There are relatively less number of comparisons in binary search than that in linear search. In average case, linear search takes O(n) time to search a list of n elements while Binary search takes O(log n) time to search a list of n elements.

Difference between file structure and storage structure:

The main difference between file structure and storage structure is based on memory area that is being accessed.

**Storage structure:** It is the representation of the data structure in the computer memory.

**File structure:** It is the representation of the storage structure in the auxiliary memory.

A linked list is considered both linear and non-linear data structure depending upon the situation.

- On the basis of data storage, it is considered as a non-linear data structure.
- On the basis of the access strategy, it is considered as a linear data-structure.

Overflow occurs when top = Maxsize -1

Queue data structure

A queue can be defined as an ordered list which enables insert operations to be performed at one end called REAR and delete operations to be performed at another end called FRONT.

The Tree is a recursive data structure containing the set of one or more data nodes where one node is designated as the root of the tree while the remaining nodes are called as the children of the root. The nodes other than the root node are partitioned into the nonempty sets where each one of them is to be called sub-tree.

Arrays are defined as the collection of similar types of data items stored at contiguous memory locations. It is the simplest data structure in which each data element can be randomly accessed by using its index number.

A graph G can be defined as an ordered set G(V, E) where V(G) represents the set of vertices and E(G) represents the set of edges which are used to connect these vertices. A graph can be seen as a cyclic tree, where the vertices (Nodes) maintain any complex relationship among them instead of having parent-child relations.

It can be done by using an indexed loop such that the counter runs from 0 to the array size minus one. In this manner, you can reference all the elements in sequence by using the loop counter as the array subscript.

- It is simple and easy to implement.
- It can be used for small data sets.
- It is 60 per cent more efficient than bubble sort.

There are six types of tree given as follows.

- General Tree
- Forests
- Binary Tree
- Binary Search Tree
- Expression Tree
- Tournament Tree

- RDBMS uses Array data structure
- Network data model uses Graph
- Hierarchal data model uses Trees

- The size of a linked list can be incremented at runtime which is impossible in the case of the array.
- The List is not required to be contiguously present in the main memory, if the contiguous space is not available, the nodes can be stored anywhere in the memory connected through the links.
- The List is dynamically stored in the main memory and grows as per the program demand while the array is statically stored in the main memory, size of which must be declared at compile time.
- The number of elements in the linked list are limited to the available memory space while the number of elements in the array is limited to the size of an array.

PUSH and POP operations specify how data is stored and retrieved in a stack.

**PUSH:** PUSH specifies that data is being “inserted” into the stack.

**POP:** POP specifies data retrieval. It means that data is being deleted from the stack.

**The Applications of the queue is given as follows:**

- Queues are widely used as waiting lists for a single shared resource like a printer, disk, CPU.
- Queues are used in the asynchronous transfer of data (where data is not being transferred at the same rate between two processes) for eg. pipes, file IO, sockets.
- Queues are used as buffers in most of the applications like MP3 media player, CD player, etc.
- Queues are used to maintain the playlist in media players to add and remove the songs from the play-list.
- Queues are used in operating systems for handling interrupts.

**int** count (struct node* t)

{

if(t)

{

int l, r;

l = count(t->left);

r=count(t->right);**return** (1+l+r);

}

else

{

return 0;

}

}

**Path:** A Path is the sequence of adjacent vertices connected by the edges with no restrictions.**Cycle:** A Cycle can be defined as the closed path where the initial vertex is identical to the end vertex. Any vertex in the path can not be visited twice**Circuit:** A Circuit can be defined as the closed path where the intial vertex is identical to the end vertex. Any vertex may be repeated.

A binary Tree is a special type of generic tree in which, each node can have at most two children. Binary tree is generally partitioned into three disjoint subsets, i.e. the root of the node, left sub-tree and Right binary sub-tree.

