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101
Cormen Edition 3 Exercise 1.1 Question 3 (Page No. 11)
Select a data structure that you have seen previously, and discuss its strengths and limitations.
Select a data structure that you have seen previously, and discuss its strengths and limitations.
112
views
asked
Jun 25, 2019
Algorithms
cormen
algorithms
descriptive
+
–
0
votes
0
answers
102
Cormen Edition 3 Exercise 1.1 Question 2 (Page No. 11)
Other than speed, what other measures of efficiency might one use in a real-world setting?
Other than speed, what other measures of efficiency might one use in a real-world setting?
168
views
asked
Jun 25, 2019
Algorithms
cormen
algorithms
descriptive
+
–
0
votes
0
answers
103
Cormen Edition 3 Exercise 1.1 Question 1 (Page No. 11)
Give a real-world example that requires sorting or a real-world example that requires computing a convex hull.
Give a real-world example that requires sorting or a real-world example that requires computing a convex hull.
178
views
asked
Jun 25, 2019
Algorithms
cormen
algorithms
+
–
1
votes
3
answers
104
ISI2018-PCB-CS10
Consider two $n \times 1$ vectors $u$ and $v$ , stored as table $U(\text{ind,val})$ and $V(\text{ind,val})$ with the same schema A row $(i,u_i)$ of table $U$ specifies the $i^{th}$ element of vector $u$ has value $u_i$ ... $u + v$ of the two vectors $u$ and $v$. Explain your solution.
Consider two $n \times 1$ vectors $u$ and $v$ , stored as table $U(\text{ind,val})$ and $V(\text{ind,val})$ with the same schema A row $(i,u_i)$ of table $U$ specifies th...
1.1k
views
asked
May 12, 2019
Databases
isi2018-pcb-cs
databases
relational-algebra
sql
descriptive
+
–
2
votes
1
answer
105
ISI2018-PCB-CS9
The data link layer uses a fixed-size sliding window protocol, where the window size for the connection is equal to twice the bandwidth-delay product of the network path. Consider the following three scenarios, in each of which only the given parameter changes as specified (no ... minimum value of the round trip time $R$ increases to $1.8R$; the window size $W$ decreases to $W/3$
The data link layer uses a fixed-size sliding window protocol, where the window size for the connection is equal to twice the bandwidth-delay product of the network path....
1.1k
views
asked
May 12, 2019
Computer Networks
isi2018-pcb-cs
computer-networks
data-link-layer
descriptive
+
–
1
votes
2
answers
106
ISI2018-PCB-CS8
Consider a $5$ ... $\text{(in ns)}$ needed to execute the program.
Consider a $5$-stage instruction pipeline. The stages and the corresponding stage delays are given below.$$\begin{array}{|l|l|}\hline \textbf{Instruction}&\textbf{Stage d...
1.3k
views
asked
May 12, 2019
Operating System
isi2018-pcb-cs
co-and-architecture
pipelining
descriptive
+
–
1
votes
2
answers
107
ISI2018-PCB-CS7
A context switch from a process $P_{old}$ to a process $P_{new}$ consists of the following steps: Step I:saving the context of $P_{old}$; Step II: running the scheduling algorithm to pick $P_{new}$; Step III: restoring the saved context of $P_{new}$. Suppose Steps ... in the order $P_1, P_2, . . . , P_k;$ each process requires exactly one CPU burst of $20$ms and no I/O burst.
A context switch from a process $P_{old}$ to a process $P_{new}$ consists of the following steps:Step I:saving the context of $P_{old}$;Step II: running the scheduling al...
1.2k
views
asked
May 12, 2019
Operating System
isi2018-pcb-cs
operating-system
process-scheduling
descriptive
+
–
0
votes
1
answer
108
ISI2018-PCB-CS6
The following function computes an array $SPF$, where, for any integer $1 < i < 1000$, $SPF[i]$ is the smallest prime factor of $i$. For example, $SPF[6]$ is $2$, and $SPF[11]$ is $11$. There are five missing parts in the following code, commented as $/* Blank */$. For each of them ... < 1000; j+= i) { /* Blank 4 */ if (SPF[j] == j) { SPF[j] = _____; /* Blank 5 */ } } } } }
The following function computes an array $SPF$, where, for any integer $1 < i < 1000$, $SPF[i]$ is the smallest prime factor of $i$. For example, $SPF[6]$ is $2$, and $S...
