Advanced Algorithm (Eldan) 1 (200)

What does the following function do for a given Linked List with first node as head?
void fun1(struct node* head)
{
if(head == NULL)
return;

fun1(head->next);
printf("%d ", head->data);
}

Which of the following points is/are true about Linked List data structure when it is compared with array

Consider the following function that takes reference to head of a Doubly Linked List as parameter. Assume that a node of doubly linked list has previous pointer as prev and next pointer as next.
void fun(struct node **head_ref)
{
struct node *temp = NULL;
struct node *current = *head_ref;

while (current != NULL)
{
temp = current->prev;
current->prev = current->next;
current->next = temp;
current = current->prev;
}

if(temp != NULL )
*head_ref = temp->prev;
}
Assume that reference of head of following doubly linked list is passed to above function 1 <--> 2 <--> 3 <--> 4 <--> 5 <-->6. What should be the modified linked list after the function call?

Which of the following sorting algorithms can be used to sort a random linked list with minimum time complexity?

The following function reverse() is supposed to reverse a singly linked list. There is one line missing at the end of the function.
/* Link list node */
struct node
{
int data;
struct node* next;
};
/* head_ref is a double pointer which points to head (or start) pointer
of linked list */
static void reverse(struct node** head_ref)
{
struct node* prev = NULL;
struct node* current = *head_ref;
struct node* next;
while (current != NULL)
{
next = current->next;
current->next = prev;
prev = current;
current = next;
}
/*ADD A STATEMENT HERE*/
}
What should be added in place of "/*ADD A STATEMENT HERE*/", so that the function correctly reverses a linked list.

What is the output of following function for start pointing to first node of following linked list? 1->2->3->4->5->6
void fun(struct node* start)
{
if(start == NULL)
return;
printf("%d ", start->data);

if(start->next != NULL )
fun(start->next->next);
printf("%d ", start->data);
}

The following C function takes a simply-linked list as input argument. It modifies the list by moving the last element to the front of the list and returns the modified list. Some part of the code is left blank. Choose the correct alternative to replace the blank line.
typedef struct node
{
int value;
struct node *next;
}Node;

Node *move_to_front(Node *head)
{
Node *p, *q;
if ((head == NULL: || (head->next == NULL))
return head;
q = NULL; p = head;
while (p-> next !=NULL)
{
q = p;
p = p->next;
}
_______________________________
return head;
}

The following C function takes a single-linked list of integers as a parameter and rearranges the elements of the list. The function is called with the list containing the integers 1, 2, 3, 4, 5, 6, 7 in the given order. What will be the contents of the list after the function completes execution?
struct node
{
int value;
struct node *next;
};
void rearrange(struct node *list)
{
struct node *p, * q;
int temp;
if ((!list) || !list->next)
return;
p = list;
q = list->next;
while(q)
{
temp = p->value;
p->value = q->value;
q->value = temp;
p = q->next;
q = p?p->next:0;
}
}

In the worst case, the number of comparisons needed to search a singly linked list of length n for a given element is (GATE CS 2002)

Suppose each set is represented as a linked list with elements in arbitrary order. Which of the operations among union, intersection, membership, cardinality will be the slowest? (GATE CS 2004)

Consider the function f defined below.
struct item
{
int data;
struct item * next;
};

int f(struct item *p)
{
return (
(p == NULL) ||
(p->next == NULL) ||
(( P->data <= p->next->data) && f(p->next))
);
}
For a given linked list p, the function f returns 1 if and only if (GATE CS 2003)

What are the time complexities of finding 8th element from beginning and 8th element from end in a singly linked list? Let n be the number of nodes in linked list, you may assume that n > 8.

Is it possible to create a doubly linked list using only one pointer with every node.

Given pointer to a node X in a singly linked list. Only one pointer is given, pointer to head node is not given, can we delete the node X from given linked list?

You are given pointers to first and last nodes of a singly linked list, which of the following operations are dependent on the length of the linked list?

Consider the following function to traverse a linked list.
void traverse(struct Node *head)
{
while (head->next != NULL)
{
printf("%d ", head->data);
head = head->next;
}
}
Which of the following is FALSE about above function?