The multidimensional array can be defined as the array of arrays in which, the data is stored in tabular form consists of rows and columns. 2D arrays are created to implement a relational database lookalike data structure. It provides ease of holding the bulk of data at once which can be passed to any number of functions wherever required.

Stack data structure is used in recursion due to its last in first out nature. Operating system maintains the stack in order to save the iteration variables at each function call

struct node

{

int data;

struct node *next;

};

struct node *head, *ptr;

ptr = (struct node *)malloc(sizeof(struct node));

**Push:**

- Increment the variable top so that it can refer to the next memory allocation
- Copy the item to the at the array index value equal to the top
- Repeat step 1 and 2 until stack overflows
**Pop:** - Store the topmost element into the an another variable
- Decrement the value of the top
- Return the topmost element

- Sparse matrix,
- Index generation.

**Memory Wastage:** The space of the array, which is used to store queue elements, can never be reused to store the elements of that queue because the elements can only be inserted at front end and the value of front might be so high so that, all the space before that, can never be filled.**Array Size:** There might be situations in which, we may need to extend the queue to insert more elements if we use an array to implement queue, It will almost be impossible to extend the array size, therefore deciding the correct array size is always a problem in array implementation of queue.

**int** countHeight(struct node* t)

{**int** l,r;

if(!t)**return** 0;

if((!(t->left)) && (!(t->right)))**return** 0;

l=countHeight(t->left);

r=countHeight(t->right);**return** (1+((l>r)?l:r));

}

The data structure is a way that specifies how to organize and manipulate the data. It also defines the relationship between them. Some examples of Data Structures are arrays, Linked List, Stack, Queue, etc. Data Structures are the central part of many computer science algorithms as they enable the programmers to handle the data in an efficient way

There are two techniques by using which, the elements of a 2D array can be stored in the memory.

**Row-Major Order:** In row-major ordering, all the rows of the 2D array are stored into the memory contiguously. First, the 1st row of the array is stored into the memory completely, then the 2nd row of the array is stored into the memory completely and so on till the last row.**Column-Major Order:** In column-major ordering, all the columns of the 2D array are stored into the memory contiguously. first, the 1st column of the array is stored into the memory completely, then the 2nd row of the array is stored into the memory completely and so on till the last column of the array.

void in-order(struct treenode *tree)

{

if(tree != NULL)

{

in-order(tree→ left);

printf(“%d”,tree→ root);

in-order(tree→ right);

}

}

- Null is actually a value, whereas Void is a data type identifier.
- A null variable simply indicates an empty value, whereas void is used to identify pointers as having no initial size.

Stack is an ordered list in which, insertion and deletion can be performed only at one end that is called the top. It is a recursive data structure having pointer to its top element. The stack is sometimes called as Last-In-First-Out (LIFO) list i.e. the element which is inserted first in the stack will be deleted last from the stack.

The heterogeneous linked list contains different data types, so it is not possible to use ordinary pointers for this. For this purpose, you have to use a generic pointer type like void pointer because the void pointer is capable of storing a pointer to any type.

An expression in which operators follow the operands is known as postfix expression. The main benefit of this form is that there is no need to group sub-expressions in parentheses or to consider operator precedence.

The expression “a + b” will be represented as “ab+” in postfix notation.

- If (rear + 1)%maxsize = front, the queue is full. In that case, overflow occurs and therefore, insertion can not be performed in the queue.
- If rear != max – 1, the rear will be incremented to the mod(maxsize) and the new value will be inserted at the rear end of the queue.
- If front != 0 and rear = max – 1, it means that queue is not full therefore, set the value of rear to 0 and insert the new element there.

**For the graph implementation, following data structures are used.**

- In sequential representation, Adjacency matrix is used.
- In Linked representation, Adjacency list is used.

AVL tree controls the height of the binary search tree by not letting it be skewed. The time taken for all operations in a binary search tree of height h is O(h). However, it can be extended to O(n) if the BST becomes skewed (i.e. worst case). By limiting this height to log n, AVL tree imposes an upper bound on each operation to be O(log n) where n is the number of nodes.

