Answers by soujanyareddy13 / GATE Overflow for GATE CSE

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121

CMI2013-A-05
You have $n$ lists, each consisting of $m$ integers sorted in ascending order. Merging these lists into a single sorted list will take time: $O(nm \log m)$ $O(mn \log n)$ $O(m + n)$ $O(mn)$

You have $n$ lists, each consisting of $m$ integers sorted in ascending order. Merging these lists into a single sorted list will take time:$O(nm \log m)$$O(mn \log n)$...

6.8k views

answered May 7, 2021

0 votes

122

CMI2013-A-04
Consider the set of all words over the alphabet $\{x, y, z\}$ where the number of $y$’s is not divisible by 2 or 7 and no $x$ appears after a $z$. This language is: regular not known to be regular context-free but not regular recursively enumerable but not context-free

Consider the set of all words over the alphabet $\{x, y, z\}$ where the number of $y$’s is not divisible by 2 or 7 and no $x$ appears after a $z$. This language is:...

376 views

answered May 7, 2021

0 votes

123

CMI2013-A-03
When a user submits a query, a search engine does the following. For every webpage that has been visited by the search engine, it computes a score indicating how relevant that page is to the query. Finally, it reports the pages with the top k scores on the ... the user. A good data structure for accumulating the scores and ranking them is: a queue a heap a stack a binary search tree

When a user submits a query, a search engine does the following. For every webpage that has been visited by the search engine, it computes a score indicating how relevant...

1.2k views

answered May 7, 2021

0 votes

124

CMI2013-A-02
$10\%$ of all email you receive is spam. Your spam filter is $90\%$ reliable: that is, $90\%$ of the mails it marks as spam are indeed spam and $90\%$ of spam mails are correctly labeled as spam. If you see a mail marked spam by your filter, what is the probability that it really is spam? $10\%$ $50\%$ $70\%$ $90\%$

$10\%$ of all email you receive is spam. Your spam filter is $90\%$ reliable: that is, $90\%$ of the mails it marks as spam are indeed spam and $90\%$ of spam mails are c...

7.9k views

answered May 7, 2021

0 votes

125

CMI2013-A-01
Ball Mart has $10^7$ different items in stock across all its stores worldwide. The company has collected billing data for $10^{10}$ customer transactions. Each individual bill has at most $10$ distinct items in it. Ball Mart's CEO wants to optimize the company's ... the most precise upper bound one can compute for the number of such items, given the data? $500$ $1000$ $5000$ $20000$

Ball Mart has $10^7$ different items in stock across all its stores worldwide. The company has collected billing data for $10^{10}$ customer transactions. Each individual...

676 views

answered May 7, 2021

0 votes

126

CMI2014-B-07c
Consider the code below, defining the function $A$: A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if (n == 0) return m; else return A(m, A(m,n-1,p), p-1); } Compute $A(2, 2, 3)$ and $A(2, 3, 3)$.

Consider the code below, defining the function $A$:A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if ...

640 views

answered May 7, 2021

0 votes

127

CMI2014-B-07b
Consider the code below, defining the function $A$: A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if (n == 0) return m; else return A(m, A(m,n-1,p), p-1); } Express $A(m, n, 2)$ as a function of $m$ and $n$.

Consider the code below, defining the function $A$:A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if ...

651 views

answered May 7, 2021

0 votes

128

CMI2014-B-07a
Consider the code below, defining the function $A$: A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if (n == 0) return m; else return A(m, A(m,n-1,p), p-1); } Express $A(m, n, 1)$ as a function of $m$ and $n$.

Consider the code below, defining the function $A$:A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if ...

666 views

answered May 7, 2021

0 votes

129

CMI2014-B-06b
Let $A$ be array of $n$ integers that is not assumed to be sorted. You are given a number $x$. The aim is to find out if there are indices $k,\: l$ and $m$ such that $A[k] + A[l] + A[m] = x$. Design an algorithm for this problem that works in time $O(n^2)$.

