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Recent questions and answers in Algorithms
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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
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14 hours
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jenilS7
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recurrence-relation
algorithms
sequence-series
0
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0
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2
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
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Algorithms
1 day
ago
by
Ujjal Das
35
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algorithms
merge-sort
0
votes
1
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3
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
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Algorithms
3 days
ago
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DEBANJAN DAS2k
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algorithms
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time-complexity
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1
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2
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4
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
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Algorithms
4 days
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by
Priyam Garg
623
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0
votes
0
answers
5
Prove that n! = Ω(n^100)
wtquevb123
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Algorithms
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ago
by
wtquevb123
30
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theory-of-computation
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time-complexity
21
votes
7
answers
6
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
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in
Algorithms
4 days
ago
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ritiksri8
7.6k
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1
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1
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7
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
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in
Algorithms
Mar 10
by
mishraamulya
235
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drdocse-2022-paper1
2-marks
descriptive
1
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2
answers
8
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
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in
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Mar 8
by
SkillIssue
1.7k
views
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5
votes
3
answers
9
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
by
teja1521
3.6k
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isro2007
algorithms
identify-function
0
votes
1
answer
10
#algorithm
how many spanning trees are possible for complete graph of 4 vertices
closed
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Mar 3
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78
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algorithms
data-structures
graph-theory
1
vote
3
answers
11
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
by
skypaul101
1.8k
views
gatecse2024-set1
algorithms
2
votes
4
answers
12
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 28
by
Priyam Garg
1.9k
views
gatecse2024-set2
algorithms
recurrence-relation
asymptotic-notation
21
votes
4
answers
13
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
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in
Algorithms
Feb 24
by
KG
11.2k
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gatecse-2023
algorithms
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2-marks
0
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0
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14
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
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in
Algorithms
Feb 23
by
tim20
58
views
algorithms
probability
0
votes
1
answer
15
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
by
ashmit.26
219
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algorithms
time-complexity
asymptotic-notation
functions
1
vote
1
answer
16
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
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in
Algorithms
Feb 20
by
gate.datascience_ai
216
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gate2024-da-memory-based
goclasses
algorithms
quick-sort
numerical-answers
1
vote
1
answer
17
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
1.5k
views
gatecse2024-set2
numerical-answers
algorithms
minimum-spanning-tree
4
votes
2
answers
18
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 18
by
minip
3.0k
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gatecse2024-set1
algorithms
multiple-selects
0
votes
1
answer
19
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? P Q R S T U V P R Q V SUT P Q R S V U T P R Q S V T U Consider the directed acyclic graph (DAG) below: Which of the ... from a topological sort of the DAG? P Q R S T U V P R Q V SUT P Q R S V U T P R Q S V T U
liontig37
answered
in
Algorithms
Feb 18
by
liontig37
645
views
gate-ds-ai-2024
algorithms
topological-sort
directed-acyclic-graph
0
votes
2
answers
20
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
by
Hira Thakur
732
views
gate-ds-ai-2024
algorithms
match-the-following
0
votes
1
answer
21
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
1.5k
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gatecse2024-set1
numerical-answers
0
votes
3
answers
22
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
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in
Algorithms
Feb 17
by
gaurav0to1
1.1k
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gate-ds-ai-2024
numerical-answers
algorithms
quick-sort
0
votes
1
answer
23
GATE DS&AI 2024 | Question: 35
Consider the following sorting algorithms: (i) Bubble sort (ii) Insertion sort (iii) 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? ... after exactly two passes over the array? (i) only (iii) only (i) and (iii) only (ii) and (iii) only
Rahiman159
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in
Algorithms
Feb 17
by
Rahiman159
768
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gate-ds-ai-2024
algorithms
sorting
0
votes
1
answer
24
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 17
by
NarutoUzumaki
747
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gate-ds-ai-2024
algorithms
binary-search
0
votes
1
answer
25
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 17
by
shishir__roy
2.0k
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gatecse2024-set1
algorithms
1
vote
1
answer
26
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 17
by
supreetshukla
1.7k
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gatecse2024-set2
algorithms
1
vote
2
answers
27
GATE CSE 2024 | Set 2 | Question: 25
Let $\text{A}$ be an array containing integer values. The distance of $\text{A}$ is defined as the minimum number of elements in $\text{A}$ that must be replaced with another integer so that the resulting array is sorted in non-decreasing order. The distance of the array $[2,5,3,1,4,2,6]$ is ___________.
supreetshukla
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Algorithms
Feb 17
by
supreetshukla
1.8k
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gatecse2024-set2
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1
vote
1
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28
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 _________.
