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

36 votes

5 answers

4351

GATE CSE 2007 | Question: 41
In an unweighted, undirected connected graph, the shortest path from a node $S$ to every other node is computed most efficiently, in terms of time complexity, by Dijkstra’s algorithm starting from $S$. Warshall’s algorithm. Performing a DFS starting from $S$. Performing a BFS starting from $S$.

In an unweighted, undirected connected graph, the shortest path from a node $S$ to every other node is computed most efficiently, in terms of time complexity, byDijkstra�...

18.6k views

Kathleen asked Sep 21, 2014

24 votes

4 answers

4352

GATE CSE 2007 | Question: 14
Which of the following sorting algorithms has the lowest worse-case complexity? Merge sort Bubble sort Quick sort Selection sort

Which of the following sorting algorithms has the lowest worse-case complexity?Merge sortBubble sortQuick sortSelection sort

10.9k views

Kathleen asked Sep 21, 2014

47 votes

7 answers

4353

GATE CSE 2004 | Question: 84
The recurrence equation $ T(1) = 1$ $T(n) = 2T(n-1) + n, n \geq 2$ evaluates to $2^{n+1} - n - 2$ $2^n - n$ $2^{n+1} - 2n - 2$ $2^n + n $

The recurrence equation$ T(1) = 1$$T(n) = 2T(n-1) + n, n \geq 2$evaluates to$2^{n+1} - n - 2$$2^n - n$$2^{n+1} - 2n - 2$$2^n + n $

17.6k views

Kathleen asked Sep 18, 2014

31 votes

6 answers

4354

GATE CSE 2004 | Question: 83, ISRO2015-40
The time complexity of the following C function is (assume $n > 0$) int recursive (int n) { if(n == 1) return (1); else return (recursive (n-1) + recursive (n-1)); } $O(n)$ $O(n \log n)$ $O(n^2)$ $O(2^n)$

The time complexity of the following C function is (assume $n 0$)int recursive (int n) { if(n == 1) return (1); else return (recursive (n-1) + recursive (n-1)); }$O(n)$$...

19.4k views

Kathleen asked Sep 18, 2014

66 votes

13 answers

4355

GATE CSE 2004 | Question: 82
Let $A[1,\ldots,n]$ be an array storing a bit ($1$ or $0$) at each location, and $f(m)$ is a function whose time complexity is $\Theta(m)$. Consider the following program fragment written in a C like language: counter = 0; for (i=1; i<=n; i++) { if ( ... The complexity of this program fragment is $\Omega(n^2)$ $\Omega (n\log n) \text{ and } O(n^2)$ $\Theta(n)$ $o(n)$

Let $A[1,\ldots,n]$ be an array storing a bit ($1$ or $0$) at each location, and $f(m)$ is a function whose time complexity is $\Theta(m)$. Consider the following program...

20.3k views

Kathleen asked Sep 18, 2014

55 votes

11 answers

4356

GATE CSE 2004 | Question: 81
Let $G_1=(V,E_1)$ and $G_2 =(V,E_2)$ be connected graphs on the same vertex set $V$ with more than two vertices. If $G_1 \cap G_2= (V,E_1\cap E_2)$ is not a connected graph, then the graph $G_1\cup G_2=(V,E_1\cup E_2)$ cannot have a cut vertex must have a cycle must have a cut-edge (bridge) has chromatic number strictly greater than those of $G_1$ and $G_2$

Let $G_1=(V,E_1)$ and $G_2 =(V,E_2)$ be connected graphs on the same vertex set $V$ with more than two vertices. If $G_1 \cap G_2= (V,E_1\cap E_2)$ is not a connected gr...

11.9k views

Kathleen asked Sep 18, 2014

37 votes

3 answers

4357

GATE CSE 2004 | Question: 44
Suppose we run Dijkstra’s single source shortest path algorithm on the following edge-weighted directed graph with vertex $P$ as the source. In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized? $P,Q,R,S,T,U$ $P,Q,R,U,S,T$ $P,Q,R,U,T,S$ $P,Q,T,R,U,S$

Suppose we run Dijkstra’s single source shortest path algorithm on the following edge-weighted directed graph with vertex $P$ as the source.In what order do the nodes g...

15.6k views

Kathleen asked Sep 18, 2014

33 votes

6 answers

4358

GATE CSE 2004 | Question: 42
What does the following algorithm approximate? (Assume $m > 1, \epsilon >0$). x = m; y = 1; While (x-y > ϵ) { x = (x+y)/2; y = m/x; } print(x); $\log \, m$ $m^2$ $m^{\frac{1}{2}}$ $m^{\frac{1}{3}}$

What does the following algorithm approximate? (Assume $m 1, \epsilon >0$).x = m; y = 1; While (x-y ϵ) { x = (x+y)/2; y = m/x; } print(x);$\log \, m$$m^2$$m^{\frac{1}{...

14.3k views

Kathleen asked Sep 18, 2014

15 votes

3 answers

4359

GATE CSE 2004 | Question: 41
Consider the following C program main() { int x, y, m, n; scanf("%d %d", &x, &y); /* Assume x>0 and y>0*/ m = x; n = y; while(m != n) { if (m > n) m = m-n; else n = n-m; } printf(" ... $x+y$ using repeated subtraction $x \mod y$ using repeated subtraction the greatest common divisor of $x$ and $y$ the least common multiple of $x$ and $y$

Consider the following C programmain() { int x, y, m, n; scanf("%d %d", &x, &y); /* Assume x>0 and y>0*/ m = x; n = y; while(m != n) { if (m n) m = m-n; else n = n-m; } ...

