Data Structures and Algorithms: Ordered Lists and Binary Trees, Study notes of Data Structures and Algorithms

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Data Structures and Algorithms Ordered Lists and Binary Trees

Chris BrooksDepartment of Computer ScienceUniversity of San Francisco^ Department of Computer Science — University of San Francisco – p.1/

6-0:^ Ordered Lists

We will often want to have a list in which all the elementsare ordered. As we add or remove elements, order is maintained.^ List of names in alphabetical order^ List of files from smallest to largest^ List of records from earliest to most recent

Department of Computer Science — University of San Francisco – p.2/

6-2:^ Implementing Ordered List

Using an Ordered Array – Running times:CheckInsertRemovePrint

Department of Computer Science — University of San Francisco – p.4/

6-3:^ Implementing Ordered List

Using an Ordered Array – Running times:Check

  Insert

  Remove

  Print

 

Department of Computer Science — University of San Francisco – p.5/

6-5:^ Implementing Ordered List

Using an^ Unordered

Array – Running times: Check

  Insert

^  Remove

  Print

   (Given a fast sorting algorithm) Keeping the array ordered makes insertion require

  time. Department of Computer Science — University of San Francisco – p.7/

6-6:^ Implementing Ordered List

Using an Ordered Linked List – Running times:CheckInsertRemovePrint

Department of Computer Science — University of San Francisco – p.8/

6-8:^ The Best of Both Worlds

Linked Lists – Insert fast / Find slow Arrays – Find fast / Insert slow The only way to examine nth element in a linked list is totraverse (n-1) other elements 4 8

12 15

22 25

28

If we could leap to the middle of the list ...

Department of Computer Science — University of San Francisco – p.10/

6-9:^ The Best of Both Worlds

4 8

12 15

22 25

(^28) Department of Computer Science — University of San Francisco – p.11/

6-11:^ The Best of Both Worlds

4 8

12 15

22 25

28

Move the initial pointer to the middle of the list:^4 8 12

15 22

25 28

We’ve cut our search time in half! Have we changed the



running time?Repeat the process!

Department of Computer Science — University of San Francisco – p.13/

6-12:^ The Best of Both Worlds

4 8

12 15

22 25

28

4 8

12 15

22 25

28

4 8

12 15

22 25

28 Department of Computer Science — University of San Francisco – p.14/

6-14:^ Binary Trees

Binary Trees are Recursive Data Structures^ Base Case: Empty Tree^ Recursive Case: Node, consisting of:^ Left Child (Tree)^ Right Child (Tree)^ Data

Department of Computer Science — University of San Francisco – p.16/

6-15:^ Binary Tree Examples

The following are all Binary Trees (Though not Binary

Search

Trees)

A B C^ D^ E^ F

A B C D A B C^ F^ GD E^ Department of Computer Science — University of San Francisco – p.17/

6-17:^ Full Binary Tree

Each node has 0 or 2 children Full Binary Trees Not^ Full Binary Trees

Department of Computer Science — University of San Francisco – p.19/

6-18:^ Complete Binary Tree

Can be build by starting at the root, and filling the tree bylevels from left to right Complete Binary Trees Not^ Complete Binary Trees

Department of Computer Science — University of San Francisco – p.20/