WELL COME

Guide ByDEVENDRA KUSHWAH

Presented by SALONI TIWARI

MANALI MAHESHWARI

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CS 103

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LINKED LISTS

Definition of Linked Lists Examples of Linked Lists Operations on Linked Lists Linked List as a Class Linked Lists as Implementations of

Stacks, Sets, etc.

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DEFINITION OF LINKED LISTS A linked list is a sequence of items

(objects) where every item is linked to the next.

Graphically:data data data data

head_ptr tail_ptr

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EXAMPLES OF LINKED LISTS(A WAITING LINE)

A waiting line of customers: John, Mary, Dan, Sue (from the head to the tail of the line)

A linked list of strings can represent this line:

John Mary Dan Sue

head_ptr tail_ptr

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EXAMPLES OF LINKED LISTS(A STACK OF NUMBERS)

A stack of numbers (from top to bottom): 10, 8, 6, 8, 2

A linked list of ints can represent this stack:

10 8 6 2

head_ptr tail_ptr

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OPERATIONS ON LINKED LISTS Insert a new item

At the head of the list, or At the tail of the list, or Inside the list, in some designated position

Search for an item in the list The item can be specified by position, or by

some value Delete an item from the list

Search for and locate the item, then remove the item, and finally adjust the surrounding pointers

size( ); isEmpty( )

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INSERT– AT THE HEAD Insert a new data A. Call new: newPtr List before insertion:

After insertion to head:

data data data data

head_ptr tail_ptr

A

data data data data

head_ptr tail_ptrA

•The link value in the new item = old head_ptr•The new value of head_ptr = newPtr

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INSERT – AT THE TAIL Insert a new data A. Call new: newPtr

List before insertion

After insertion to tail:

data data data data

head_ptr tail_ptr

A

data data data data

head_ptr tail_ptr

A

•The link value in the new item = NULL•The link value of the old last item = newPtr

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INSERT – INSIDE THE LIST Insert a new data A. Call new: newPtr

List before insertion:

After insertion in 3rd position:

data data data data

head_ptr tail_ptr

data

data A data data

head_ptr tail_ptrdata

•The link-value in the new item = link-value of 2nd item•The new link-value of 2nd item = newPtr

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DELETE – THE HEAD ITEM List before deletion:

List after deletion of the head item:

data data data data

head_ptr tail_ptr

data data data data

head_ptr tail_ptr

data

•The new value of head_ptr = link-value of the old head item•The old head item is deleted and its memory returned

data

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DELETE – THE TAIL ITEM List before deletion:

List after deletion of the tail item:

data data data data

head_ptr tail_ptr

data data data

head_ptr tail_ptr

•New value of tail_ptr = link-value of the 3rd from last item•New link-value of new last item = NULL.

data

datadata

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DELETE – AN INSIDE ITEM List before deletion:

List after deletion of the 2nd item:

data data data data

head_ptr tail_ptr

data data

head_ptr tail_ptr

•New link-value of the item located before the deleted one = the link-value of the deleted item

data

data datadata

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SEARCHING FOR AN ITEM Suppose you want to find the item whose

data value is A You have to search sequentially starting from

the head item rightward until the first item whose data member is equal to A is found.

At each item searched, a comparison between the data member and A is performed.

STACKS

STACK SPECIFICATION Definitions: (provided by the user)

MAX_ITEMS: Max number of items that might be on the stack

ItemType: Data type of the items on the stack

Operations MakeEmpty Boolean IsEmpty Boolean IsFull Push (ItemType newItem) Pop (ItemType& item) (or pop and top)

POP (ITEMTYPE& ITEM) Function: Removes topItem from stack

and returns it in item. Preconditions: Stack has been

initialized and is not empty. Postconditions: Top element has been

removed from stack and item is a copy of the removed element.

Stack overflow The condition resulting from trying

to push an element onto a full stack.

if(!stack.IsFull()) stack.Push(item);

Stack underflow The condition resulting from trying

to pop an empty stack.if(!stack.IsEmpty()) stack.Pop(item);

IMPLEMENTING STACKS USING TEMPLATES Templates allow the compiler to

generate multiple versions of a class type or a function by allowing parameterized types.