Let P be a singly linked list. Let Q be the pointer to an intermediate node x in the list. What is the worst-case time complexity of the best known algorithm to delete the node x from the list?

N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on which the operation is to be performed. An algorithm performs the following operations on the list in this order: Θ(N) delete, O(log N) insert, O(log N) find, and Θ(N) decrease-key What is the time complexity of all these operations put together

The concatenation of two lists is to be performed in O(1) time. Which of the following implementations of a list should be used?

Consider the following statements:
i. First-in-first out types of computations are efficiently supported by STACKS.
ii. Implementing LISTS on linked lists is more efficient than implementing LISTS on
an array for almost all the basic LIST operations.
iii. Implementing QUEUES on a circular array is more efficient than implementing QUEUES
on a linear array with two indices.
iv. Last-in-first-out type of computations are efficiently supported by QUEUES.

Following is C like pseudo code of a function that takes a number as an argument, and uses a stack S to do processing.
void fun(int n)
{
Stack S; // Say it creates an empty stack S
while (n > 0)
{
// This line pushes the value of n%2 to stack S
push(&S, n%2);

n = n/2;
}

// Run while Stack S is not empty
while (!isEmpty(&S))
printf("%d ", pop(&S)); // pop an element from S and print it
}

Which one of the following is an application of Stack Data Structure?

Which of the following is true about linked list implementation of stack?

Consider the following pseudocode that uses a stack
declare a stack of characters
while ( there are more characters in the word to read )
{
read a character
push the character on the stack
}
while ( the stack is not empty )
{
pop a character off the stack
write the character to the screen
}

Following is an incorrect pseudocode for the algorithm which is supposed to determine whether a sequence of parentheses is balanced:
declare a character stack
while ( more input is available)
{
read a character
if ( the character is a '(' )
push it on the stack
else if ( the character is a ')' and the stack is not empty )
pop a character off the stack
else
print "unbalanced" and exit
}
print "balanced"
Which of these unbalanced sequences does the above code think is balanced?

The following postfix expression with single digit operands is evaluated using a stack:
8 2 3 ^ / 2 3 * + 5 1 * -
Note that ^ is the exponentiation operator. The top two elements of the stack after the first * is evaluated are:

Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operation take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m >= 1, define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S. The average stack-life of an element of this stack is

A single array A[1..MAXSIZE] is used to implement two stacks. The two stacks grow from opposite ends of the array. Variables top1 and top2 (topl< top 2) point to the location of the topmost element in each of the stacks. If the space is to be used efficiently, the condition for “stack full” is (GATE CS 2004)

Assume that the operators +, -, × are left associative and ^ is right associative. The order of precedence (from highest to lowest) is ^, x , +, -. The postfix expression corresponding to the infix expression a + b × c - d ^ e ^ f is

To evaluate an expression without any embedded function calls:

The result evaluating the postfix expression 10 5 + 60 6 / * 8 – is

A function f defined on stacks of integers satisfies the following properties. f(∅) = 0 and f (push (S, i)) = max (f(S), 0) + i for all stacks S and integers i.
If a stack S contains the integers 2, -3, 2, -1, 2 in order from bottom to top, what is f(S)?

Consider the following C program:
#include
#define EOF -1
void push (int); /* push the argument on the stack */
int pop (void); /* pop the top of the stack */
void flagError ();
int main ()
{ int c, m, n, r;
while ((c = getchar ()) != EOF)
{ if (isdigit (c) )
push (c);
else if ((c == '+') || (c == '*'))
{ m = pop ();
n = pop ();
r = (c == '+') ? n + m : n*m;
push (r);
}
else if (c != ' ')
flagError ();
}
printf("% c", pop ());
}
What is the output of the program for the following input ? 5 2 * 3 3 2 + * +

Suppose a stack is to be implemented with a linked list instead of an array. What would be the effect on the time complexity of the push and pop operations of the stack implemented using linked list (Assuming stack is implemented efficiently)?