- In BFS algorithm, Queue data structure is used.
- In DFS algorithm, Stack data structure is used.

**Data Structures are mainly classified into two types:**

**Linear Data Structure:** A data structure is called linear if all of its elements are arranged in the sequential order. In linear data structures, the elements are stored in a non-hierarchical way where each item has the successors and predecessors except the first and last element.

**Non-Linear Data Structure:** The Non-linear data structure does not form a sequence i.e. each item or element is connected with two or more other items in a non-linear arrangement. The data elements are not arranged in the sequential structure.

2k+1-1 where k >= 1

- Expression evaluation
- Backtracking
- Memory Management
- Function calling and return

The doubly linked list is a complex type of linked list in which a node contains a pointer to the previous as well as the next node in the sequence. In a doubly linked list, a node consists of three parts:

- node data
- pointer to the next node in sequence (next pointer)
- pointer to the previous node (previous pointer).

**Row-Major Order:** If array is declared as a[m][n] where m is the number of rows while n is the number of columns, then address of an element a[i][j] of the array stored in row major order is calculated as,

Address(a[i][j]) = B. A. + (i * n + j) * size

**Column-Major Order:** If array is declared as a[m][n] where m is the number of rows while n is the number of columns, then address of an element a[i][j] of the array stored in column major order is calculated as

Address(a[i][j]) = ((j*m)+i)*Size + BA.

Dequeue (also known as double-ended queue) can be defined as an ordered set of elements in which the insertion and deletion can be performed at both the ends, i.e. front and rear.

A B tree of order m contains all the properties of an M way tree. In addition, it contains the following properties.

- Every node in a B-Tree contains at most m children.
- Every node in a B-Tree except the root node and the leaf node contain at least m/2 children.
- The root nodes must have at least 2 nodes.
- All leaf nodes must be at the same level.

Two queues are needed. One queue is used to store the data elements, and another is used for storing priorities.

**Data structures are applied extensively in the following areas of computer science:**

- Compiler Design,
- Operating System,
- Database Management System,
- Statistical analysis package,
- Numerical Analysis,
- Graphics,
- Artificial Intelligence,
- Simulation

Linked List is the collection of randomly stored data objects called nodes. In Linked List, each node is linked to its adjacent node through a pointer. A node contains two fields, i.e. Data Field and Link Field.

Queue data structure

- Push Operations
- Pop Operations
- Peek Operations

#include

#include

void beg_insert(int);

struct node

{

int data;

struct node *next;

};

struct node *head;

void main ()

{

int choice,item;

do

{

printf(“\nEnter the item which you want to insert?\n”);

scanf(“%d”,&item);

beg_insert(item);

printf(“\nPress 0 to insert more ?\n”);

scanf(“%d”,&choice);

}while(choice == 0);

}

void beg_insert(int item)

{

struct node *ptr = (struct node *)malloc(sizeof(struct node));

struct node *temp;

if(ptr == NULL)

{

printf(“\nOVERFLOW”);

}

else

{

ptr -> data = item;

if(head == NULL)

{

head = ptr;

ptr -> next = head;

}

else

{

temp = head;

while(temp->next != head)

temp = temp->next;

ptr->next = head;

temp -> next = ptr;

head = ptr;

}

printf(“\nNode Inserted\n”);

}

}

**The graph has the following applications:**

- Graphs are used in circuit networks where points of connection are drawn as vertices and component wires become the edges of the graph.
- Graphs are used in transport networks where stations are drawn as vertices and routes become the edges of the graph.
- Graphs are used in maps that draw cities/states/regions as vertices and adjacency relations as edges.
- Graphs are used in program flow analysis where procedures or modules are treated as vertices and calls to these procedures are drawn as edges of the graph.

Polish and Reverse Polish notations.

**Applications of Tree- data structure:**

- The manipulation of Arithmetic expression,
- Symbol Table construction,
- Syntax analysis
- Hierarchal data model