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.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&3&2&3&2&0&2&2&3&3&0&2.2&3
\\\hline\textbf{2 Marks Count}&3&4&4&2&4&2&3&2&3&2&3&4
\\\hline\textbf{Total Marks}&9&10&11&6&8&6&8&7&9&\bf{6}&\bf{8.2}&\bf{11}\\\hline
\end{array}}}$$

Recent questions in Algorithms

4 votes

3 answers

GATE CSE 2021 Set 2 | Question: 1
Let $G$ be a connected undirected weighted graph. Consider the following two statements. $S_1$: There exists a minimum weight edge in $G$ which is present in every minimum spanning tree of $G$. $S_2$: If every edge in $G$ has distinct weight, then $G$ has a ... are true $S_1$ is true and $S_2$ is false $S_1$ is false and $S_2$ is true Both $S_1$ and $S_2$ are false

Let $G$ be a connected undirected weighted graph. Consider the following two statements. $S_1$: There exists a minimum weight edge in $G$ which is present in every minimum spanning tree of $G$. $S_2$: If every edge in $G$ has distinct weight, then $G$ has a unique minimum spanning ... $S_1$ is true and $S_2$ is false $S_1$ is false and $S_2$ is true Both $S_1$ and $S_2$ are false

asked Feb 18 in Algorithms Arjun 1k views

0 votes

2 answers

GATE CSE 2021 Set 2 | Question: 8
What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size $n$? $\Theta ( \sqrt{n})$ $\Theta (\log _2(n))$ $\Theta(n^2)$ $\Theta(n)$

What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size $n$? $\Theta ( \sqrt{n})$ $\Theta (\log _2(n))$ $\Theta(n^2)$ $\Theta(n)$

asked Feb 18 in Algorithms Arjun 643 views

2 votes

2 answers

GATE CSE 2021 Set 2 | Question: 26
Consider the string $\textrm{abbccddeee}$. Each letter in the string must be assigned a binary code satisfying the following properties: For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter. ... which satisfy the above two properties, what is the minimum length of the encoded string? $21$ $23$ $25$ $30$

Consider the string $\textrm{abbccddeee}$. Each letter in the string must be assigned a binary code satisfying the following properties: For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter. For any two letters ... assignments which satisfy the above two properties, what is the minimum length of the encoded string? $21$ $23$ $25$ $30$

asked Feb 18 in Algorithms Arjun 513 views

3 votes

3 answers

GATE CSE 2021 Set 2 | Question: 39
For constants $a \geq 1$ and $b>1$, consider the following recurrence defined on the non-negative integers: $T(n) = a \cdot T \left(\dfrac{n}{b} \right) + f(n)$ Which one of the following options is correct about the recurrence $T(n)$? If $f(n)$ is $n \log_2(n)$, ... $f(n)$ is $\Theta(n^{\log_b(a)})$, then $T(n)$ is $\Theta(n^{\log_b(a)})$

For constants $a \geq 1$ and $b>1$, consider the following recurrence defined on the non-negative integers: $T(n) = a \cdot T \left(\dfrac{n}{b} \right) + f(n)$ Which one of the following options is correct about the recurrence $T(n)$? If $f(n)$ is $n \log_2(n)$, then $T(n)$ ... $\Theta(n^{\log_b(a)})$ If $f(n)$ is $\Theta(n^{\log_b(a)})$, then $T(n)$ is $\Theta(n^{\log_b(a)})$

asked Feb 18 in Algorithms Arjun 669 views

2 votes

2 answers

GATE CSE 2021 Set 2 | Question: 46
Consider the following directed graph: Which of the following is/are correct about the graph? The graph does not have a topological order A depth-first traversal starting at vertex $S$ classifies three directed edges as back edges The graph does not have a strongly connected component For each pair of vertices $u$ and $v$, there is a directed path from $u$ to $v$

Consider the following directed graph: Which of the following is/are correct about the graph? The graph does not have a topological order A depth-first traversal starting at vertex $S$ classifies three directed edges as back edges The graph does not have a strongly connected component For each pair of vertices $u$ and $v$, there is a directed path from $u$ to $v$

asked Feb 18 in Algorithms Arjun 555 views

2 votes

1 answer

GATE CSE 2021 Set 2 | Question: 55
In a directed acyclic graph with a source vertex $\textsf{s}$, the $\textit{quality-score}$ of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex $v$ other than $\textsf{s}$, the quality ... $\textsf{s}$ is assumed to be $1$. The sum of the quality-scores of all vertices on the graph shown above is _______

In a directed acyclic graph with a source vertex $\textsf{s}$, the $\textit{quality-score}$ of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex $v$ other than $\textsf{s}$, the quality-score of $v$ is ... quality-score of $\textsf{s}$ is assumed to be $1$. The sum of the quality-scores of all vertices on the graph shown above is _______

asked Feb 18 in Algorithms Arjun 559 views

2 votes

3 answers

GATE CSE 2021 Set 1 | Question: 3
Consider the following three functions. $f_1=10^n\; f_2=n^{\log n}\;f_3=n^{\sqrt {n}}$ Which one of the following options arranges the functions in the increasing order of asymptotic growth rate? $f_3, f_2, f_1$ $f_2, f_1, f_3$ $f_1, f_2,f_3$ $f_2, f_3, f_1$