Consider n elements that are equally distributed in k stacks. In each stack, elements of it are arranged in ascending order (min is at the top in each of the stack and then increasing downwards). Given a queue of size n in which we have to put all n elements in increasing order. What will be the time complexity of the best known algorithm?

A priority queue Q is used to implement a stack S that stores characters. PUSH(C) is implemented as INSERT(Q, C, K) where K is an appropriate integer key chosen by the implementation. POP is implemented as DELETEMIN(Q). For a sequence of operations, the keys chosen are in

Consider the following statements:
i. First-in-first out types of computations are efficiently supported by STACKS.
ii. Implementing LISTS on linked lists is more efficient than implementing LISTS on
an array for almost all the basic LIST operations.
iii. Implementing QUEUES on a circular array is more efficient than implementing QUEUES
on a linear array with two indices.
iv. Last-in-first-out type of computations are efficiently supported by QUEUES.

Following is C like pseudo code of a function that takes a Queue as an argument, and uses a stack S to do processing.
void fun(Queue *Q)
{
Stack S; // Say it creates an empty stack S

// Run while Q is not empty
while (!isEmpty(Q))
{
// deQueue an item from Q and push the dequeued item to S
push(&S, deQueue(Q));
}

// Run while Stack S is not empty
while (!isEmpty(&S))
{
// Pop an item from S and enqueue the poppped item to Q
enQueue(Q, pop(&S));
}
}
What does the above function do in general?

Which one of the following is an application of Queue Data Structure

How many stacks are needed to implement a queue. Consider the situation where no other data structure like arrays, linked list is available to you.

How many queues are needed to implement a stack. Consider the situation where no other data structure like arrays, linked list is available to you.

A priority queue can efficiently implemented using which of the following data structures? Assume that the number of insert and peek (operation to see the current highest priority item) and extraction (remove the highest priority item) operations are almost same.

Which of the following is true about linked list implementation of queue?

Suppose a circular queue of capacity (n – 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operation are carried out using REAR and FRONT as array index variables, respectively. Initially, REAR = FRONT = 0. The conditions to detect queue full and queue empty are

A Priority-Queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is given below: 10, 8, 5, 3, 2 Two new elements ”1‘ and ”7‘ are inserted in the heap in that order. The level-order traversal of the heap after the insertion of the elements is:

An implementation of a queue Q, using two stacks S1 and S2, is given below:
void insert(Q, x) {
push (S1, x);
}

void delete(Q){
if(stack-empty(S2)) then
if(stack-empty(S1)) then {
print(“Q is empty”);
return;
}
else while (!(stack-empty(S1))){
x=pop(S1);
push(S2,x);
}
x=pop(S2);
}
Let n insert and m (<=n) delete operations be performed in an arbitrary order on an empty queue Q. Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n?

Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter.
MultiDequeue(Q){
m = k
while (Q is not empty and m > 0) {
Dequeue(Q)
m = m - 1
}
}
What is the worst case time complexity of a sequence of n MultiDequeue() operations on an initially empty queue? (GATE CS 2013)

Consider the following pseudo code. Assume that IntQueue is an integer queue. What does the function fun do?
void fun(int n)
{
IntQueue q = new IntQueue();
q.enqueue(0);
q.enqueue(1);
for (int i = 0; i < n; i++)
{
int a = q.dequeue();
int b = q.dequeue();
q.enqueue(b);
q.enqueue(a + b);
ptint(a);
}
}

Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter.
MultiDequeue(Q){
m = k
while (Q is not empty and m > 0) {
Dequeue(Q)
m = m - 1
}
}
What is the worst case time complexity of a sequence of n MultiDequeue() operations on an initially empty queue? (GATE CS 2013)

Suppose implementation supports an instruction REVERSE, which reverses the order of elements on the stack, in addition to the PUSH and POP instructions. Which one of the following statements is TRUE with respect to this modified stack?

A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT (n refers to the number of items in the queue)?

