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Searching, Sorting, Hashing, Asymptotic worst case time and Space complexity, Algorithm design techniques: Greedy, Dynamic programming, and Divide‐and‐conquer, Graph search, Minimum spanning trees, Shortest paths.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 2 &3&2&3&2&0&2&2&3&3&0&2.2&3
\\\hline\textbf{2 Marks Count} & 2 &3&4&4&2&4&2&3&2&3&2&2.9&4
\\\hline\textbf{Total Marks} & 6 &9&10&11&6&8&6&8&7&9&\bf{6}&\bf{8}&\bf{11}\\\hline
\end{array}}}$$

Recent questions in Algorithms

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1

Output Of C Program
#include<stdio.h> int main(){ int x,sum; sum=0; for(x=0;x<=500;x+=10){ sum=sum+x; } printf("%d",sum); return 0; } What is output of above C-program? Actually, Answer when compiled on computer is 12750. But i want explanation about How for loop is running and what is behaviour of sum value ?

ShubhamMeher asked in Algorithms 4 days ago

by ShubhamMeher

61 views

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1 answer

2

Consider a divide and conquer algorithm that divides an input of size n into a subproblems, each of size n/b, and the cost of dividing and merging the problems is given by f(n) = Θ(n^c). The Master Theorem classifies this into different cases based on the value of c in relation to log_b(a). Could you explain the intuition and reasoning behind these classifications?

dhruba asked in Algorithms 6 days ago

by dhruba

83 views

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3

Çșȇ ʛấẗẻ asked in Algorithms May 11

by Çșȇ ʛấẗẻ

60 views

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4

Sort the following array using quicksort algorithm. [40,11,4,72,17,2,49]
Sort the following array using quicksort algorithm. [40,11,4,72,17,2,49]

Ajink123 asked in Algorithms May 10

76 views

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5

(x+k)^m=O(x^m) is true or false for x and k being constants?

James_Gosling asked in Algorithms Apr 25

by James_Gosling

101 views

1 vote

1 answer

6

GO Classes 2023 | IIITH Mock Test 3 | Question: 10
Suppose you are given the following set of keys to insert into a hash table that holds exactly $10$ values: $13, 107, 49 , 50 , 64 , 98 , 16 , 33.$ Which of the following best demonstrates the contents of the hash table after all the keys have been inserted using linear ... $50\;-\;-\;33\;64\;13\;16\;107\;98\;49$

GO Classes asked in Algorithms Apr 15

158 views

1 vote

1 answer

7

GO Classes 2023 | IIITH Mock Test 3 | Question: 11
Maximum Subarray Sum problem is to find the subarray with maximum sum. For example, given an array $\{12, -13, -5, 25, -20, 30, 10\}$, the maximum subarray sum is $45$. The best possible algorithm to compute the maximum subarray sum will run in (Mark all the appropriate choices) $O(n)$ $\Omega(n \log n)$ $O( \log n)$ $O(n^2)$

GO Classes asked in Algorithms Apr 15

234 views

1 vote

0 answers

8

GO Classes 2023 | IIITH Mock Test 3 | Question: 12
Consider the following functions $\log_{10}n, \log_2 n, \lceil \log_2 n \rceil, \lfloor \log_2 n \rfloor $ Which of the following is/are TRUE? (Mark all the appropriate choices) $\log_{10} n=O(\log_2 n)$ ... $\lceil \log_2 n \rceil = \Omega(\lfloor \log_2 n \rfloor)$

GO Classes asked in Algorithms Apr 15

204 views

1 vote

1 answer

9

GO Classes 2023 | IIITH Mock Test 3 | Question: 13
Given a directed graph where weight of every edge is same, we can efficiently find the shortest path from a given source to destination using _______ Breadth First Traversal Dijkstra's Shortest Path Algorithm Bellman-Ford Algorithm Depth First Search

GO Classes asked in Algorithms Apr 15

123 views

1 vote

1 answer

10

GO Classes 2023 | IIITH Mock Test 3 | Question: 14
Consider the DAG $G$ with vertex set $V = \{a, b, c, d, e, f, g\}$ given below. Which of the following is/are a topological ordering of $G$? (Mark all the correct options) $a \ b \ c \ d \ e \ f \ g$ $a \ c \ b \ e \ f \ d \ g$ $a \ c \ b \ d \ f \ e \ g$ $a \ c \ b \ f \ e \ g\ d$

GO Classes asked in Algorithms Apr 15

125 views

1 vote

1 answer

11

GO Classes 2023 | IIITH Mock Test 3 | Question: 15
Consider a undirected graph $G$ with $n$ vertices and every edge weight being distinct. Edge $e_1$ is edge with minimum weight and edge $e_2$ is edge with maximum weight. Then, which of the following is/are FALSE? (Mark all the ... No minimum spanning tree contains $e_2$ $G$ has a unique minimum spanning tree if $e_2$ is in a minimum spanning tree

