10 data structures

Data Structures *Property of STI of 49

Data Structures and Algorithms

@ There are instances when you do not know theelement number, but you do know the value of theelement. In this case a search must be made onthe array to find the correct element. The easiestway to search an array is called a sequential search.

SequentialSearch



Binary Search



Example of a Binary Search

Binary Search

5

7

9

12

15

20

25

28

33

35

40

44

47

A

1

2

3

4

5

6

7

8

9

10

11

12

13

Order of comparisons to find the elementnumber of 44:

1. Element 7 (UB = 13, LB = 1, ElementNumber = 7)

2. Element 10 (UB = 13, LB = 8, ElementNumber 10)

3. Element 12 (UB = 13, LB = 11,Element Number = 12)

Number 44 is found in three comparisons,compared to 12 with the sequentialsearch.



PointerTechnique



PointerTechnique

The element number of the frequencydistribution array is the number of pointscorrect and the value of the element isthe number of students that received thatgrade. Therefore, the frequencydistribution array F shows that there is 1student who received 1 point, 1 thatreceived 2 points, 2 that received 3 points,1 that received 4 points, 1 that received5 points, 3 that received 6 points, 4 thatreceived 7 points, 5 that received 8 points,6 that received 9 points and 6 thatreceived 10 points.



Cross-Tabulation



SortingTechniques

Selection Exchange Sort Technique

@ Sorting – is the process of putting data inalphabetical or numeric order using one key fieldor a concatenation of two or more fields. Data aresorted according to the primary key.

Once the data are in order, they can be accessed byvarious means, including the sequential search andthe binary search.



The Selection Exchange Sort

SortingTechniques



Flowchart and Algorithm for SWAP Module

SortingTechniques



SortingTechniques

Example Pass, I = 1



SortingTechniques

Bubble Sort



SortingTechniques

Flowchart and Algorithm for Bubble Sort



Shell Sort

SortingTechniques



SortingTechniques

Algorithm and Flowchart for the Shell Sort



Stacks

@ A Stack is a list of numbers, such as an array ofnumbers, to which all additions are at one endand all deletions are at the same end. This is alast-in, first-out procedure.

When a value (X) is added to the stack it is calledpushing the stack.

When a value (X) is used from the stack it is calledpopping the stack.

PUSH 3PUSH 4PUSH 7POP XPOP XPUSH 6



Stacks

Example of a Stack That Has Been Pushed andPopped



Algorithm and Flowchart to Push and Pop a Stack

Stacks



Linked List

@ A Linked List is a file in which each record points toits successor, except for the last record, which hasan end-of-list indicator.

@ The method of pointing to the next record is a field,which contains the record number of the next recordin order. This is called the linking field, since thevalue in this field links the records in proper order.

Example of an Initially Created Linked List



Linked List

Example of A Linked List After Multiple Adds andDeletions



Original File

Linked List

Comment: Notice thatrecords 5 and 9 are recordsthat have been deleted inthe past and are included inthe empty list, even thoughthere are data in the record.The used list skips theserecords.



File After The Additions and Deletions

Linked List



Add 69

Linked List



Linked List

Delete 17



Linked List

Delete 44



Linked List

Add 37



Delete 29

Linked List



Add 40

Linked List



Linked List

Add 90



Linked List

Add 1



Linked List

Add 16



Linked List

Algorithm and Flowchart to Create a Linked List



Linked List

Algorithm and Flowchart for Processing andUpdating a Linked List



Linked List

10 data structures

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