Suppose you are given an implementation of a queue of integers. The operations that can be performed on the queue are:
i. isEmpty (Q) — returns true if the queue is empty, false otherwise.
ii. delete (Q) — deletes the element at the front of the queue and returns its value.
iii. insert (Q, i) — inserts the integer i at the rear of the queue.
Consider the following function:
void f (queue Q) {
int i ;
if (!isEmpty(Q)) {
i = delete(Q);
f(Q);
insert(Q, i);
}
}
What operation is performed by the above function f ?

Consider the following statements:
i. First-in-first out types of computations are efficiently supported by STACKS.
ii. Implementing LISTS on linked lists is more efficient than implementing LISTS on
an array for almost all the basic LIST operations.
iii. Implementing QUEUES on a circular array is more efficient than implementing QUEUES
on a linear array with two indices.
iv. Last-in-first-out type of computations are efficiently supported by QUEUES.

Which of the following is a true about Binary Trees

If arity of operators is fixed, then which of the following notations can be used to parse expressions without parentheses?
a) Infix Notation (Inorder traversal of a expression tree)
b) Postfix Notation (Postorder traversal of a expression tree)
c) Prefix Notation (Preorder traversal of a expression tree)

What are the main applications of tree data structure? 1) Manipulate hierarchical data 2) Make information easy to search (see tree traversal). 3) Manipulate sorted lists of data 4) Router algorithms 5) Form of a multi-stage decision-making, like Chess Game. 6) As a workflow for compositing digital images for visual effects

Level of a node is distance from root to that node. For example, level of root is 1 and levels of left and right children of root is 2. The maximum number of nodes on level i of a binary tree is

In a complete k-ary tree, every internal node has exactly k children or no child. The number of leaves in such a tree with n internal nodes is:

The maximum number of binary trees that can be formed with three unlabeled nodes is

The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:

A weight-balanced tree is a binary tree in which for each node. The number of nodes in the left sub tree is at least half and at most twice the number of nodes in the right sub tree. The maximum possible height (number of nodes on the path from the root to the farthest leaf) of such a tree on n nodes is best described by which of the following?

A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height h is:

A scheme for storing binary trees in an array X is as follows. Indexing of X starts at 1 instead of 0. the root is stored at X[1]. For a node stored at X[i], the left child, if any, is stored in X[2i] and the right child, if any, in X[2i+1]. To be able to store any binary tree on n vertices the minimum size of X should be. (GATE CS 2006)

Postorder traversal of a given binary search tree, T produces the following sequence of keys 10, 9, 23, 22, 27, 25, 15, 50, 95, 60, 40, 29 Which one of the following sequences of keys can be the result of an in-order traversal of the tree T? (GATE CS 2005)

Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stress, respectively, of node X. Note that Y and Z may be NULL, or further nested. Which of the following represents a valid binary tree?

Consider a node X in a Binary Tree. Given that X has two children, let Y be Inorder successor of X. Which of the following is true about Y?

In a binary tree with n nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child?

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height h is:

The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are

A binary tree T has 20 leaves. The number of nodes in T having two children is

Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap is

An array of integers of size n can be converted into a heap by adjusting the heaps rooted at each internal node of the complete binary tree starting at the node ⌊(n - 1) /2⌋, and doing this adjustment up to the root node (root node is at index 0) in the order ⌊(n - 1)/2⌋, ⌊(n - 3)/ 2⌋, ....., 0. The time required to construct a heap in this manner is

In a binary tree, for every node the difference between the number of nodes in the left and right subtrees is at most 2. If the height of the tree is h > 0, then the minimum number of nodes in the tree is:

Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is ________

In a binary tree, the number of internal nodes of degree 1 is 5, and the number of internal nodes of degree 2 is 10. The number of leaf nodes in the binary tree is

The following three are known to be the preorder, inorder and postorder sequences of a binary tree. But it is not known which is which.
MBCAFHPYK
KAMCBYPFH
MABCKYFPH
Pick the true statement from the following.

A binary tree with n > 1 nodes has n1, n2 and n3 nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.
n3 can be expressed as

A binary tree with n > 1 nodes has n1, n2 and n3 nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.
Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?

A binary search tree contains the values 1, 2, 3, 4, 5, 6, 7, 8. The tree is traversed in pre-order and the values are printed out. Which of the following sequences is a valid output?