Let $A$ be array of $n$ integers that is not assumed to be sorted. You are given a number $x$. The aim is to find out if there are indices $k,\: l$ and $m$ such that $A[...

449 views

answered May 7, 2021

0 votes

130

CMI2014-B-06a
Let $A$ be an array of $n$ integers, sorted so that $A[1] \leq A[2] \leq \dots \leq A[n]$. You are given a number $x$x. The aim is to find out if there are indices $k$ and $l$ such that $A[k] + A[l] = x$. Design an algorithm for this problem that works in time $O(n)$.

Let $A$ be an array of $n$ integers, sorted so that $A \leq A \leq \dots \leq A[n]$. You are given a number $x$x. The aim is to find out if there are indices $k$ and $l...

443 views

answered May 7, 2021

0 votes

131

CMI2014-B-05
At the end of its fifth successful season, the Siruseri Premier League is planning to give an award to the Most Improved Batsman over the five years. For this, an Improvement Index will be computed for each batsman. This is defined as the longest ... to compute the Improvement Index for a batsman with an overall sequence of $n$ scores. Analyze the complexity of your algorithm.

At the end of its fifth successful season, the Siruseri Premier League is planning to give an award to the Most Improved Batsman over the five years. For this, an Improve...

536 views

answered May 7, 2021

0 votes

132

CMI2014-B-04
The frequency of a number in an array is the number of times it appears in the array. Describe an algorithm that finds the most frequent number in an array of $n$ numbers. If there are multiple numbers with highest frequency then list them all. Analyze the complexity of your algorithm.

The frequency of a number in an array is the number of times it appears in the array. Describe an algorithm that finds the most frequent number in an array of $n$ numbers...

472 views

answered May 7, 2021

0 votes

133

CMI2014-B-03
$\text{Air CMI }$operates direct flights between different cities. For any pair of cities $A$ and $B$, there is at most one flight in a day from $A$ to $B$. The online site $FakeTrip$ is tryingto compile a list of all routes available ... list all pairs of cities connected by a route on which all connections are feasible within the same day. Analyze the complexity of your algorithm.

$\text{Air CMI }$operates direct flights between different cities. For any pair of cities $A$ and $B$, there is at most one flight in a day from $A$ to $B$. The online si...

486 views

answered May 7, 2021

0 votes

134

CMI2014-B-01
Let $A$ be a regular language. Consider the following operations on $A$: $2A:=\{xy \mid x, \: y \in A \text{ and } x=y\}$ $A^2 :=\{xy \mid x, \: y \in A\}$ One of these operations necessarily leads to a regular language and the ... that it is regular. For the non-regular operation, give an example of an $A$ such that applying the operation on it results in a non-regular language.

Let $A$ be a regular language. Consider the following operations on $A$:$2A:=\{xy \mid x, \: y \in A \text{ and } x=y\}$$A^2 :=\{xy \mid x, \: y \in A\}$One of these oper...

842 views

answered May 7, 2021

0 votes

135

CMI2014-A-10
Avinash is taller than Abhay. Bharat is taller than Vinu and Vinay is taller than Bharat. Which of the following is a minimal set of additional information that can determine the tallest person? Vinay is taller than Avinash and Abhay is taller than Bharat. Avinash is taller than Vinay. Abhay is shorter than Vinay. None of the above.

Avinash is taller than Abhay. Bharat is taller than Vinu and Vinay is taller than Bharat. Which of the following is a minimal set of additional information that can deter...

752 views

answered May 7, 2021

0 votes

136

CMI2014-A-09
A company is due to send a shipment to a client and the CEO has resigned. To select a new CEO, some candidates have been interviewed. One of them will be chosen through a vote. If the workers union resort to a strike and the candidates have to be ... B). If the workers union resorted to a strike, then the number of voters was greater than or equal to the number of abstainers.

