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Recent questions tagged cmi2014

2 votes
1 answer
1
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 $A(2, 3, 3)$.
asked May 27, 2016 in Algorithms jothee 165 views
2 votes
1 answer
2
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 $n$.
asked May 27, 2016 in Algorithms jothee 287 views
3 votes
1 answer
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 (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 $n$.
asked May 27, 2016 in Algorithms jothee 174 views
2 votes
1 answer
4
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 $O(n^2)$.
asked May 27, 2016 in Algorithms jothee 105 views
2 votes
0 answers
5
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 $O(n)$.
asked May 27, 2016 in Algorithms jothee 110 views
2 votes
0 answers
6
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 sequence ... programming to compute the Improvement Index for a batsman with an overall sequence of $n$ scores. Analyze the complexity of your algorithm.
asked May 27, 2016 in Algorithms jothee 132 views
1 vote
1 answer
7
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.
asked May 27, 2016 in Algorithms jothee 110 views
1 vote
0 answers
8
$\text{Air CMI }$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 $FakeTrip$ ... to 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.
asked May 27, 2016 in Algorithms jothee 118 views
1 vote
1 answer
9
There are $n$ students in a class. The students have formed $k$ committees. Each committee consists of more than half of the students. Show that there is at least one student who is a member of more than half of the committees.
asked May 27, 2016 in Quantitative Aptitude jothee 179 views
1 vote
1 answer
10
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 other may ... proof 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.
asked May 27, 2016 in Theory of Computation jothee 249 views
2 votes
2 answers
11
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.
asked May 27, 2016 in Quantitative Aptitude jothee 240 views
2 votes
1 answer
12
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 interviewed again, ... (B). If the workers union resorted to a strike, then the number of voters was greater than or equal to the number of abstainers.
asked May 27, 2016 in Quantitative Aptitude jothee 165 views
1 vote
0 answers
13
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
asked May 27, 2016 in Quantitative Aptitude jothee 153 views
1 vote
0 answers
14
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: $M < 25$ $25 \leq M < 40$ $40 \leq M < 55$ $M \geq 55$
asked May 27, 2016 in Quantitative Aptitude jothee 165 views
6 votes
1 answer
15
Suppose we are working with a programming language that supports automatic garbage collection. This means that: Uninitialized variables are assigned null values. Unreferenced dynamically allocated memory is added back to free space. Unreachable $\text{if – then – else}$ branches are pruned. Expressions where array indices exceed array bounds are flagged.
asked May 27, 2016 in Compiler Design jothee 454 views
2 votes
1 answer
16
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 following language: $L:=\{ xy \mid x, \: y \in \Sigma^*, \: \: n_a(x) = n_b(y)\}$ What can we say about $L$? $L$ is regular, but not context-free $L$ is context-free, but not regular $L$ is $\Sigma^*$ None of these
asked May 27, 2016 in Theory of Computation jothee 182 views
1 vote
1 answer
17
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 Halting Problem, ... $P$. The existence of $A$ says nothing about whether there is an algorithm for $P$. The Halting Problem can be solved using $A$.
asked May 27, 2016 in Algorithms jothee 144 views
3 votes
2 answers
18
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; if (prime(m)){ i := i + m; }else{ j := j + m; } } $k < i+j$ $k = i+j$ $k > i+j$ Depends on $\text{start}$ and $\text{end}$
asked May 27, 2016 in Algorithms jothee 180 views
10 votes
2 answers
19
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 houses with numbers strictly greater than $14$. $\frac{7}{11}$ $\frac{5}{12}$ $\frac{4}{11}$ $\frac{5}{22}$
asked May 27, 2016 in Probability jothee 1.1k views
19 votes
2 answers
20
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. $260$ $340$ $720$ $440$
asked May 27, 2016 in Combinatory jothee 1.2k views
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