Joseph Lindo

AbstractDataTypesSir Joseph Lindo

University of the Cordilleras

Joseph Lindo

Abstract Data TypesArray (A review)

• a contiguous block of memory, divided into a number of slots

• stores multiple data items of the same data type

List

Stack

Queue

Case

ADTArray

ADT

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ADT

Abstract Data TypesAbstract DataType• a design tool• concern on the important

concept or model• access is restricted

• Array is an ADT?

List

Stack

Queue

Case

ArrayADT

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ADT

Abstract Data TypesAbstract DataType• List• Stack• Queue

List

Stack

Queue

Case

ArrayADT

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Abstract Data TypesList

• Array List• Linked List• Doubly Linked List• Circular Linked list

List

Stack

Queue

Case

ArrayADT

List

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AbstractDataTypes

-- end --Sir Joseph Lindo

University of the Cordilleras

Joseph Lindo

AbstractDataTypes-- end na --Sir Joseph Lindo

University of the Cordilleras

Joseph Lindo

1D Array

Array (A review)

1-dimensional array x = [a, b, c, d]map into contiguous memory locations

Memorya b c d

start

location(x[i]) = start + i

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2D Array

Array (A review)

The elements of a 2-dimensional array a declared as:

int [][]a = new int[3][4];

may be shown as a tablea[0][0] a[0][1] a[0][2] a[0][3]a[1][0] a[1][1] a[1][2] a[1][3]a[2][0] a[2][1] a[2][2] a[2][3]

Joseph Lindo

2D Array

Array (A review)

view 2D array as a 1D array of rows x = [row0, row1, row 2] row 0 = [a,b, c, d] row 1 = [e, f, g, h] row 2 = [i, j, k, l]and store as 4 1D arrays

2-dimensional array x a, b, c, d

e, f, g, hi, j, k, l

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2D Array to 1D

Array (A review)

x.length = 3x[0].length = x[1].length = x[2].length = 4

a b c d

e f g h

i j k l

x[]

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Locating Element x[i][j]

Array (A review)

• assume x has r rows and c columns• each row has c elements• i rows to the left of row i• so ic elements to the left of x[i][0]• so x[i][j] is mapped to position ic + j of the 1D array

row 0 row 1 row 2 … row i

0 c 2c 3c ic

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Array is an ADT?

ADT

• In an array any item can be accessed, while in ADT access is restricted.

• ADT are more abstract than arrays.

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Array List

List

• The Array List ADT extends the notion of array by storing a sequence of arbitrary objects

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Array List

List

• An element can be accessed, inserted or removed by specifying its index (number of elements preceding it)

• An exception is thrown if an incorrect index is given (e.g., a negative index)

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Array List

List

Applications:• Direct applications

Sorted collection of objects (elementary database)

• Indirect applicationsAuxiliary data

structure for algorithmsComponent of other

data structures

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Array-Based Implementation

List

Use an array A of size NA variable n keeps track of the size of the

array listOperation get(i) is implemented in

returning A[i]Operation set(i,o) is implemented

performing t = A[i], A[i] = o, and returning t.

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Array-Based Implementation

List

InsertionIn operation add(i, o), we need to make

room for the new element by shifting forward the n – I elements A[i], …, A[n - 1]

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Array-Based Implementation

List

DeletionIn operation remove(i), we need to fill the

hole left by the removed element by shifting backward the n - i – 1 elements A[i + 1], …, A[n - 1]

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Array-Based Implementation

List

Main Methods:get(integer i): returns the elementset(integer i, object o): replace the element

at index i with o and return the old elementadd(integer i, object o): insert a new

element o to have index iremove(integer i): removes and returns the

element at index i

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Linked List

List

• Various cells of memory are not allocated consecutively in memory.

• Not enough to store the elements of the list.• With arrays, the second element was right next

to the first element.• Now the first element must explicitly tell us

where to look for the second element.• Do this by holding the memory address of the

second element

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Linked List

List

Create a structure called a Node.

• The objectfield will hold the actual list element.• The nextfield in the structure will hold the

starting location of the next node.• Chain the nodes together to form a linkedlist.

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Linked List

List

Picture of our list (2, 6, 7, 8, 1) stored as a linked list:

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Linked List

List

Actual picture in memory:

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Doubly-Linked List

List

• Moving forward in a singly-linked list is easy; moving backwards is not so easy.

• To avoid this we can use two pointers in a node: one to point to next node and another to point to the previous node:

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Doubly-Linked List

List

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Circular - Linked List

List

• The next field in the last node in a singly-linked list is set to NULL.

• Moving along a singly-linked list has to be done in a watchful manner.

• Doubly-linked lists have two NULL pointers: prev in the first node and next in the last node.

• A way around this potential hazard is to link the last node with the first node in the list to create a circularly-linked list.

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Circular - Linked List

List

• Two views of a circular linked list:

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Josephus Problem

List

• A case where circularly linked list comes in handy is the solution of the Josephus Problem.

• Consider there are 10 persons. They would like to choose a leader.

• The way they decide is that all 10 sit in a circle.• They start a count with person 1 and go in

clockwise direction and skip 3. Person 4 reached is eliminated.

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Josephus Problem

List

• The count starts with the fifth and the next person to go is the fourth in count.

• Eventually, a single person remains.

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Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

List

Joseph Lindo

Josephus Problem

Comprehension Check

• Given fifteen person named: Akang, Bebeng, Chito, Dingdong, Eman, Feng, Gina, Henry, Ikong, Joseph, Kekang, Lina, Neneng, Mario, Omar

• They are arranged in the same manner as mentioned above

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Josephus Problem

Comprehension Check

• Using the circular-linked list and the Josephus problem

• Using 5 movements

• Answer the questions in the next slide.

• Show the complete solution/cycle

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Josephus Problem

Comprehension Check

1. Which of the persons will be selected as the leader?

2. Which of them will be the third to be eliminated?3. Which of them will be the 10th to be eliminated?4. Which of them will be the 7th to be eliminated?5. Which of them will be the 13th to be eliminated?

Joseph Lindo

AbstractDataTypes

-- end --Sir Joseph Lindo

University of the Cordilleras

Joseph Lindo

AbstractDataTypes-- end na --Sir Joseph Lindo

University of the Cordilleras