A company is due to send a shipment to a client and the CEO has resigned. To select a new CEO, some candidates have been interviewed. One of them will be chosen through a...

567 views

answered May 7, 2021

0 votes

137

CMI2014-A-08
What are the possible values of $gcd(7p + 94,\: 7p^2 + 97p + 47)$, where $p$ is an arbitrary integer? Either $1$ or $94$ Either $94$ or $47$ Either $1$ or $47$ None of these

What are the possible values of $gcd(7p + 94,\: 7p^2 + 97p + 47)$, where $p$ is an arbitrary integer?Either $1$ or $94$Either $94$ or $47$Either $1$ or $47$None of these

533 views

answered May 7, 2021

0 votes

138

CMI2014-A-07
Let $M$ be the maximum number of unit disks (disks of radius $1$) that can be placed inside a disk of radius $10$ so that each unit disk lies entirely within the larger disk and no two unit disks overlap. Then: $M < 25$ $25 \leq M < 40$ $40 \leq M < 55$ $M \geq 55$

Let $M$ be the maximum number of unit disks (disks of radius $1$) that can be placed inside a disk of radius $10$ so that each unit disk lies entirely within the larger d...

606 views

answered May 7, 2021

0 votes

139

CMI2014-A-05
Let $\Sigma = \{a, b\}$. For a word $w \: \: \in \Sigma^*$ let $n_a(x)$ denote the number of $a$'s in $w$ and let $n_b(x)$ denote the number of $b$'s in $w$ ... $L$? $L$ is regular, but not context-free $L$ is context-free, but not regular $L$ is $\Sigma^*$ None of these

Let $\Sigma = \{a, b\}$. For a word $w \: \: \in \Sigma^*$ let $n_a(x)$ denote the number of $a$'s in $w$ and let $n_b(x)$ denote the number of $b$'s in $w$. Consider the...

660 views

answered May 7, 2021

1 votes

140

CMI2014-A-04
Alan's task is to design an algorithm for a decision problem $P$. He knows that there is an algorithm $A$ that transforms instances of $P$ to instances of the Halting Problem such that $\text{yes}$ instances of $P$ map to $\text{yes}$ instances of the ... $A$ says nothing about whether there is an algorithm for $P$. The Halting Problem can be solved using $A$.

Alan’s task is to design an algorithm for a decision problem $P$. He knows that there is an algorithm $A$ that transforms instances of $P$ to instances of the Halting P...

676 views

answered May 7, 2021

0 votes

141

CMI2014-A-03
In the code fragment on the right, start and end are integer values and $\text{prime}(x)$ is a function that returns true if $x$ is a prime number and $\text{false}$ otherwise. At the end of the loop: i := 0; j := 0; k := 0; for (m := start; m <= end; m := m+1){ k := k + m ... + m; }else{ j := j + m; } } $k < i+j$ $k = i+j$ $k > i+j$ Depends on $\text{start}$ and $\text{end}$

In the code fragment on the right, start and end are integer values and $\text{prime}(x)$ is a function that returns true if $x$ is a prime number and $\text{false}$ othe...

917 views

answered May 7, 2021

0 votes

142

CMI2014-A-02
The $12$ houses on one side of a street are numbered with even numbers starting at $2$ and going up to $24$. A free newspaper is delivered on Monday to $3$ different houses chosen at random from these $12$. Find the probability that at least $2$ of these newspapers are delivered to ... with numbers strictly greater than $14$. $\frac{7}{11}$ $\frac{5}{12}$ $\frac{4}{11}$ $\frac{5}{22}$

The $12$ houses on one side of a street are numbered with even numbers starting at $2$ and going up to $24$. A free newspaper is delivered on Monday to $3$ different hous...

