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Arjun asked in Algorithms Apr 15

by Arjun

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qwer: 1
What is the Cardinality of the Power set of the set $\{0,1,2\}$? $8$ $6$ $7$ $9$

Arjun answered in Algorithms Apr 3

by Arjun

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1 answer

3

qwer: 2
The symmetric difference of sets $\text{A}=\{1,2, 3,4, 5, 6, 7, 8\}$ and $\text{B}= \{1, 3, 5, 6, 7,8,9\}$ is: $\{1, 3, 5, 6, 7,8\}$ $\{2, 4, 9\}$ $\{2, 4\}$ $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$

Arjun answered in Algorithms Apr 3

by Arjun

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4

qwer: 3
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \: \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$

Arjun answered in Algorithms Apr 3

by Arjun

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qwer: 4
The power set of the set $\{ \Phi \}$ is $\{ \Phi \}$ $\{ \Phi, \{ \Phi \} \}$ $\{ 0 \}$ $\{ 0, \Phi , \{ \Phi \} \}$

Arjun answered in Algorithms Apr 3

by Arjun

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qwer: 5
Let $A, B$ be two sets. Let $\bar{A}$ denote the complement of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are not in $B$. Set $(A - (A - B))$ is equal to: $B$ $A\cap \bar{B}$ $A - B$ $A\cap B$

Arjun answered in Algorithms Apr 3

by Arjun

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qwer: 6
Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Then at least one of the sets $S_i$ is a finite set not more than one of the sets $S_i$ can be finite at least one of the sets $S_i$ is an infinite None of the above

Arjun answered in Algorithms Apr 3

by Arjun

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8

qwer: 7
Power set of empty set has exactly how many subset(s) One Two Zero Three

Arjun answered in Algorithms Apr 3

by Arjun

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qwer: 8
Which of the following is/are true? If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$. If $S$ is a set and $|S| = 103$, then $S$ is a power set of some set (that is, there is some ... is a set and $|S| = 8$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.

Arjun answered in Algorithms Apr 3

by Arjun

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qwer: 9
Which of the following statements is /are TRUE? $2 \in A \cup B$ implies that if $2 \notin A$ then $2 \in B$. $\{2,3\} \subseteq A$ implies that $2 \in A$ and $3 \in A$. $A \cap B \supseteq\{2,3\}$ implies that $\{2,3\} \subseteq A$ and $\{2,3\} \subseteq B$. $A-B \supseteq\{3\}$ and $\{2\} \subseteq B$ implies that $\{2,3\} \subseteq A \cup B$.

Arjun asked in Algorithms Apr 3

by Arjun

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11

qwer: 10
Which of the following statements is /are False? $\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$. $A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3,4\} \subseteq A$ and $\{2,3,4\} \subseteq B$. $A-B \supseteq\{3,4\}$ ... $\{2,3\} \subseteq A \cup B$ implies that if $\{2,3\} \cap A=\emptyset$ then $\{2,3\} \subseteq B$.

Arjun asked in Algorithms Apr 3

by Arjun

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2 answers

12

Prove that for any constant c > 0, (log n)^c = o(n).

Teet Makor answered in Algorithms Mar 23

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1 answer

13

Prove that n! = Ω(n^100)

Teet Makor answered in Algorithms Mar 23

59 views

34 votes

4 answers

14

GATE IT 2007 | Question: 3, UGCNET-June2012-III: 34
Consider a weighted, undirected graph with positive edge weights and let $uv$ be an edge in the graph. It is known that the shortest path from the source vertex $s$ to $u$ has weight 53 and the shortest path from $s$ to $v$ has weight 65. Which one of the ... $(u,v) \leq 12$ Weight $(u,v) = 12$ Weight $(u,v) \geq 12$ Weight $(u,v) > 12$

ritiksri8 answered in Algorithms Mar 21

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2 votes

2 answers

15

GATE CSE 2024 | Set 1 | Question: 24
The number of spanning trees in a complete graph of $4$ vertices labelled $\text{A, B, C,}$ and $\text{D}$ is _________.

ritiksri8 answered in Algorithms Mar 20

1.6k views

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16

Recurrence relation
What is the returned value by the given function below. Algo fun(n) { If(x<=2) return 1; Else { Return fun(n1/2) + n; } } Note : Assume that all the syntax and data type constraints are valid and just check algorithm.

jenilS7 asked in Algorithms Mar 18

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17

Merge Sort
Calculate the minimum and maximum number of element comparisons involved in 2 way merge sort assuming n is power of 2.

Ujjal Das asked in Algorithms Mar 17

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1 answer

18

Sorting Algorithm
For flag based approach in Bubble sort we can check first by a flag if the list is sorted or not in O(n), and if it is sorted, then no need to sort and the operation ends in Best case = O(n). Why isn't the same concept applicable to selection sort? Why it never comes down from O(n$^2$)?