Consider the following three functions. $f_1=10^n\; f_2=n^{\log n}\;f_3=n^{\sqrt {n}}$ Which one of the following options arranges the functions in the increasing order of asymptotic growth rate? $f_3, f_2, f_1$ $f_2, f_1, f_3$ $f_1, f_2,f_3$ $f_2, f_3, f_1$

asked Feb 18 in Algorithms Arjun 462 views

1 vote

3 answers

GATE CSE 2021 Set 1 | Question: 9
Consider the following array. $\begin{array}{|l|l|l|l|l|l|} \hline 23&32&45&69&72&73&89&97 \\ \hline\end{array}$ Which algorithm out of the following options uses the least number of comparisons ( ... elements) to sort the above array in ascending order? Selection sort Mergesort Insertion sort Quicksort using the last element as pivot

Consider the following array. $\begin{array}{|l|l|l|l|l|l|} \hline 23&32&45&69&72&73&89&97 \\ \hline\end{array}$ Which algorithm out of the following options uses the least number of comparisons (among the array elements) to sort the above array in ascending order? Selection sort Mergesort Insertion sort Quicksort using the last element as pivot

asked Feb 18 in Algorithms Arjun 416 views

0 votes

3 answers

GATE CSE 2021 Set 1 | Question: 17
Consider the following undirected graph with edge weights as shown: The number of minimum-weight spanning trees of the graph is ___________.

Consider the following undirected graph with edge weights as shown: The number of minimum-weight spanning trees of the graph is ___________.

asked Feb 18 in Algorithms Arjun 432 views

4 votes

5 answers

GATE CSE 2021 Set 1 | Question: 30
Consider the following recurrence relation. $T\left ( n \right )=\left\{\begin{array} {lcl} T(n/2)+T(2n/5)+7n & \text{if} \; n>0\\1 & \text{if}\; n=0 \end{array}\right.$ Which one of the following options is correct? $T(n)=\Theta (n^{5/2})$ $T(n)=\Theta (n\log n)$ $T(n)=\Theta (n)$ $T(n)=\Theta ((\log n)^{5/2})$

Consider the following recurrence relation. $T\left ( n \right )=\left\{\begin{array} {lcl} T(n/2)+T(2n/5)+7n & \text{if} \; n>0\\1 & \text{if}\; n=0 \end{array}\right.$ Which one of the following options is correct? $T(n)=\Theta (n^{5/2})$ $T(n)=\Theta (n\log n)$ $T(n)=\Theta (n)$ $T(n)=\Theta ((\log n)^{5/2})$

asked Feb 18 in Algorithms Arjun 1.2k views

1 vote

2 answers

GATE CSE 2021 Set 1 | Question: 40
Define $R_n$ to be the maximum amount earned by cutting a rod of length $n$ meters into one or more pieces of integer length and selling them. For $i>0$, let $p[i]$ denote the selling price of a rod whose length is $i$ meters. ... $R_7=18$ $R_7=19$ $R_7$ is achieved by three different solutions $R_7$ cannot be achieved by a solution consisting of three pieces

Define $R_n$ to be the maximum amount earned by cutting a rod of length $n$ meters into one or more pieces of integer length and selling them. For $i>0$, let $p[i]$ denote the selling price of a rod whose length is $i$ meters. Consider the array of prices: ... $R_7$? $R_7=18$ $R_7=19$ $R_7$ is achieved by three different solutions $R_7$ cannot be achieved by a solution consisting of three pieces

asked Feb 18 in Algorithms Arjun 868 views

0 votes

1 answer

GATE CSE 2021 Set 1 | Question: 47
Consider a $\textit{dynamic}$ hashing approach for $4$-bit integer keys: There is a main hash table of size $4$. The $2$ least significant bits of a key is used to index into the main hash table. Initially, the main hash table entries are empty. Thereafter, when more keys are hashed ... notation)? $5,9,4,13,10,7$ $9,5,10,6,7,1$ $10,9,6,7,5,13$ $9,5,13,6,10,14$

Consider a $\textit{dynamic}$ hashing approach for $4$-bit integer keys: There is a main hash table of size $4$. The $2$ least significant bits of a key is used to index into the main hash table. Initially, the main hash table entries are empty. Thereafter, when more keys are hashed into it, to resolve ... in decimal notation)? $5,9,4,13,10,7$ $9,5,10,6,7,1$ $10,9,6,7,5,13$ $9,5,13,6,10,14$

asked Feb 18 in Algorithms Arjun 383 views

0 votes

2 answers

CMI-2020-DataScience-A: 1
Consider the following program. Assume that $x$ and $y$ are integers. f(x, y) { if (y != 0) return (x * f(x,y-1)); else return 1; } What is $f(6,3)?$ $243$ $729$ $125$ $216$