TREES AND BINARY TREES

Become Rich

Force Others to be Poor

Rob Bank

s

StockFrau

dThe class notes are a compilation and edition from many sources. The instructor does not claim intellectual property or ownership of the lecture notes.

WHAT IS A TREE A tree is a finite

nonempty set of elements.

It is an abstract model of a hierarchical structure.

consists of nodes with a parent-child relation.

Applications: Organization charts File systems Programming

environments

Computers”R”Us

Sales

R&D

Manufacturing

Laptops

Desktops

US

International

Europe

Asia

Canada

subtree

TREE TERMINOLOGY Root: node without parent (A) Siblings: nodes share the same

parent Internal node: node with at least

one child (A, B, C, F) External node (leaf ): node

without children (E, I, J, K, G, H, D) Ancestors of a node: parent,

grandparent, grand-grandparent, etc.

Descendant of a node: child, grandchild, grand-grandchild, etc.

Depth of a node: number of ancestors

Height of a tree: maximum depth of any node (3)

Degree of a node: the number of its children

Degree of a tree: the maximum number of its node.

A

B DC

G HE F

I J K

Subtree: tree consisting of a node and its descendants

LEFT CHILD, RIGHT SIBLING REPRESENTATION

Data

Left Child

Right Sibling A

B C D

IHGFE

J K L

TREE TRAVERSAL Two main methods:

Preorder Postorder

Recursive definition

Preorder: visit the root traverse in preorder the children (subtrees)

Postorder traverse in postorder the children (subtrees) visit the root

PREORDER TRAVERSAL A traversal visits the nodes of a

tree in a systematic manner In a preorder traversal, a node

is visited before its descendants Application: print a structured

document

Become Rich

1. Motivations

3. Success Stories

2. Methods

2.1 Get a CS PhD

2.2 Start a Web Site

1.1 Enjoy Life

1.2 Help Poor

Friends2.3 Acquired

by Google

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Algorithm preOrder(v)visit(v)for each child w of v

preorder (w)

POSTORDER TRAVERSAL In a postorder traversal, a

node is visited after its descendants

Application: compute space used by files in a directory and its subdirectories

Algorithm postOrder(v)

for each child w of v

postOrder (w)visit(v)cs16

/

homeworks/

todo.txt

1Kprograms

/

DDR.java

10K

Stocks.java

25K

h1c.doc

3K

h1nc.doc

2K

Robot.java

20K

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BINARY TREE A binary tree is a tree with the

following properties: Each internal node has at most

two children (degree of two) The children of a node are an

ordered pair

We call the children of an internal node left child and right child

Alternative recursive definition: a binary tree is either

a tree consisting of a single node, OR

a tree whose root has an ordered pair of children, each of which is a binary tree

Applications:arithmetic expressionsdecision processessearching

A

B C

F GD E

H I

Examples of the Binary Tree

A

B C

GE

I

D

H

F

Complete Binary Tree

1

2

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A

B

A

B

Skewed Binary Tree

E

C

D

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Maximum Number of Nodes in a Binary Tree

The maximum number of nodes on depth i of a binary tree is 2i, i>=0.

The maximum nubmer of nodes in a binary tree of height k is 2k+1-1, k>=0.

Prove by induction.122 1

0

kk

i

i

FULL BINARY TREE

A full binary tree of a given height k has 2k+1–1 nodes.

Height 3 full binary tree.

Complete Binary Trees

A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so on.A binary tree with n nodes and level k is complete iff its nodes correspond to the nodes numbered from 1 to n in the full binary tree of level k.

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98 15141312Full binary tree of depth 3

1

2 3

75

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Complete binary tree

Binary Tree Traversals

Let l, R, and r stand for moving left, visiting the node, and moving right.

There are six possible combinations of traversallRr, lrR, Rlr, Rrl, rRl, rlR

Adopt convention that we traverse left before right, only 3 traversals remain

lRr, lrR, Rlrinorder, postorder, preorder

INORDER TRAVERSAL In an inorder traversal a

node is visited after its left subtree and before its right subtree

Algorithm inOrder(v)if isInternal (v)

inOrder (leftChild (v))visit(v)if isInternal (v)

inOrder (rightChild (v))

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