DEBANJAN DAS2k answered in Algorithms Mar 15

by DEBANJAN DAS2k

138 views

1 vote

2 answers

19

CMI2010-B-01b
An international cellphone company provides service on 7 different frequencies. They wish to set up business in Tamil Nadu and have fixed the locations of 100 towers for their new service. The company has to ensure that two towers broadcasting on the same ... should say feasible if it is feasible, otherwise output the minimum number of frequencies needed to utilise all 100 towers.

Priyam Garg answered in Algorithms Mar 15

643 views

21 votes

7 answers

20

GATE CSE 2007 | Question: 5
Consider the DAG with $V = \{1,2,3,4,5,6\}$ shown below. Which of the following is not a topological ordering? $1$ $2$ $3$ $4$ $5$ $6$ $1$ $3$ $2$ $4$ $5$ $6$ $1$ $3$ $2$ $4$ $6$ $5$ $3$ $2$ $4$ $1$ $6$ $5$

ritiksri8 answered in Algorithms Mar 14

7.7k views

1 vote

1 answer

21

DRDO CSE 2022 Paper 1 | Question: 33 (b)
Consider the following graph. How many nodes (apart from $s$) does the Depth First Search algorithm discover before discovering $t$ when starting from $s.$

mishraamulya answered in Algorithms Mar 10

by mishraamulya

252 views

1 vote

2 answers

22

GATE CSE 2024 | Set 2 | Question: 41
Let $\text{G}$ be an undirected connected graph in which every edge has a positive integer weight. Suppose that every spanning tree in $\text{G}$ has even weight. Which of the following statements is/are TRUE for every such graph $\text{G}$ ... $\text{C}$ have even weight $\text{OR}$ all edges in $\text{C}$ have odd weight

SkillIssue answered in Algorithms Mar 8

1.8k views

5 votes

3 answers

23

ISRO2007-23
Study the following program //precondition: x>=0 public void demo(int x) { System.out.print(x % 10); if (x % 10 != 0) { demo(x/10); } System.out.print(x%10); } Which of the following is printed as a result of the call demo $(1234)$? $1441$ $3443$ $12344321$ $43211234$

teja1521 answered in Algorithms Mar 4

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24

#algorithm
how many spanning trees are possible for complete graph of 4 vertices closed

꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ answered in Algorithms Mar 3

by ꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂

97 views

1 vote

3 answers

25

GATE CSE 2024 | Set 1 | Question: 32
Consider the following recurrence relation: $T(n)=\left\{\begin{array}{c}\sqrt{n} T(\sqrt{n})+n \text { for } n \geq 1, \\ 1 \quad \text { for } n=1\end{array}\right.$ Which one of the following options is CORRECT? $T(n)=\Theta(n \log \log n)$ $T(n)=\Theta(n \log n)$ $T(n)=\Theta\left(n^2 \log n\right)$ $T(n)=\Theta\left(n^2 \log \log n\right)$

skypaul101 answered in Algorithms Feb 29

1.9k views

2 votes

4 answers

26

GATE CSE 2024 | Set 2 | Question: 5
Let $\text{T(n)}$ be the recurrence relation defined as follows: \[ \begin{array}{l} T(0)=1, \\ T(1)=2, \text { and } \\ T(n)=5 T(n-1)-6 T(n-2) \text { for } n \geq 2 \end{array} \] Which one of the following statements is TRUE? $T(n)=\Theta\left(2^{n}\right)$ $T(n)=\Theta\left(n 2^{n}\right)$ $T(n)=\Theta\left(3^{n}\right)$ $T(n)=\Theta\left(n 3^{n}\right)$

Priyam Garg answered in Algorithms Feb 27

2.0k views

21 votes

4 answers

27

GATE CSE 2023 | Question: 44
Consider functions $\textsf{Function_1}$ and $\textsf{Function_2}$ ... $f_{1}(n) \in \omega\left(f_{2}(n)\right)$ $f_{1}(n) \in O(n)$

KG answered in Algorithms Feb 24

by KG

11.3k views

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28

In rural Ireland, a century ago, the students had to form a line. The student at the front of the line would be asked to spell a word. If he spelled it correctly, he was allowed to sit down. If not, he received a whack on the hand with a switch and was sent to the end of the line. Suppose that a student could spell correctly 70% of the words in the lesson. What is the probability that the student would be able to sit down before receiving four whacks on the hand? Assume that the master chose the words to be spelled randomly and independently.

tim20 asked in Algorithms Feb 22

by tim20

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1 answer

29

TS
$\text{Please explain True or False and Why ?}$ $\text{1. f(n) = O(f(n/2))}$ $\text{2. f(n) = O($f(n)^{2}$) }$

ashmit.26 answered in Algorithms Feb 21

240 views

1 vote

1 answer

30

Memory Based GATE DA 2024 | Question: 25
Consider the QuickSort algorithm with the last element chosen as the pivot. If the goal is to sort the given array \(a = [30, 40, 50, 60, 70, 80]\) in ascending order, how many swaps will occur during the execution of the algorithm?