In the balanced binary tree in the below figure, how many nodes will become unbalanced when a node is inserted as a child of the node “g”?
a
/ \
b e
/ \ /
c d f
/
g

Which of the following sequences denotes the post order traversal sequence of the given tree?
a
/ \
b e
/ \ /
c d f
/
g

What is the worst case time complexity for search, insert and delete operations in a general Binary Search Tree?

In delete operation of BST, we need inorder successor (or predecessor) of a node when the node to be deleted has both left and right child as non-empty. Which of the following is true about inorder successor needed in delete operation?

We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree? (GATE CS 2011)

How many distinct binary search trees can be created out of 4 distinct keys?

Which of the following traversal outputs the data in sorted order in a BST?

Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree?

The following numbers are inserted into an empty binary search tree in the given order: 10, 1, 3, 5, 15, 12, 16. What is the height of the binary search tree (the height is the maximum distance of a leaf node from the root)? (GATE CS 2004)

The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42. Which one of the following is the postorder traversal sequence of the same tree?

Consider the following Binary Search Tree

10
/ \
5 20
/ / \
4 15 30
/
11
If we randomly search one of the keys present in above BST, what would be the expected number of comparisons?

Which of the following traversals is sufficient to construct BST from given traversals
1) Inorder
2) Preorder
3) Postorder

Consider the following code snippet in C. The function print() receives root of a Binary Search Tree (BST) and a positive integer k as arguments.
// A BST node
struct node {
int data;
struct node *left, *right;
};

int count = 0;

void print(struct node *root, int k)
{
if (root != NULL && count <= k)
{
print(root->right, k);
count++;
if (count == k)
printf("%d ", root->data);
print(root->left, k);
}
}
What is the output of print(root, 3) where root represent root of the following BST.
15
/ \
10 20
/ \ / \
8 12 16 25

Consider the same code as given in above question. What does the function print() do in general? The function print() receives root of a Binary Search Tree (BST) and a positive integer k as arguments.
// A BST node
struct node {
int data;
struct node *left, *right;
};

int count = 0;

void print(struct node *root, int k)
{
if (root != NULL && count <= k)
{
print(root->right, k);
count++;
if (count == k)
printf("%d ", root->data);
print(root->left, k);
}
}

You are given the postorder traversal, P, of a binary search tree on the n elements 1, 2, ..., n. You have to determine the unique binary search tree that has P as its postorder traversal. What is the time complexity of the most efficient algorithm for doing this?

Suppose we have a balanced binary search tree T holding n numbers. We are given two numbers L and H and wish to sum up all the numbers in T that lie between L and H. Suppose there are m such numbers in T. If the tightest upper bound on the time to compute the sum is O(nalogb n + mc logd n), the value of a + 10b + 100c + 1000d is ____.

What are the worst-case complexities of insertion and deletion of a key in a binary search tree?

While inserting the elements 71, 65, 84, 69, 67, 83 in an empty binary search tree (BST) in the sequence shown, the element in the lowest level is

The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary search tree, such that the resulting tree has height 6, is _____________ Note: The height of a tree with a single node is 0.

Suppose that we have numbers between 1 and 100 in a binary search tree and want to search for the number 55. Which of the following sequences CANNOT be the sequence of nodes examined?

When searching for the key value 60 in a binary search tree, nodes containing the key values 10, 20, 40, 50, 70 80, 90 are traversed, not necessarily in the order given. How many different orders are possible in which these key values can occur on the search path from the root to the node containing the value 60?

A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys.

I. 81, 537, 102, 439, 285, 376, 305

II. 52, 97, 121, 195, 242, 381, 472

III. 142, 248, 520, 386, 345, 270, 307

IV. 550, 149, 507, 395, 463, 402, 270

Suppose the BST has been unsuccessfully searched for key 273. Which all of the above sequences list nodes in the order in which we could have encountered them in the search?

A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys.
I. 81, 537, 102, 439, 285, 376, 305
II. 52, 97, 121, 195, 242, 381, 472
III. 142, 248, 520, 386, 345, 270, 307
IV. 550, 149, 507, 395, 463, 402, 270
Which of the following statements is TRUE?