Hira Thakur
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in
Algorithms
Feb 17
by
Hira Thakur
1.5k
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0
votes
1
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29
GATE CSE 2024 | Set 1 | Question: 7
Given an integer array of size $N$, we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass through the array and comparing each element of the array only with its adjacent elements. The ... $\Omega(N)$ but not $\mathrm{O}(N)$ neither $\mathrm{O}(N)$ nor $\Omega(N)$
shishir__roy
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in
Algorithms
Feb 17
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shishir__roy
2.8k
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4
votes
1
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30
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 46
We have a procedure $P(n)$ that makes multiple calls to a procedure $Q(m)$, and runs in polynomial time in $n$. Unfortunately, a significant flaw was discovered in $Q(m)$, and it had to be replaced by $R(m)$, which runs in exponential ... $P(n)$ runs in polynomial time in $n$ if, for each call $Q(m),m \underline<\log \;n.$
꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂
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Feb 11
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0
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0
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31
GATE 2024
Consider an n element array which is to be sorted either in ascending or descending order. The given restriction is only one pass will be used for completely sorting the array and an element can compare with only it's adjacent pair. What will be the worst time complexity? Is this related to bubble sort algorithm or not?
TusharRana
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in
Algorithms
Feb 11
by
TusharRana
329
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algorithms
sorting
2
votes
2
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32
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 20
Consider the following array$: [32, 33, 5, 2, 14, -4, 22, 39, 34, -9].$ ... sorting algorithms could we possibly have applied? Merge sort (top-down approach) Bubble sort Quicksort (Using First element as pivot) Insertion sort
Philosophical_Virus
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Algorithms
Feb 7
by
Philosophical_Virus
482
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33
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 18
Bob writes down a number between 1 and 1,000. Mary must identify that number by asking "yes/no" questions of Bob. Mary knows that Bob always tells the truth. If Mary uses an optimal strategy then she will determine that answer at the end of exactly how many questions on the worst case? 999 500 32 10
Kamlesh Maurya
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in
Algorithms
Feb 6
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Kamlesh Maurya
391
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4
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34
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 19
Which of the following frequencies for A,B,C and D can generate the following Huffman tree? (Select all that apply.) $p_A=0.4, p_B=0.3, p_C=0.2, p_D=0.1$ $p_A=0.35, p_B=0.25, p_C=0.2, p_D=0.2$ $p_A=0.25, p_B=0.25, p_C=0.25, p_D=0.25$ $p_A=0.2, p_B=0.35, p_C=0.2, p_D=0.25$
thecoderyabham
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in
Algorithms
Feb 6
by
thecoderyabham
391
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35
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 17
Consider the following function. If $n$ and $\mathrm{k}$ are positive integers, then the least value of $\mathrm{k}$ such that $\mathrm{f}(\mathrm{k})>n$ is approximately $\log _2\left(\log _2 n\right)$ $\log _2 n$ $n \log _2 n$ $2^n$
krishnajsw
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in
Algorithms
Feb 6
by
krishnajsw
432
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goclasses2024-mockgate-14
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3
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0
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36
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 47
A $\text{stable sort}$ preserves the order of values that are equal with respect to the comparison function. We have a list of three-dimensional points $[(7, 1, 8),(3, 5, 7),(6, 1, 4),(6, 5, 9),(0, 2, 5),(9, 0, 9)].$ We sort these in ascending order by the ... $[(9, 0, 9),(6, 1, 4),(7, 1, 8),(0, 2, 5),(3, 5, 7),(6, 5, 9)]$
GO Classes
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Feb 5
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GO Classes
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0
votes
0
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37
Memory Based GATE DA 2024 | Question: 18
Consider a directed acyclic graph (DAG) with vertices labeled as P, Q, R, S, T, U, and V. Which of the following sequences represents a possible topological sort of the graph? PRQVSUT PQRSVUT PQRSTUV PRQSVUT
GO Classes
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Feb 5
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GO Classes
117
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gate2024-da-memory-based
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47
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8
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38
GATE CSE 2019 | Question: 37
There are $n$ unsorted arrays: $A_1, A_2, \dots, A_n$. Assume that $n$ is odd.Each of $A_1, A_2, \dots, A_n$ contains $n$ distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of $A_1, A_2, \dots , A_n$ is $O(n)$ $O(n \: \log \: n)$ $O(n^2)$ $\Omega (n^2 \log n)$
sohamm20
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Feb 5
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sohamm20
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39
GATE CSE 2008 | Question: 45
Dijkstra's single source shortest path algorithm when run from vertex $a$ in the above graph, computes the correct shortest path distance to only vertex $a$ only vertices $a, e, f, g, h$ only vertices $a, b, c, d$ all the vertices
kirtijyotisenapati
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Jan 31
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kirtijyotisenapati
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