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Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

AVL TREES

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Trees

AVL Tree

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 1

• Insert 14, 17, 11, 7, 53, 4, 13 into an empty AVL tree

AVL Tree Example:

14

1711

7 53

4

AVL Tree Example:• Insert 14, 17, 11, 7, 53, 4, 13 into an empty AVL tree

14

177

4 5311

13

AVL Tree Example:• Now insert 12

14

177

4 5311

13

12

AVL Tree Example:• Now insert 12

14

177

4 5311

12

13

AVL Tree Example:

• Now the AVL tree is balanced.

14

177

4 5312

1311

AVL Tree Example:

• Now insert 8

14

177

4 5312

1311

8

AVL Tree Example:• Now insert 8

14

177

4 5311

128

13

AVL Tree Example:

• Now the AVL tree is balanced.

14

17

7

4

53

11

12

8 13

AVL Tree Example:

• Now remove 53

14

17

7

4

53

11

12

8 13

AVL Tree Example:

• Now remove 53, unbalanced

14

17

7

4

11

12

8 13

AVL Tree Example:

• Balanced! Remove 11

14

17

7

4

11

128

13

AVL Tree Example:

• Remove 11, replace it with the largest in its left branch

14

17

7

4

8

12

13

AVL Tree Example:

• Remove 8, unbalanced

14

17

4

7

12

13

AVL Tree Example:

• Remove 8, unbalanced

14

17

4

7

12

13

AVL Tree Example:

•Balanced!!

14

174

7

12

13

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 2

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 2

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 2

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 2

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 3

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 4

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 4

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 4

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 4

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 4

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 5

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 5

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 5

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 5

Foundations of Data Structures - 2013/Spring, Amihai Savir & Ilya Mirsky

Question 5