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Recent questions tagged cmi2019
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CMI2019A1
Let $L_{1}:=\{a^{n}b^{m}\mid m,n\geq 0\: \text{and}\: m\geq n\}$ and $L_{2}:=\{a^{n}b^{m}\mid m,n\geq 0\: \text{and}\: m < n\}.$ The language $L_{1}\cup L_{2}$ is: regular, but not contextfree contextfree, but not regular both regular and contextfree neither regular nor contextfree
asked
Sep 13, 2019
in
Theory of Computation
by
gatecse
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(
17.5k
points)

107
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cmi2019
regularlanguages
contextfreelanguages
closureproperty
0
votes
1
answer
2
CMI2019A2
Let $A$ be an $NFA$ with $n$ states. Which of the following is necessarily true? The shortest word in $L(A)$ has length at most $n1.$ The shortest word in $L(A)$ has length at least $n.$ The shortest word not in $L(A)$ has length at most $n1.$ The shortest word not in $L(A)$ has length at least $n.$
asked
Sep 13, 2019
in
Theory of Computation
by
gatecse
Boss
(
17.5k
points)

63
views
cmi2019
finiteautomata
nfadfa
+4
votes
2
answers
3
CMI2019A3
Suppose that the figure to the right is a binary search tree. The letters indicate the names of the nodes, not the values that are stored. What is the predecessor node, in terms of value, of the root node $A?$ $D$ $H$ $I$ $M$
asked
Sep 13, 2019
in
DS
by
gatecse
Boss
(
17.5k
points)

146
views
cmi2019
datastructures
trees
binarysearchtree
+2
votes
1
answer
4
CMI2019A4
There are five buckets, each of which can be open or closed. An arrangement is a specification of which buckets are open and which bucket are closed. Every person likes some of the arrangements and dislikes the rest. You host a party, and amazingly, no two people on the guest list have the ... What is the maximum number of guests possible? $5^{2}$ $\binom{5}{2}$ $2^{5}$ $2^{2^{5}}$
asked
Sep 13, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

46
views
cmi2019
permutationandcombination
arrangements
+2
votes
1
answer
5
CMI2019A5
Let $\pi=[x_{1},x_{2},\cdots,x_{n}]$ be a permutation of $\{1,2,\cdots,n\}.$ For $k<n,$ we say that $\pi$ has its first ascent at $k$ if $x_{1}>x_{2}\cdots>x_{k}$ and $x_{k}<x_{k+1}.$ How many permutations have their first ascent at $k?$ $\binom{n}{k}\binom{n}{(k+1)}$ $\frac{n!}{k!}\frac{n!}{(k+1)!}$ $\frac{n!}{(k+1)!}\frac{n!}{(k+2)!}$ $\binom{n}{(k+1)}\binom{n}{(k+2)}$
asked
Sep 13, 2019
in
Combinatory
by
gatecse
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(
17.5k
points)

46
views
cmi2019
permutationandcombination
+2
votes
2
answers
6
CMI2019A6
Suppose you alternate between throwing a normal sixsided fair die and tossing a fair coin. You start by throwing the die. What is the probability that you will see a $5$ on the die before you see tails on the coin? $\frac{1}{12}$ $\frac{1}{6}$ $\frac{2}{9}$ $\frac{2}{7}$
asked
Sep 13, 2019
in
Probability
by
gatecse
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(
17.5k
points)

121
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cmi2019
probability
+1
vote
1
answer
7
CMI2019A7
An interschool basketball tournament is being held at the Olympic sports complex. There are multiple basketball courts. Matches are scheduled in parallel, with staggered timings, to ensure that spectators always have some match or other available to watch. Each match ... solve? Find a minimal colouring. Find a minimal spanning tree. Find a minimal cut. Find a minimal vertex cover.
asked
Sep 13, 2019
in
Graph Theory
by
gatecse
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(
17.5k
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63
views
cmi2019
graphtheory
graphcoloring
spanningtree
vertexcover
descriptive
0
votes
1
answer
8
CMI2019A8
We have constructed a polynomial time reduction from problem A to problem B. Which of the following is not a possible scenario? We know of polynomial time algorithms for both A and B. We only know of exponential time algorithms for both A and B. We only ... polynomial time algorithm for B. We only know an exponential time algorithm for B, but we have a polynomial time algorithm for A.
asked
Sep 13, 2019
in
Theory of Computation
by
gatecse
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(
17.5k
points)

35
views
cmi2019
reduction
pnpnpcnph
+2
votes
1
answer
9
CMI2019A9
The next two questions refer to the following program. In the code below reverse$(A,i,j)$ takes an array $A,$ indices $i$ and $j$ with $i\leq j,$ and reverses the segment $A[i],A[i+1],\cdots,A[j].$ ... } reverse(A,i,m); } return; } When the procedure terminates, the array A has been: Sorted in descending order Sorted in ascending order Reversed Left unaltered
asked
Sep 13, 2019
in
Programming
by
gatecse
Boss
(
17.5k
points)