How many distinct BSTs can be constructed with 3 distinct keys?

A binary search tree is generated by inserting in order the following integers:
50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24
The number of nodes in the left subtree and right subtree of the root respectively is

The worst case running time to search for an element in a balanced in a binary search tree with n2^n elements is

What is the maximum height of any AVL-tree with 7 nodes? Assume that the height of a tree with a single node is 0.

What is the worst case possible height of AVL tree?

Which of the following is AVL Tree?
A
100
/ \
50 200
/ \
10 300

B
100
/ \
50 200
/ / \
10 150 300
/
5

C
100
/ \
50 200
/ \ / \
10 60 150 300
/ \ \
5 180 400

Consider the following AVL tree.
60
/ \
20 100
/ \
80 120
Which of the following is updated AVL tree after insertion of 70
A
70
/ \
60 100
/ / \
20 80 120

B
100
/ \
60 120
/ \ /
20 70 80

C
80
/ \
60 100
/ \ \
20 70 120

D
80
/ \
60 100
/ / \
20 70 120

Consider the following left-rotate and right-rotate functions commonly used in self-adjusting BSTs
T1, T2 and T3 are subtrees of the tree rooted with y (on left side)
or x (on right side)
y x
/ \ Right Rotation / \
x T3 – - – - – - – > T1 y
/ \ < - - - - - - - / \
T1 T2 Left Rotation T2 T3
Which of the following is tightest upper bound for left-rotate and right-rotate operations.

Which of the following is true

Which of the following is true about Red Black Trees?

Which of the following is true about AVL and Red Black Trees?

What is the worst case possible height of Red-Black tree? Assume base of Log as 2 in all options

Which of the following is a self-adjusting or self-balancing Binary Search Tree

Is the following statement valid? A Red-Black Tree which is also a perfect Binary Tree can have all black nodes

Which of the following operations are used by Red-Black trees to maintain balance during insertion/deletion?

a) Recoloring of nodes
b) Rotation (Left and Right)

A program takes as input a balanced binary search tree with n leaf nodes and computes the value of a function g(x) for each node x. If the cost of computing g(x) is min{no. of leaf-nodes in left-subtree of x, no. of leaf-nodes in right-subtree of x} then the worst-case time complexity of the program is

Which of the following is TRUE?

Given two Balanced binary search trees, B1 having n elements and B2 having m elements, what is the time complexity of the best known algorithm to merge these trees to form another balanced binary tree containing m+n elements ?

Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph?

The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
I. 7, 6, 5, 4, 4, 3, 2, 1
II. 6, 6, 6, 6, 3, 3, 2, 2
III. 7, 6, 6, 4, 4, 3, 2, 2
IV. 8, 7, 7, 6, 4, 2, 1, 1

The time complexity of computing the transitive closure of a binary relation on a set of n elements is known to be:

The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has time complexity.

Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct? (GATE CS 2001)

How many undirected graphs (not necessarily connected) can be constructed out of a given set V= {V 1, V 2,…V n} of n vertices ?

Which of the following statements is/are TRUE for an undirected graph?
P: Number of odd degree vertices is even
Q: Sum of degrees of all vertices is even

Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?

Given an undirected graph G with V vertices and E edges, the sum of the degrees of all vertices is

How many undirected graphs (not necessarily connected) can be constructed out of a given set V = {v1, v2, ... vn} of n vertices?

What is the maximum number of edges in an acyclic undirected graph with n vertices?

Let G be a weighted undirected graph and e be an edge with maximum weight in G. Suppose there is a minimum weight spanning tree in G containing the edge e. Which of the following statements is always TRUE?

