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Recent questions tagged cmi2013
2
votes
3
answers
1
CMI2013-B-06b
Your final exams are over and you are catching up on watching sports on TV. You have a schedule of interesting matches coming up all over the world during the next week. You hate to start or stop watching a match midway, so your aim is ... dynamic programming to compute the maximum number of complete matches you can watch next week. Analyze the worse-case complexity of your algorithm.
Arjun
asked
in
Algorithms
Jun 8, 2016
by
Arjun
1.7k
views
cmi2013
descriptive
algorithms
dynamic-programming
4
votes
3
answers
2
CMI2013-B-07
Consider the code below, defining the function $\text{mystery}:$ mystery(a,b){ if (a < 0 or b < 0) return 0; else if (a == 0) return b+1; else if (b == 0) return mystery(a-1,1); else return mystery(a-1, mystery(a,b-1)); } Express $\text{mystery}(1, \:n)$ ... of $n$. Express $\text{mystery}(2,\: n)$ as a function of $n$. Compute $\text{mystery}(3, \:2)$ and $\text{mystery}(3, 3)$.
go_editor
asked
in
Algorithms
May 23, 2016
by
go_editor
1.1k
views
cmi2013
descriptive
recurrence-relation
1
vote
2
answers
3
CMI2013-B-06a
Your final exams are over and you are catching up on watching sports on TV. You have a schedule of interesting matches coming up all over the world during the next week. You hate to start or stop watching a match midway, so your aim is to ... match whose starting time is strictly later than the finishing time of the current match? Analyze the worse-case complexity of your algorithm.
go_editor
asked
in
Algorithms
May 23, 2016
by
go_editor
906
views
cmi2013
descriptive
algorithms
algorithm-design
3
votes
1
answer
4
CMI2013-B-05
You are going abroad and you have to complete a number of formalities before you leave. Each task takes a full day to complete. Fortunately, you have an army of friends to help you and each task can be done by either you or any of ... . Model this problem formally using graphs. Describe an efficient algorithm for the problem and analyze the worst-case complexity of your algorithm.
go_editor
asked
in
Algorithms
May 23, 2016
by
go_editor
385
views
cmi2013
descriptive
algorithms
graph-algorithms
7
votes
1
answer
5
CMI2013-B-04
You are given two sorted lists of integers of size $m$ and $n$. Describe a divide and conquer algorithm for computing the $k$-th smallest element in the union of the two lists in time $O(\log m + \log n)$.
go_editor
asked
in
Algorithms
May 23, 2016
by
go_editor
904
views
cmi2013
algorithms
sorting
divide-and-conquer
descriptive
1
vote
4
answers
6
CMI2013-B-03
A simple graph is one in which there are no self loops and each pair of distinct vertices is connected by at most one edge. Show that any finite simple graph has at least two vertices with the same degree.
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
991
views
cmi2013
descriptive
graph-theory
graph-connectivity
14
votes
3
answers
7
CMI2013-B-02
A complete graph on $n$ vertices is an undirected graph in which every pair of distinct vertices is connected by an edge. A simple path in a graph is one in which no vertex is repeated. Let $G$ be a complete graph on $10$ vertices. Let $u$, $v$, $ w$ be three distinct vertices in $G$. How many simple paths are there from $u$ to $v$ going through $w$?
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
3.0k
views
cmi2013
descriptive
graph-theory
graph-connectivity
2
votes
2
answers
8
CMI2013-B-01
For a binary string $x = a_0a_1 \dots a_{nā1}$ define $val(x)$ to be the value of $x$ interpreted as a binary number, where $a_0$ is the most significant bit. More formally, $val(x)$ is given by $\Sigma_{0 \leq i < n} 2^{n-1-i} .a_i$ Design a finite automaton that accepts exactly the set of binary strings $x$ such that $val(x)$ is divisible by either 4 or 5.
go_editor
asked
in
Theory of Computation
May 23, 2016
by
go_editor
447
views
cmi2013
descriptive
theory-of-computation
finite-automata
6
votes
3
answers
9
CMI2013-A-10
The below question is based on following program: procedure mystery (A : array [1..100] of int) int i,j,position,tmp; begin for j := 1 to 100 do position := j; for i := j to 100 do if (A[i] > A[position]) then position := i; endfor tmp := A[j]; ... endfor end The number of times the test $A[i] > A[\text{position}]$ is executed is: $100$ $5050$ $10000$ Depends on contents of $A$
go_editor
asked
in
Algorithms
May 23, 2016
by
go_editor
1.3k
views
cmi2013
algorithms
time-complexity
9
votes
3
answers
10
CMI2013-A-09
The below question is based on the following program. procedure mystery (A : array [1..100] of int) int i,j,position,tmp; begin for j := 1 to 100 do position := j; for i := j to 100 do if (A[i] > A[position]) then ... A[position] := tmp; endfor end When the procedure terminates, the array A has been: Reversed Left unaltered Sorted in descending order Sorted in ascending order
go_editor
asked
in
Algorithms
May 23, 2016
by
go_editor
1.1k
views
cmi2013
algorithms
identify-function
3
votes
2
answers
11
CMI2013-A-08
In the passing out batch, $54$ students know Java, $39$ know Python and $43$ know C++. Of these, $15$ know both Java and Python, $17$ know both Python and C++ and $23$ know both Java and C++ and $11$ know all three languages. If there are $100$ students in the class, how many know none of these three languages? $3$ $8$ $17$ $19$
go_editor
asked
in
Quantitative Aptitude
May 23, 2016
by
go_editor
583
views
cmi2013
quantitative-aptitude
set-theory
17
votes
5
answers
12
CMI2013-A-07
Consider the following two statements. There are infinitely many interesting whole numbers. There are finitely many uninteresting whole numbers. Which of the following is true? Statements $1$ and $2$ are equivalent. Statement $1$ implies statement $2$. Statement $2$ implies statement $1$. None of the above.
go_editor
asked
in
Mathematical Logic
May 23, 2016
by
go_editor
2.3k
views
cmi2013
mathematical-logic
logical-reasoning
19
votes
6
answers
13
CMI2013-A-06
A simple graph is one in which there are no self-loops and each pair of distinct vertices is connected by at most one edge. Let $G$ be a simple graph on $8$ vertices such that there is a vertex of degree $1$, a vertex of degree $2$, a vertex of degree $3$, a vertex ... degree $6$ and a vertex of degree $7$. Which of the following can be the degree of the last vertex? $3$ $0$ $5$ $4$
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
5.2k
views
cmi2013
graph-theory
normal
degree-of-graph
32
votes
5
answers
14
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: $O(nm \log m)$ $O(mn \log n)$ $O(m + n)$ $O(mn)$
go_editor
asked
in
Algorithms
May 23, 2016
by
go_editor
6.6k
views
cmi2013
algorithms
sorting
1
vote
2
answers
15
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
go_editor
asked
in
Theory of Computation
May 23, 2016
by
go_editor
361
views
cmi2013
theory-of-computation
identify-class-language
2
votes
2
answers
16
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
go_editor
asked
in
DS
May 23, 2016
by
go_editor
1.2k
views
cmi2013
data-structures
binary-search-tree
13
votes
5
answers
17
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? $10\%$ $50\%$ $70\%$ $90\%$
go_editor
asked
in
Probability
May 23, 2016
by
go_editor
7.7k
views
cmi2013
probability
conditional-probability
1
vote
1
answer
18
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? $500$ $1000$ $5000$ $20000$
go_editor
asked
in
Quantitative Aptitude
May 23, 2016
by
go_editor
638
views
cmi2013
quantitative-aptitude
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