Consider the following program. Assume that $x$ and $y$ are integers. f(x, y) { if (y != 0) return (x * f(x,y-1)); else return 1; } What is $f(6,3)?$ $243$ $729$ $125$ $216$

asked Jan 29 in Algorithms soujanyareddy13 74 views

1 vote

0 answers

CMI-2020-DataScience-B: 1
For any string $\text{str, length(str)}$ returns the length of the string, $\text{append(str1, str2)}$ concatenates $\text{str1}$ with another string $\text{str2}$, and $\text{trim(str)}$ removes any spaces that exist at the end of the string $\text{str}$ ... 1) { if(str[i] is ' ') { reverse(str, j, i-1); j = i + 1; } } trim(str); return str; }

For any string $\text{str, length(str)}$ returns the length of the string, $\text{append(str1, str2)}$ concatenates $\text{str1}$ with another string $\text{str2}$, and $\text{trim(str)}$ removes any spaces that exist at the end of the string $\text{str}$. The function $\text{reverse(str, i, j)}$ ... n; i=i+1) { if(str[i] is ' ') { reverse(str, j, i-1); j = i + 1; } } trim(str); return str; }

asked Jan 29 in Algorithms soujanyareddy13 39 views

0 votes

1 answer

UGCNET-Oct2020-II: 25
If algorithm $A$ and another algorithm $B$ take $\log_2 (n)$ and $\sqrt{n}$ microseconds, respectively, to solve a problem, then the largest size $n$ of a problem these algorithms can solve, respectively, in one second are ______ and ______. $2^{10^n}$ and $10^6$ $2^{10^n}$ and $10^{12}$ $2^{10^n}$ and $6.10^6$ $2^{10^n}$ and $6.10^{12}$

If algorithm $A$ and another algorithm $B$ take $\log_2 (n)$ and $\sqrt{n}$ microseconds, respectively, to solve a problem, then the largest size $n$ of a problem these algorithms can solve, respectively, in one second are ______ and ______. $2^{10^n}$ and $10^6$ $2^{10^n}$ and $10^{12}$ $2^{10^n}$ and $6.10^6$ $2^{10^n}$ and $6.10^{12}$

asked Nov 20, 2020 in Algorithms jothee 402 views

0 votes

0 answers

UGCNET-Oct2020-II: 52
The running time of an algorithm is $O(g(n))$ if and only if its worst-case running time is $O(g(n))$ and its best-case running time is $\Omega(g(n)) \cdot (O= \textit{ big }O)$ its worst-case running time is $\Omega (g(n))$ and its best-case running ... $(a)$ only $(b)$ only $(c)$ only $(d)$ only

The running time of an algorithm is $O(g(n))$ if and only if its worst-case running time is $O(g(n))$ and its best-case running time is $\Omega(g(n)) \cdot (O= \textit{ big }O)$ its worst-case running time is $\Omega (g(n))$ ... , $(o = \textit{ small } o)$ Choose the correct answer from the options given below: $(a)$ only $(b)$ only $(c)$ only $(d)$ only

asked Nov 20, 2020 in Algorithms jothee 172 views

0 votes

1 answer

UGCNET-Oct2020-II: 69
Match $\text{List I}$ with $\text{List II}$ ... $A-I, B-II, C-III, D-IV$ $A-II, B-I, C-III, D-IV$ $A-II, B-IV, C-III, D-I$

Match $\text{List I}$ with $\text{List II}$ ... $A-I, B-II, C-III, D-IV$ $A-II, B-I, C-III, D-IV$ $A-II, B-IV, C-III, D-I$

asked Nov 20, 2020 in Algorithms jothee 107 views

0 votes

2 answers

UGCNET-Oct2020-II: 70
Match $\text{list I}$ with $\text{List II}$ ... $A-III, B-I, C-IV, D-II$ $A-III, B-I, C-II, D-IV$ $A-I, B-III, C-II, D-IV$

Match $\text{list I}$ with $\text{List II}$ ... : $A-I, B-III, C-IV, D-II$ $A-III, B-I, C-IV, D-II$ $A-III, B-I, C-II, D-IV$ $A-I, B-III, C-II, D-IV$

asked Nov 20, 2020 in Algorithms jothee 107 views

0 votes

1 answer

UGCNET-Oct2020-II: 73
Match $\text{List I}$ with $\text{List II}$ ... $A-II, B-III, C-I, D-IV$ $A-III, B-II, C-IV, D-I$ $A-III, B-IV, C-II, D-I$

Match $\text{List I}$ with $\text{List II}$ ... $A-II, B-III, C-I, D-IV$ $A-III, B-II, C-IV, D-I$ $A-III, B-IV, C-II, D-I$

asked Nov 20, 2020 in Algorithms jothee 93 views

0 votes

2 answers

UGCNET-Oct2020-II: 78
Consider the undirected graph below: Using Prim's algorithm to construct a minimum spanning tree starting with node $a$ ... $(a,b), (g,h), (g,f), (c,f), (c,i), (f,e), (b,c), (d,e)$

Consider the undirected graph below: Using Prim's algorithm to construct a minimum spanning tree starting with node $a$ ... $(a,b), (g,h), (g,f), (c,f), (c,i), (f,e), (b,c), (d,e)$

asked Nov 20, 2020 in Algorithms jothee 121 views

Page:

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