Stacks Queues Trees

8/17/2019 Stacks Queues Trees

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Stacks

- A stack is an ordered collection of items intowhich new items may be inserted and fromwhich items may be deleted at one end,called the top of the stack.

- A stack can be thought of a data structure inwhich only the top element can be accessed.

- A Stack is a LIFO (Last In First Out) structure.

The item that is put last to the stack, is taken first.- Storing an item in a stack is called pushing it onto

the stack (push). Removing a value from a stackis called popping the stack (pop).


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Stacks

• Stacks can be implemented as linkedlists or using array.

• Array Implementation:

– an integer number showing the top of the stack

– an array to hold data items


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Stacks

Operations:

Operation Linked List ImplementationArray

Implementation

initialize stack assign NULL to head initialize top

push an item to the

stacklike add_begin

increment top and

store data

pop an item from

the stack

similar to delete_begin but

returns data

get data and

decrement top

check if stack isempty if (head == NULL) like if (top == -1)

check if stack is full (Not applicable)life if (top >=

STACKSIZE - 1)


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Stacks

• Examples on stack implementation: – Reverse a given array using a stack.

– Evaluate an arithmetic expression in postfix

notation.

A * S A * M * P * L * E S * T * * * A * C K * *

Show the dynamic characteristics of a stack by tracing the

stack in every movement. Each letter in the list means

“push (the letter)”; each asterisk mean “pop.


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Stacks Application

- Stacks evaluating arithmeticexpression.- Suppose that one wants to find the value of a

simple arithmetic expression involvingmultiplication and addition of integers, such as

5*(((9+8)*(4*6))+7).

- This expression must first be converted intopost f ix notation. Customary way of writing

arithmetic expression is called inf ix .


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Stacks Application (continuation..)

Algorithm

- Convert into postfix notation.- Disregard all left parenthesis.

- Scan the expression from left to right. Output an

operand if found. If an Operator is found push to

the stack. If a right parenthesis is found,

perform a pop and output to the operand.- Following the algorithm we have

5 9 8 + 4 6 * * 7 + *


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Queues

- A queue is an ordered collection of items in whichall insertions take place at one end and all

deletions take place at the opposite end. The first

element inserted into a queue is the first element

removed.

- A queue is a FIFO (First In First Out) structure.

The item that is put first to the queue, is taken first.

- Items are inserted at the rear of the queue if thereis place, and removed from the front of the queue.


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Queues

- “Enqueue, pu t, o r insert ” to add an item

- “Dequeue, get, o r remove ” to serve or

remove an item.


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Queues

• Operations: – initialize a queue

– insert an item to the queue

– remove an item from the queue – check if queue is empty

– check if queue is full

• Examples of queues:

– Queues in a restaurant.

– Queues in a bank.

– Queues in a theater.


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Queues

- Queues may be implemented using linked lists orarrays.


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Queues

A * S A * M * P * L E * Q * * * U * E U * * E *

Show how a sample queue evolves throughthe series of get and put operations

represented by the sequence.


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Trees

- Is a nonempty collection of vert ices andedges that satisfies certain requirements.

- One node in the tree is designated as the

roo t

- A path in a tree is a list of distinct vertices in

which successive vertices are connected by

edges in the tree.- There is exactly one path between the root

and each of the other nodes in the tree.


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Trees

- Each node (except the root) has exactly onenode above it, which is called its parent.

- The nodes directly below a node are called

its chi ldren - Nodes with no children are called leaves orterminal nodes also called external nodes

- Nodes with children are also callednonterminal nodes or internal nodes

- Any node is the root of a subtree consistingof it and the nodes below it.


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Trees

- A set of tress is called a forest- Sometimes the way in which the children of

each node are ordered is significant,

sometimes not. Trees wherein the order ofthe children matter are called ordered trees

- The modes of a tree are divided into levels:

the level of a node is the number of nodeson the path from the node to the root ( not

including itself).


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Trees

- The height of a tree is the maximum levelamong all nodes in the tree

- The path leng th of a tree is the sum of the

levels of all the nodes of the tree.- the internal path leng th is the sum of the

levels of all the internal nodes of the tree

- The external path leng th is the sum of thelevels of all external nodes of the tree.


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Trees

- If each node must have a specific number ofchildren appearing in a specific order, then we

have a mult iway tree.

- A binary tree is a multiway tree consisting of two

types of nodes: external nodes with no children

and internal nodes with exactly two children. Since

the two children of each internal node are ordered,

we refer to the lef t ch i ld and r ight ch i ld ofinternal nodes. Each internal node must both have

a left and a right child, though one or both of them

might be an external node.


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Trees

- A fu l l b inary tree is one in which theinternal nodes completely fill every level.

- The simplest way to define trees recursively

is as follows: “ a tree is either a single nodeor a root node connected to a set of trees”

and “a binary tree is either an external node

or a root (internal) node connected to a leftbinary tree and a right binary tree.”


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Trees

- There is exactly one path connecting anytwo nodes in a tree

- A tree with N nodes has N-1 edges

- A binary tree with N internal nodes has N+1 external nodes

- the height of a full binary tree with N internal

nodes is about log2N.


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Trees

- A binary tree


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Trees

- Tree traversals- Preorder: Visit the root, then the left subtree,

then the right subtree.

- Inorder : Visit the left subtree, then the root,then the right subtree.

- Postorder : Visit the left subtree, then the right

subtree, then the root.

- Level-order : Visit the nodes from left to right

level by level.

Stacks Queues Trees

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