A sink in a directed graph is a vertex i such that there is an edge from every vertex j ≠ i to i and there is no edge from i to any other vertex. A directed graph G with n vertices is represented by its adjacency matrix A, where A[i] [j] = 1 if there is an edge directed from vertex i to j and 0 otherwise. The following algorithm determines whether there is a sink in the graph G.
i = 0
do {
j = i + 1;
while ((j < n) && E1) j++;
if (j < n) E2;
} while (j < n);

flag = 1;
for (j = 0; j < n; j++)
if ((j! = i) && E3)
flag = 0;

if (flag)
printf("Sink exists");
else
printf("Sink does not exist");
Choose the correct expressions for E3

The cyclomatic complexity of the flow graph of a program provides

What is the largest integer m such that every simple connected graph with n vertices and n edges contains at least m different spanning trees?

Consider a directed graph with n vertices and m edges such that all edges have same edge weights. Find the complexity of the best known algorithm to compute the minimum spanning tree of the graph?

You are given a graph containing n vertices and m edges and given that the graph doesn’t contain cycle of odd length. Time Complexity of the best known algorithm to find out whether the graph is bipartite or not is ?

Let G be a simple graph with 20 vertices and 8 components. If we delete a vertex in G, then number of components in G should lie between ____.

Let G be the graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent iff |i−j|=8 or |i−j|=12. The number of connected components in G is

How many different insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above?

Consider a hash table of size seven, with starting index zero, and a hash function (3x + 4)mod7. Assuming the hash table is initially empty, which of the following is the contents of the table when the sequence 1, 3, 8, 10 is inserted into the table using closed hashing? Note that ‘_’ denotes an empty location in the table.

Given the following input (4322, 1334, 1471, 9679, 1989, 6171, 6173, 4199) and the hash function x mod 10, which of the following statements are true?
i. 9679, 1989, 4199 hash to the same value
ii. 1471, 6171 has to the same value
iii. All elements hash to the same value
iv. Each element hashes to a different value (GATE CS 2004)

Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first 3 insertions?

Which one of the following hash functions on integers will distribute keys most uniformly over 10 buckets numbered 0 to 9 for i ranging from 0 to 2020?

Given a hash table T with 25 slots that stores 2000 elements, the load factor α for T is __________

Which of the following statement(s) is TRUE?
1) A hash function takes a message of arbitrary length and generates a fixed length code.
2) A hash function takes a message of fixed length and generates a code of variable length.
3) A hash function may give the same hash value for distinct messages.

Consider a hash function that distributes keys uniformly. The hash table size is 20. After hashing of how many keys will the probability that any new key hashed collides with an existing one exceed 0.5.

An advantage of chained hash table (external hashing) over the open addressing scheme is

A program P reads in 500 integers in the range [0..100] exepresenting the scores of 500 students. It then prints the frequency of each score above 50. What would be the best way for P to store the frequencies?

Which of the following operations is not O(1) for an array of sorted data. You may assume that array elements are distinct.

The minimum number of comparisons required to determine if an integer appears more than n/2 times in a sorted array of n integers is

Let A be a square matrix of size n x n. Consider the following program. What is the expected output?
C = 100
for i = 1 to n do
for j = 1 to n do
{
Temp = A[i][j] + C
A[i][j] = A[j][i]
A[j][i] = Temp - C
}
for i = 1 to n do
for j = 1 to n do
Output(A[i][j]);

An algorithm performs (logN)^1/2 find operations, N insert operations, (logN)^1/2 operations, and (logN)^1/2 decrease-key operations on a set of data items with keys drawn from a linearly ordered set. For a delete operation, a pointer is provided to the record that must be deleted. For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?

Consider an array consisting of –ve and +ve numbers. What would be the worst time comparisons an algorithm can take in order to segregate the numbers having same sign altogether i.e all +ve on one side and then all -ve on the other ?

What is the time complexity of Build Heap operation. Build Heap is used to build a max(or min) binary heap from a given array. Build Heap is used in Heap Sort as a first step for sorting.

Suppose we are sorting an array of eight integers using heapsort, and we have just finished some heapify (either maxheapify or minheapify) operations. The array now looks like this: 16 14 15 10 12 27 28 How many heapify operations have been performed on root of heap?

A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be represented by an array as follows: The root is stored in the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to a[3]. The nodes from the second level of the tree from left to right are stored from a[4] location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property. Which one of the following is a valid sequence of elements in an array representing 3-ary max heap?