8.0k views

Kathleen asked Sep 18, 2014

42 votes

4 answers

4360

GATE CSE 2004 | Question: 39
Two matrices $M_1$ and $M_2$ are to be stored in arrays $A$ and $B$ ... column-major order best if both are in row-major order best if both are in column-major order independent of the storage scheme

Two matrices $M_1$ and $M_2$ are to be stored in arrays $A$ and $B$ respectively. Each array can be stored either in row-major or column-major order in contiguous memory ...

12.1k views

Kathleen asked Sep 18, 2014

15 votes

7 answers

4361

GATE CSE 2004 | Question: 30, ISRO2017-10
The problem $\text{3-SAT}$ and $\text{2-SAT}$ are both in $\text{P}$ both $\text{NP}$ complete $\text{NP}$-complete and in $\text{P}$ respectively undecidable and $\text{NP}$ complete respectively

The problem $\text{3-SAT}$ and $\text{2-SAT}$ are both in $\text{P}$both $\text{NP}$ complete$\text{NP}$-complete and in $\text{P}$ respectivelyundecidable and $\text{NP}...

11.8k views

Kathleen asked Sep 18, 2014

77 votes

5 answers

4362

GATE CSE 2004 | Question: 29
The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order of $n$ $n^2$ $n \log n$ $n \log^2n$

The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order of$n$$n^2$$n \log n$$n \log^2n$

33.5k views

Kathleen asked Sep 18, 2014

59 votes

7 answers

4363

GATE CSE 2006 | Question: 17
An element in an array $X$ is called a leader if it is greater than all elements to the right of it in $X$. The best algorithm to find all leaders in an array solves it in linear time using a left to right pass of the array solves it in linear time using ... pass of the array solves it using divide and conquer in time $\Theta (n\log n)$ solves it in time $\Theta( n^2)$

An element in an array $X$ is called a leader if it is greater than all elements to the right of it in $X$. The best algorithm to find all leaders in an array solves it i...

17.9k views

Rucha Shelke asked Sep 17, 2014

21 votes

5 answers

4364

GATE CSE 2006 | Question: 16, ISRO-DEC2017-27
Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of the following statements is true? R is NP-complete R is NP-hard Q is NP-complete Q is NP-hard

Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Whic...

18.1k views

Rucha Shelke asked Sep 17, 2014

35 votes

10 answers

4365

GATE CSE 2006 | Question: 15
Consider the following C-program fragment in which $i$, $j$ and $n$ are integer variables. for( i = n, j = 0; i > 0; i /= 2, j +=i ); Let $val(j)$ denote the value stored in the variable $j$ after termination of the for loop. Which one of the following is true? $val(j)=\Theta(\log n)$ $val(j)=\Theta (\sqrt{n})$ $val(j)=\Theta( n)$ $val(j)=\Theta (n\log n)$

Consider the following C-program fragment in which $i$, $j$ and $n$ are integer variables. for( i = n, j = 0; i 0; i /= 2, j +=i );Let $val(j)$ denote the value stored i...

19.5k views

Rucha Shelke asked Sep 17, 2014

39 votes

4 answers

4366

GATE CSE 2006 | Question: 14, ISRO2011-14
Which one of the following in place sorting algorithms needs the minimum number of swaps? Quick sort Insertion sort Selection sort Heap sort

Which one of the following in place sorting algorithms needs the minimum number of swaps?Quick sortInsertion sortSelection sortHeap sort

25.4k views

Rucha Shelke asked Sep 17, 2014

56 votes

7 answers

4367

GATE CSE 2003 | Question: 88
In the following $C$ program fragment, $j$, $k$, $n$ and TwoLog_n are integer variables, and $A$ is an array of integers. The variable $n$ is initialized to an integer $\geqslant 3$, and TwoLog_n is initialized to the value of $2^*\lceil \log_2(n) \rceil$ for (k = 3; k ... $\left\{m \mid m \leq n, \text{m is prime} \right\}$ { }

In the following $C$ program fragment, $j$, $k$, $n$ and TwoLog_n are integer variables, and $A$ is an array of integers. The variable $n$ is initialized to an integer $\...

12.3k views

Kathleen asked Sep 17, 2014

61 votes

4 answers

4368

GATE CSE 2003 | Question: 70
Let $G= (V,E)$ be a directed graph with $n$ vertices. A path from $v_i$ to $v_j$ in $G$ is a sequence of vertices ($v_{i},v_{i+1}, \dots , v_j$) such that $(v_k, v_{k+1}) \in E$ for all $k$ in $i$ through $j-1$. A simple path is a path in ... length from $j$ to $k$ If there exists a path from $j$ to $k$, every simple path from $j$ to $k$ contains at most $A[j,k]$ edges

Let $G= (V,E)$ be a directed graph with $n$ vertices. A path from $v_i$ to $v_j$ in $G$ is a sequence of vertices ($v_{i},v_{i+1}, \dots , v_j$) such that $(v_k, v_{k+1})...

17.6k views

Kathleen asked Sep 17, 2014

50 votes

11 answers

4369

GATE CSE 2003 | Question: 69
The following are the starting and ending times of activities $A, B, C, D, E, F, G$ and $H$ ... a room only if the room is reserved for the activity for its entire duration. What is the minimum number of rooms required? $3$ $4$ $5$ $6$

The following are the starting and ending times of activities $A, B, C, D, E, F, G$ and $H$ respectively in chronological order: $“a_s \: b_s \: c_s \: a_e \: d_s \: c_...

14.4k views

Kathleen asked Sep 17, 2014

25 votes

3 answers

4370

GATE CSE 2003 | Question: 68
What is the weight of a minimum spanning tree of the following graph? $29$ $31$ $38$ $41$

What is the weight of a minimum spanning tree of the following graph?$29$$31$$38$$41$

7.6k views

Kathleen asked Sep 17, 2014

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