2.2k views

answered May 7, 2021

0 votes

143

CMI2014-A-01
For the inter-hostel six-a-side football tournament, a team of $6$ players is to be chosen from $11$ players consisting of $5$ forwards, $4$ defenders and $2$ goalkeepers. The team must include at least $2$ forwards, at least $2$ defenders and at least $1$ goalkeeper. Find the number of different ways in which the team can be chosen. $260$ $340$ $720$ $440$

For the inter-hostel six-a-side football tournament, a team of $6$ players is to be chosen from $11$ players consisting of $5$ forwards, $4$ defenders and $2$ goalkeepers...

2.4k views

answered May 7, 2021

0 votes

144

CMI2017-A-05
Let $G$ be an arbitrary graph on $n$ vertices with $4n − 16$ edges. Consider the following statements: There is a vertex of degree smaller than $8$ in $G$. There is a vertex such that there are less than $16$ vertices at a distance exactly $2$ from it. Which of the following is true: I Only II Only Both I and II Neither I nor II

Let $G$ be an arbitrary graph on $n$ vertices with $4n − 16$ edges. Consider the following statements:There is a vertex of degree smaller than $8$ in $G$.There is a ver...

1.2k views

answered May 7, 2021

0 votes

145

CMI2016-B-2b
A $\textit{simple path}$ (respectively cycle) in a graph is a path (respectively cycle) in which no edge or vertex is repeated. The $length$ of such a path (respectively cycle) is the number of edges in the path (respectively cycle). Let $G$ be an undirected graph with minimum degree $k \geq 2$. Show that $G$ contains a simple cycle of length at least $k+1$.

A $\textit{simple path}$ (respectively cycle) in a graph is a path (respectively cycle) in which no edge or vertex is repeated. The $length$ of such a path (respectively ...

474 views

answered May 7, 2021

0 votes

146

CMI2016-B-2a
A $\textit{simple path}$ (respectively cycle) in a graph is a path (respectively cycle) in which no edge or vertex is repeated. The $\textit{length}$ of such a path (respectively cycle) is the number of edges in the path (respectively cycle). Let $G$ be an undirected graph with minimum degree $k \geq 2$. Show that $G$ contains a simple path of length at least $k$.

A $\textit{simple path}$ (respectively cycle) in a graph is a path (respectively cycle) in which no edge or vertex is repeated. The $\textit{length}$ of such a path (resp...

521 views

answered May 7, 2021

0 votes

147

CMI2015-B-06c
Consider the code below, defining the functions $f$ and $g$: f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n == 0) return m; else { q = m div 10; r = m mod 10; return g(f(f(q, 0), r), n-1); } } How much time does it take to compute $f(m, n)$ and $g(m, n)$?

Consider the code below, defining the functions $f$ and $g$:f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n ...

721 views

answered May 7, 2021

0 votes

148

CMI2015-B-06b
Consider the code below, defining the functions $f$ and $g$: f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n == 0) return m; else { q = m div 10; r = m mod 10; return g(f(f(q, 0), r), n-1); } } What does $g(m, n)$ compute, for nonnegative numbers $m$ and $n$?

Consider the code below, defining the functions $f$ and $g$:f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n ...

567 views

answered May 7, 2021

0 votes

149

CMI2015-B-06a
Consider the code below, defining the functions $f$ and $g$: f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n == 0) return m; else { q = m div 10; r = m mod 10; return g(f(f(q, 0), r), n-1); } } Compute $g(3, 7), \: g(345, 1), \: g(345, 4) \text{ and } \: g(345, 0)$.

Consider the code below, defining the functions $f$ and $g$:f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n ...

523 views

answered May 7, 2021

0 votes

150

CMI2015-A-10
The school athletics coach has to choose $4$ students for the relay team. He calculates that there are $3876$ ways of choosing the team if the order in which the runners are placed is not considered. How many ways are there of choosing the team if the order of the runners is to be ... $12,000$ and $25,000$ Between $75,000$ and $99,999$ Between $30,000$ and $60,000$ More than $100,000$

The school athletics coach has to choose $4$ students for the relay team. He calculates that there are $3876$ ways of choosing the team if the order in which the runners ...

737 views

answered May 6, 2021

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