138
views
cmi2019
identifyfunction
0
votes
2
answers
10
CMI2019A10
The next two questions refer to the following program. In the code below reverse$(A,i,j)$ takes an array $A,$ indices $i$ and $j$ with $i\leq j,$ and reverses the segment $A[i],A[i+1],\cdots,A[j].$ For instance if $A=[0,1,2,3,4,5,6,7]$ then, after we ... return; } The number of times the test $A[ j ] > A[ m ]$ is executed is: $4950$ $5050$ $10000$ Depends on the contents of $A$
asked
Sep 13, 2019
in
Programming
by
gatecse
Boss
(
17.5k
points)

79
views
cmi2019
identifyfunction
0
votes
1
answer
11
CMI2019B1
Consider an alphabet $\Sigma=\{a,b\}.$ Let $L_{1}$ be the language given by the regular expression $(a+b)^{\ast}bb(a+b)^{\ast}$ and let $L_{2}$ be the language $baa^{\ast}b.$ Define $L:=\{u\in\Sigma^{\ast}\mid \exists w\in L_{2}\: s.t.\: uw\in L_{1}\}.$ Give an example of a word in $L.$ Give an example of a word not in $L.$ Construct an NFA for $L.$
asked
Sep 13, 2019
in
Theory of Computation
by
gatecse
Boss
(
17.5k
points)

48
views
cmi2019
regularexpressions
regularlanguages
nfadfa
+1
vote
0
answers
12
CMI2019B2
Let us assume a binary alphabet $\Sigma=\{a,b\}.$ Two words $u,v\in \Sigma^{\ast}$ are said to be conjugates if there exist $w_{1},w_{2}\in \Sigma^{\ast}$ such that $u=w_{1}w_{2}$ and $v=w_{2}w_{1}.$ Prove that $u$ and $v$ are conjugates if and only if there exists $w\in \Sigma^{\ast}$ such that $uw=wv.$
asked
Sep 13, 2019
in
Theory of Computation
by
gatecse
Boss
(
17.5k
points)

31
views
cmi2019
theoryofcomputation
conjugates
strings
0
votes
0
answers
13
CMI2019B3
There is a party of $n$ people. Each attendee has at most $r$ friends in the party. The friend circle of a person includes the person and all her friends. You are required to pick some people for a party game, with the restriction that at most one person is picked from each friend circle. Show that you can pick $\dfrac{n}{r^{2}+1}$ people for the game.
asked
Sep 13, 2019
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

41
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cmi2019
permutationandcombination
pigeonholeprinciple
0
votes
1
answer
14
CMI2019B4
Consider the assertion: Any connected undirected graph $G$ with at least two vertices contains a vertex $v$ such that deleting $v$ from $G$ results in a connected graph. Either give a proof of the assertion, or give a counterexample (thereby disproving the assertion).
asked
Sep 13, 2019
in
Graph Theory
by
gatecse
Boss
(
17.5k
points)

32
views
cmi2019
graphconnectivity
0
votes
0
answers
15
CMI2019B5
In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known whether @anand was ... $ 1$ : @anand once claimed that I was a knave. Chitra : Are you by any chance @anand? Suspect $1$ : Yes.
asked
Sep 13, 2019
in
Mathematical Logic
by
gatecse
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(
17.5k
points)

49
views
cmi2019
mathematicallogic
logicalreasoning
+1
vote
1
answer
16
CMI2019B6
Let $A$ be an $n\times n $ matrix of integers such that each row and each column is arranged in ascending order. We want to check whether a number $k$ appears in $A.$ If $k$ is present, we should report its position  that is, the row $i$ and ... $A.$ Justify the complexity of your algorithm. For both algorithms, describe a worstcase input where $k$ is present in $A.$
asked
Sep 13, 2019
in
Algorithms
by
gatecse
Boss
(
17.5k
points)

35
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cmi2019
algorithms
algorithmdesign
descriptive
+1
vote
0
answers
17
CMI2019B7
A college professor gives several quizzes during the semester, with negative marking. He has become bored of the usual "Best $M$ out of $N$ quizzes" formula to award marks for internal assessment. Instead, each student will be evaluated ... , the score the professor needs to award each student. Describe the space and time complexity of your dynamic programming algorithm.
asked
Sep 13, 2019
in
Algorithms
by
gatecse
Boss
(
17.5k
points)

52
views
cmi2019
algorithms
dynamicprogramming
descriptive
nongate
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