computer notes - data structures - 11

8/3/2019 Computer Notes - Data Structures - 11

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Class No.11

Data Structures

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Code for Simulation

// print the final avaerage wait time.

double avgWait = (totalTime*1.0)/count;

cout


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Priority Queue

#include "Event.cpp"

#define PQMAX 30

class PriorityQueue {

public:

PriorityQueue() {size = 0; rear = -1;

};

~PriorityQueue() {};

int full(void)

{return ( size == PQMAX ) ? 1 : 0;

};

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4/27

Priority Queue

Event* remove()

{

if( size > 0 ) {

Event* e = nodes[0];

for(int j=0; j < size-2; j++ )

nodes[j] = nodes[j+1];

size = size-1; rear=rear-1;

if( size == 0 ) rear = -1;

return e;

}return (Event*)NULL;

cout


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Priority Queue

int insert(Event* e)

{

if( !full() ) {

rear = rear+1;

nodes[rear] = e;

size = size + 1;sortElements(); // in ascending order

return 1;

}

cout


6/27

Tree Data Structures

There are a number of applications wherelinear data structures are not appropriate.

Consider a genealogy tree of a family.

Mohammad Aslam Khan

Sohail Aslam Javed Aslam Yasmeen Aslam

SaadHaaris Qasim Asim Fahd Ahmad Sara Omer



7/27

Tree Data Structure

A linear linked list will not be able tocapture the tree-like relationship withease.

Shortly, we will see that for applicationsthat require searching, linear datastructures are not suitable.

We will focus our attention on binary trees.



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Binary Tree

A binary treeis a finite set of elements that iseither empty or is partitioned into threedisjointsubsets.

The first subset contains a single element calledthe rootof the tree.

The other two subsets are themselves binarytrees called the leftand right subtrees.

Each element of a binary tree is called a nodeofthe tree.



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Binary Tree

Binary tree with 9 nodes.

A

B

D

H

C

E F

G I



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Binary Tree

A

B

D

H

C

E F

G I

Left subtree

root

Right subtree



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Binary Tree

Recursive definitionA

B

D

H

C

E F

G ILeft subtree

root

Right subtree



12/27

Binary Tree


B

D

H

C

E F

G I

Left subtree

root



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Binary Tree


B

D

H

C

E F

G I

root



14/27

Binary Tree


B

D

H

C

E F

G I

root

Right subtree



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Binary Tree


B

D

H

C

E F

G I

root

Right subtreeLeft subtree



16/27

Not a Tree

Structures that are not trees.

A

B

D

H

C

E F

G I



17/27

Not a Tree


A

B

D

H

C

E F

G I



18/27

Not a Tree


A

B

D

H

C

E F

G I



19/27

Binary Tree: Terminology

A

B

D

H

C

E F

G I

parent

Left descendant Right descendant

Leaf nodes Leaf nodes

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20/27

Binary Tree

If every non-leaf node in a binary tree has non-empty left and right subtrees, the tree is termeda strictly binary tree.

A

B

D

H

C

E F

G I

J

K



21/27

Level of a Binary Tree Node

The levelof a node in a binary tree isdefined as follows:

Root has level 0,

Level of any other node is one more than thelevel its parent (father).

The depthof a binary tree is the maximum

level of any leaf in the tree.



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Level of a Binary Tree Node

A

B

D

H

C

E F

G I

1

0

1

2 2 2

3 3 3

Level 0

Level 1

Level 2

Level 3



23/27

Complete Binary Tree

A complete binary treeof depth dis the strictlybinary all of whose leaves are at level d.

A

B

N

C

G

O

1

0

1

2

3 3L

F

M

2

3 3H

D

I

2

3 J

E

K

2

3



24/27


A

B

Level 0: 20 nodes

H

D

I

E

J K

C

L

F

M

G

N O

Level 1: 2

1

nodes

Level 2: 22 nodes

Level 3: 23 nodes



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At level k, there are 2knodes.

Total number of nodes in the tree of depthd:

20+21+22+ . + 2d= 2j=2d+1 1

In a complete binary tree, there are 2d leafnodes and (2d- 1) non-leaf (inner) nodes.

j=0

d



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If the tree is built out of n nodes then

n =2d+1 1or log2(n+1) = d+1or d = log2(n+1) 1

I.e., the depth of the complete binary tree builtusing n nodes will be log2(n+1) 1.

For example, for n=100,000, log2(100001) isless than 20; the tree would be 20 levels deep.

The significance of this shallowness will becomeevident later.



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Operations on Binary Tree

There are a number of operations that canbe defined for a binary tree.

If pis pointing to a node in an existing treethen

left(p) returns pointer to the left subtree

right(p) returns pointer to right subtree

parent(p) returns the father of p

brother(p) returns brother of p.

info(p) returns content of the node.

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computer notes - data structures - 11

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