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The space complexity defines the storage capacity for the input data. It defines the amount of memory that is required to run a program to completion. The complexity like this depends on the size of the input data and the function that is used for the input size 'n'. The time complexity deals with the amount of time required by a program to complete the whole process of execution. The time complexity allows creating optimized code and allowing user to calculate it before writing their own functions. The time complexity can be made such that a program can be optimized on the basis of the chosen method.

Write an algorithm to show the postfix expression with the input given as : a b + c d +*f ? .

The postfix expression deals with the expression where the operators are being written after their operands. The evaluation of these operators is being done from left-to-right. The algorithm that is used to show the input of a b + c d +*f ? is as follows:

Stack is cleared for the use,

symbol = insert input character

while(not end of input)

{

if (symbol is an operand)

push in stack;

else

{

pop two operands from the stack;

result=op1 symbol op2;

push result in stack;

}

symbol = next input character;

}

return (pop (stack));

Write an algorithm through which the inserting and deleting of elements can take place in circular queue?

Circular queues are very important as it allows the element to circulate. In this queue rear end reaches the end and the first element in the list will become the rear of that queue. In this queue the front element can only become the rear element if and only if front has moved forward in the array. The algorithm that is used to represent it is as follows:

insert(queue,n,front,rear,item)

This procedure inserts an element item into a queue.

1. If front = 1 and rear = n, or if front = rear

+ 1, then:

Write: overflow, and return

2. [find new value of rear]

If front = NULL , then : [queue initially empty.]

Set front = 1 and rear=1.

Else if rear = n, then:

Set rear=1.

Else:

Set rear = rear + 1.

[end of structure.]

3. Set queue[rear] = item. [this inserts new element.]

4.Return to the beginning.

How expression trees are gets represented in data structure?

Expression trees are made up of operands like constants and variable names. The nodes also contain the operators. The tree is a binary tree on which all the binary operations are being performed. It consists of all the nodes consisting of two children. It is possible for a node to consist of only one child and other operators that can be used to evaluate the expression tree. The operator looks at the root value that is obtained by recursive evaluation of the subtrees. The expression tree is being handled to show the relationship between the operator and the operand. How can a binary tree be represented using the rotation? Binary tree can have rotations and it can be done by inserting a node in the binary search tree. There is a balancing factor that is required and it will be calculated like height of left subtree-height of right subtree. Each node in this case has 0,1,-1 factor value and beyond that there will be no modification possible to be done in the tree. If the balancing factor comes out to be either +2 or -2 then the tree becomes unbalanced. The rotation allows the tree to be balanced and it can be done with the left rotation and right rotation. The rotation also helps the searching to be quite faster than using any other tree. Using the balance factor a tree can be managed and rotation can be applied to the whole system to adjust and balance the tree.

What is the difference between B tree and Binary search tree?

Binary tree consists of only fixed number of keys and children, whereas B tree consists of variable number of keys and children. Binary tree keys are stored in decreasing order, whereas B tree consists of the keys and children in non-decreasing order.

Binary tree doesn't consists of associated child properties whereas B tree consists of keys has an association with all the nodes with the keys that are less than or equal to the preceding key. Binary tree doesn't have minimization factor concept, whereas B tree has the concept of minimization factor where each node has minimum number of allowable children.

What is the minimization factor and time complexity of B-tree?

The minimization factor of every node consists of minimum number of children and they should have at least n-1 keys. There are possibilities that the root node might violate certain properties that are having fewer than n-1 keys. By seeing this every node can have at most 2n-1 keys or 2n children. The height of the n key B-tree can be found out by keeping the minimum degree n<=2, and height as h=logt (n+1/2). The time complexity of this will be given in Big O notation that is the amount of time required to run the code to the completion. The upper bound of the B-tee is provided by this and the lower bound can also be the same. So, mathematically

O(g(n))={f(n): there exists positive constants such that 0=f

f(n)=cg(n) for all n, n=n0} , we say “f is oh of g”

How does Threaded binary tree represented in Data Structure?