gate.datascience_ai answered in Algorithms Feb 19

by gate.datascience_ai

238 views

1 vote

1 answer

31

GATE CSE 2024 | Set 2 | Question: 49
The number of distinct minimum-weight spanning trees of the following graph is

shwetanshu12 answered in Algorithms Feb 18

by shwetanshu12

1.6k views

4 votes

2 answers

32

GATE CSE 2024 | Set 1 | Question: 35
Let $G$ be a directed graph and $T$ a depth first search $\text{(DFS)}$ spanning tree in $G$ that is rooted at a vertex $v$. Suppose $T$ is also a breadth first search $\text{(BFS)}$ tree in $G$, rooted at $v$. Which of the following ... the tree $T$ There are no forward-edge in $G$ with respect to the tree $T$ The only edges in $G$ are the edges in $T$

minip answered in Algorithms Feb 17

by minip

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1 answer

33

GATE DS&AI 2024 | Question: 41
Consider the directed acyclic graph (DAG) below: Which of the following is/are valid vertex orderings that can be obtained from a topological sort of the DAG? $\text{P Q R S T U V}$ $\text{P R Q V SUT}$ $\text{P Q R S V U T}$ $\text{P R Q S V T U}$

liontig37 answered in Algorithms Feb 17

670 views

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2 answers

34

GATE DS&AI 2024 | Question: 6
Match the items in Column $1$ with the items in Column $2$ in the following table: \begin{array}{|ll|ll|} \hline & \text{Column 1} & & \text{Column 2} \\ \hline & & & \\ \text{(p)} & \text{First In First Out} & \text{ ... $(\mathrm{p})-(\mathrm{i}),(\mathrm{q})-(\mathrm{iii}),(\mathrm{r})-(\mathrm{ii})$

Hira Thakur answered in Algorithms Feb 17

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1 answer

35

GATE CSE 2024 | Set 1 | Question: 50
The number of edges present in the forest generated by the $\text{DFS}$ traversal of an undirected graph $G$ with $100$ vertices is $40$. The number of connected components in $G$ is __________.

shishir__roy answered in Algorithms Feb 17

by shishir__roy

1.6k views

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3 answers

36

GATE DS&AI 2024 | Question: 20
Consider sorting the following array of integers in ascending order using an inplace Quicksort algorithm that uses the last element as the pivot. \begin{array}{|l|l|l|l|l|} \hline 60 & 70 & 80 & 90 & 100 \\ \hline \end{array} The minimum number of swaps performed during this Quicksort is $\_\_\_\_\_\_\_\_$.

gaurav0to1 answered in Algorithms Feb 17

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1 answer

37

GATE DS&AI 2024 | Question: 35
Consider the following sorting algorithms: Bubble sort Insertion sort Selection sort Which ONE among the following choices of sorting algorithms sorts the numbers in the array $[4,3,2,1,5]$ in increasing order after exactly two passes over the array? $\text{(i)}$ only $\text{(iii)}$ only $\text{(i)}$ and $\text{(iii)}$ only $\text{(ii)}$ and $\text{(iii)}$ only

Rahiman159 answered in Algorithms Feb 17

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1 answer

38

GATE DS&AI 2024 | Question: 30
Let $F(n)$ denote the maximum number of comparisons made while searching for an entry in a sorted array of size $n$ using binary search. Which ONE of the following options is TRUE? $F(n)=F(\lfloor n / 2\rfloor)+1$ $F(n)=F(\lfloor n / 2\rfloor)+F(\lceil n / 2\rceil)$ $F(n)=F(\lfloor n / 2\rfloor)$ $F(n)=F(n-1)+1$

NarutoUzumaki answered in Algorithms Feb 16

by NarutoUzumaki

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1 answer

39

GATE CSE 2024 | Set 1 | Question: 31
An array $[82,101,90,11,111,75,33,131,44,93]$ is heapified. Which one of the following options represents the first three elements in the heapified array? $82,90,101$ $82,11,93$ $131,11,93$ $131,111,90$

shishir__roy answered in Algorithms Feb 16

by shishir__roy

2.1k views

1 vote

1 answer

40

GATE CSE 2024 | Set 2 | Question: 29
You are given a set $V$ of distinct integers. A binary search tree $T$ is created by inserting all elements of $V$ one by one, starting with an empty tree. The tree $T$ follows the convention that, at each node, all values ... determined from $V$ Preorder traversal of $T$ can be determined from $V$ Postorder traversal of $T$ can be determined from $V$

supreetshukla answered in Algorithms Feb 16

by supreetshukla

1.8k views

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