121 / 144

Inserting ‘C’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 122 / 144

Inserting ‘C’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 123 / 144

Inserting ‘C’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 124 / 144

Inserting ‘4’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 125 / 144

Inserting ‘4’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 126 / 144

Inserting ‘4’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 127 / 144

Inserting ‘4’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 128 / 144

Inserting ‘4’

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James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 129 / 144

Finding ‘A’

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T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 130 / 144

Finding ‘A’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 131 / 144

Finding ‘A’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 132 / 144

Finding ‘A’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 133 / 144

Finding ‘Z’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 134 / 144

Finding ‘Z’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 135 / 144

Finding ‘Z’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 136 / 144

Finding ‘Z’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 137 / 144

Finding ‘Z’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 138 / 144

Predecessor of ‘M’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 139 / 144

Predecessor of ‘M’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 140 / 144

Predecessor of ‘M’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 141 / 144

Predecessor of ‘M’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 142 / 144

Predecessor of ‘M’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 143 / 144

Predecessor of ‘M’

I

C

A

A

4

B

G

D

C E

H

G

O

M

J

I L

M

S

R

R R

T

T

James Clarke (University of Cambridge) Red-Black Tree Example February 7, 2015 144 / 144