Threaded binary tree consists of a node that is in the binary tree and having no left or right child. The child that comes in the end is also called as leaf node then if there is no child present, it will be represented by the null pointers. The space that is occupied by null entries can be used to store valuable information about the node that is consisting of the child and the root node information. There is a special pointer that is used to point to the higher node in the tree also called as ancestor. These pointers are termed as threads and the whole representation is called as threaded binary tree. The binary tree can be represented in in-order, pre-order and post-order form. Every node in this type of tree doesn't have a right child. This doesn't allow the recursion of the tree.

The code that is used to show the implementation is:

struct NODE

{

struct NODE *leftchild;

int node_value;

struct NODE *rightchild;

struct NODE *thread;

}

Explain the sorting algorithm that is most suitable to be used with single linked list?

The sorting algorithm that is most suitable with the single link list is the simple insertion sort. This consists of an array and link of pointers, where the pointers are pointing to each of the element in the array. For example: l[i] = i + 1 for 0 < = i < n-1 and l[n-1] = -1.

The linear link list can be pointed by the external pointer which initialized it to 0. To insert the nth element in the list the traversing time gets reduced and until the list is being sorted out completely the process doesn't end. The array that has to be traversed x[k] to sort the element and put them in the list. If the sorting is done then it reduces the time of the insertion of an element and time for searching for a particular element at proper position.

What are the standard ways in which a graph can be traversed?

There are two standard ways through which a graph can be traversed and these are:

1. The depth-first traversal: allow the graph to be traversed from a given point and then goes to the other points. The starting position is being defined as it doesn't consist of any root so, there is a specific point that is chosen to begin the traversing. In this the visits takes place at each vertex and then recursive action is taken to visit all the vertices adjacent to the node that is being visited. The graph can consists of cycles, but there is always a condition that the vertex has to be visited only once.

2. The breadth-first traversal: allow the graph to be traverse one level by another level. Breadth-first visits all the nodes from the depth 0 and it consists of a root. The vertex that has to be visited has to be specified that will be traversed. The length of the vertex has to be defined to find the shortest path to the given vertex. Breadth-first traverse the starting vertex and then all the vertices that is been adjacent to it.

How helpful is abstract data type of data structures?

Abstract data type allows the user to write the code without even worrying about the type of data being used. It is a tool that specifies the logical properties of the data type. ADT is a type consisting set of operations that are called as interface. This interface is the only mechanism through which the data type can be accessed. It defines the new type of instance that is been created by operating on different data types. There is always some additional information on which ADT acts upon. It specifies the instance of the creation time.

The abstract data type can be declared as:

LIST variable name;

How to sequentially represent max-heap?

Max heap is also known as descending heap consisting of the objects in a heap list with some keys. It is of size n and will be of the form of complete binary tree that is also of nodes n. In this max-heap each node is less than or equal to the content of its parent.

It represents the sequential complete binary tree with the formula to calculate as:

max[j] <= max[(j-1)/2] for 0 <= ((j-1)/2) < j <= n-1

Max-heap contains the root element as the highest element in the heap and from there the descending elements will be shown on the children node. It will also be traversed in an orderly manner and will be accessed by accessing the root first then their children nodes.

Write an algorithm to show the reverse of link list?

Link list is a data structure that is commonly used in programming. It is the simplest form. In this each node consists of a child node and a reference to the next node i.e. a link to another node. In this the group of nodes represents a sequence that helps in traversing of the node in an easy manner. The program is given to show the reversing of the link list:

reverse(struct node **st)

{

struct node *p, *q, *r;

p = *st;

q = NULL;

while(p != NULL)

{

r =q;

q = p;

p = p

link;

q

link = r;

}

*st = q;

}

Write an algorithm to show various operations on ordered list and arrays

Ordered list is a container holding the sequence of objects. In this each object is having a unique position in a particular sequence. The operations that are being provided and performed on the ordered list include:

FindPosition: is used to find the position of the object in an ordered list.