GO Classes asked in Algorithms Apr 15

217 views

2 votes

1 answer

12

GO Classes 2023 | IIITH Mock Test 3 | Question: 18
The time complexity of the below code is int isPalindrome ( char * string, int n ) { if (n <= 1) return 1; if (string[0] != string[n-1]) return 0; return isPalindrome(string + 1, n-2); } $\Theta(n)$ $\Theta (n \log n)$ $\Theta(\log n)$ $\Theta(n^2)$

GO Classes asked in Algorithms Apr 15

197 views

2 votes

1 answer

13

GO Classes 2023 | IIITH Mock Test 3 | Question: 24
Consider $4$ characters $a,b,c$ and $d.$ Below are the corresponding codes to encode these characters. $a=\;<00>, b=\;<01>, c=\;<11>, d=\;<101>.$ ... $\mathrm{S} 1$ is not true but $\mathrm{S} 2$ is true Both are true Both are false

GO Classes asked in Algorithms Apr 15

204 views

2 votes

1 answer

14

GO Classes 2023 | IIITH Mock Test 2 | Question: 62
Consider a source which outputs independent random letters from the alphabet $A=$ $\{a, b, c, d, e\}$ with probabilities $p_{a}=1 / 4, p_{b}=1 / 4, p_{c}=1 / 6, p_{d}=1 / 6$ and $p_{e}=1 / 6$. Let $L_{3}$ be the random ... sequence of $3$ letters from that source. Compute the expectation $\mathbb{E}\left(L_{3}\right)$. $7$ $6$ $7 / 3$ $5 / 3$

GO Classes asked in Algorithms Apr 8

233 views

1 vote

1 answer

15

GO Classes 2023 | IIITH Mock Test 2 | Question: 63
Given an undirected, weighted graph $\mathrm{G}$ with positive, integer edge weights, we want to find a path shortest path from $u$ to $v$ with the below condition. The condition is as follows as: If two paths from $u$ to $v$ are of ... not always possible to get the same shortest path in $\text{G}$ and $\text{G}^{\prime}$ by adding any constant.

GO Classes asked in Algorithms Apr 8

162 views

2 votes

1 answer

16

GO Classes 2023 | IIITH Mock Test 2 | Question: 64
The following diagram shows the set of edges (in thick black lines) selected at some intermediate step of an MST algorithm. Lighter edges are not yet in MST. Assume that we got above the intermediate state using Kruskal’s algorithm. What would be the maximum value of $x+y-z ?$ $100$ $110$ $120$ $130$

GO Classes asked in Algorithms Apr 8

294 views

1 vote

1 answer

17

GO Classes 2023 | IIITH Mock Test 2 | Question: 65
Let $T(n)=2 T(n / 2)+O(n)$, where "$O$" is big-oh. What will be asymptotic bound on $T(n)?$ $\Theta(n)$ $\Theta(n \log n)$ $\Theta\left(n^ 2\right)$ $O\left(n^ 3\right)$

GO Classes asked in Algorithms Apr 8

418 views

1 vote

1 answer

18

GO Classes 2023 | IIITH Mock Test 2 | Question: 66
Let $ T(n)=\sqrt{n} \cdot T(\sqrt{n})+n $ What will be asymptotic bound on $T(n) ?$ $\Theta(\sqrt{n} \log n)$ $\Theta(\log \log n)$ $\Theta(n \log \log n)$ $\Theta(\sqrt{n} \log \log n)$

GO Classes asked in Algorithms Apr 8

267 views

1 vote

1 answer

19

GO Classes 2023 | IIITH Mock Test 2 | Question: 67
Suppose that a randomized algorithm succeeds with probability $p$ (with $0<p<1).$ Let $n$ be independent trials we need to run the algorithm to ensure that, with probability at least $1-\epsilon$, at least one trial succeeds. Which of the following relation ... $1-p^{n} \leq \epsilon$ $p^{n} \leq \epsilon$ $p^{n} \leq \epsilon$

GO Classes asked in Algorithms Apr 8

177 views

1 vote

0 answers

20

GO Classes 2023 | IIITH Mock Test 2 | Question: 69
Which of the following statement is/are FALSE? Assume that $\log$ base is $2$ in all options. $8^{\log \left(n^{2}\right)} \in \Theta\left(n^{6}\right)$ If $f, g$, and $h$ ... $g(n)$ is a function whose value is never negative then $g(n) T(n)$ is $O(g(n) f(n))$

GO Classes asked in Algorithms Apr 8

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