Operator[]: is used to access the position of the object in the ordered list.

withdraw(Position&): is used to remove the object from a given position in an ordered list.

InsertAfter: is used to insert an object after some other object or on some position in the ordered list.

InsertBefore: is used to insert the object in an ordered list at a defined position in an array of the ordered list.

Write a program to show the insertion and deletion of an element in an array using the position

To insert the element or delete the element, there is a requirement to find out the exact location as array is a group of linear characters, so it is very important to find the position of the element in an array before performing the actions on them. The program explains the insertion and deletion operations performed on an array of elements:

void insert ( int *arr, int pos, int num )

/* This inserts an element at a given position*/

{

int i ;

for ( i = MAX - 1 ; i > = pos ; i-- )

arr[i] = arr[i - 1] ;

arr[i] = num ;

// This tells about the shifting of an element to the right

} // function of the insertion ends here

void del ( int *arr, int pos )

/* This function is used to delete the element at a given position*/

{

int i ; for ( i = pos ; i < MAX ; i++ )

arr[i - 1] = arr[i] ;

arr[i - 1] = 0 ;

}

Write an algorithm to show the procedure of insertion into a B-tree?

The procedure or the algorithm to insert an element into a B-tree is as follows:

1. There is a search function that is applied to find the place where there is any new record to be present. When there is any key inserted then there is a sorting function that works to put the elements in the sorted order. 2. Then a particular node is selected and checked that is there any way to insert the new record. If there is any way to insert the new record then an appropriate pointer being given that remains one more than number of records.

3. If the node overflows due to the increase in the size of the node and upper bound, then there is a splitting being done to decrease the size of that particular node.

4. The split will occur till all the records are not accommodated properly at their place. There can be a way to split the root as well to create the provision for the new record data.

Write an algorithm that counts number of nodes in the circular linked list

Circular linked list is a list in which the insertion and deletion can be done in two ways. There is a provision to count the number of nodes just by keeping a count variable to count the data that is being inserted in the circular list. The algorithm is given to show the count of the nodes in the circular linked list.

Keep a circular header list in memory.

Keep a count to traverse the whole list and to keep a count of the data element

set COUNT: = 0

1. Set PTR: = LINK [START]. {Initializes the pointer PTR}

2. Repeat steps 3, 4, 5 while PTR = START;

3. COUNT = COUNT + 1

4. Set PTR = LINK [PTR]. [PTR now points to next node]

[End of step 2 loop]

5. Exit

Why Boundary Tag Representation is used?

Boundary tag representation is used to show the memory management using the data structures. The memory is allocated from a large area where there is free memory available. Memory management allows the use of segment and process of allocation of resources. This allows the reservation of block of 'n' bytes of memory and a space that is larger than the space of the system. Some tasks are performed like identifying and merging of free segments that has to be released. The process of identification is simpler as it only allows the location of the preceding segment to be located and used. The identification is done to find out the neighbors using the “used/free” flags that are kept with the location. There has to be kept some information regarding the processes and the resources that has been allocated to the data element. It allows the finding of the segment that is to find both the segments (start and end) to be used as a part of boundary tag.

What does Simulation of queues mean?

Simulation is a process of forming and abstract model of the real world situation. It allows understanding the effect of modification and all the situations that are relation to the queues like its properties. It allows the arrangement of the simulation program in a systematic way so that events can occur on regular basis. This allows the transaction to be done on time, for example suppose there is a person p1 submitting a bill and there has to be a period of time that will be take to process his request. If there is any free window then the person can submit the bill and spend less time in the queue. If there is no free availability then there will be a queue. The person has the option to choose the shortest queue to get his work done quickly, but he has to wait until all the previous transactions are processed. This is the way simulation of the queue works.

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