625
views
asked
May 12, 2019
Algorithms
isi2018-pcb-cs
algorithm-design
descriptive
+
–
1
votes
2
answers
109
ISI2018-PCB-CS5
Consider a max-heap of $n$ distinct integers, $n ≥ 4$, stored in an array $\mathcal{A}[1 . . . n]$. The second minimum of $\mathcal{A}$ is the integer that is less than all integers in $\mathcal{A}$ except the minimum of $\mathcal{A}$. Find all possible array indices of $\mathcal{A}$ in which the second minimum can occur. Justify your answer.
Consider a max-heap of $n$ distinct integers, $n ≥ 4$, stored in an array $\mathcal{A}[1 . . . n]$. The second minimum of $\mathcal{A}$ is the integer that is less than...
1.1k
views
asked
May 12, 2019
Algorithms
isi2018-pcb-cs
algorithms
algorithm-design
binary-heap
descriptive
+
–
2
votes
1
answer
110
ISI2018-PCB-CS4
Let the valid moves along a staircase be $U$ (one step up) and $D$ (one step down). For example, the string $s = UUDU$ represents the sequence of moves as two steps up, then one step down, and then again one step up. Suppose a person is ... returns to the base of the staircase after the final step. Show that $L$ is not regular Write a context free grammar for accepting $L$
Let the valid moves along a staircase be $U$ (one step up) and $D$ (one step down). For example, the string $s = UUDU$ represents the sequence of moves as two steps up, t...
711
views
asked
May 12, 2019
Theory of Computation
isi2018-pcb-cs
theory-of-computation
context-free-grammar
descriptive
+
–
1
votes
1
answer
111
ISI2018-PCB-CS3
An $n-$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ denote the number of such functions. Calculate the value of $\sigma_4$. Derive an expression for $\sigma_n$ in terms of $n$.
An $n-$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ d...
480
views
asked
May 12, 2019
Set Theory & Algebra
isi2018-pcb-cs
engineering-mathematics
discrete-mathematics
set-theory&algebra
functions
descriptive
+
–
3
votes
1
answer
112
ISI2018-PCB-CS2
You can climb up a staircase of $n$ stairs by taking steps of one or two stairs at a time. Formulate a recurrence relation for counting $a_n$, the number of distinct ways in which you can climb up the staircase. Mention the boundary conditions for your recurrence relation. Find a closed form expression for $a_n$ by solving your recurrence.
You can climb up a staircase of $n$ stairs by taking steps of one or two stairs at a time.Formulate a recurrence relation for counting $a_n$, the number of distinct ways ...
720
views
asked
May 12, 2019
Algorithms
isi2018-pcb-cs
algorithms
recurrence-relation
descriptive
+
–
0
votes
1
answer
113
ISI2018-PCB-CS1
Consider an array of length n consisting only of positive and negative integers. Design an algorithm to rearrange the array so that all the negative integers appear before all the positive integers, using $O(n)$ time and only a constant amount of extra space.
Consider an array of length n consisting only of positive and negative integers. Design an algorithm to rearrange the array so that all the negative integers appear befor...
558
views
asked
May 12, 2019
Algorithms
isi2018-pcb-cs
algorithms
algorithm-design
descriptive
+
–
0
votes
1
answer
114
ISI2018-PCB-A4
Let $A$ and $B$ are two non-empty finite subsets of $\mathbb{Z}$, the set of all integers. Define $A+B=\{a+b:a\in A,b\in B\}$.Prove that $\mid A+B \mid \geq \mid A \mid + \mid B \mid -1 $, where $\mid S \mid$ denotes the cardinality of finite set $S$.
Let $A$ and $B$ are two non-empty finite subsets of $\mathbb{Z}$, the set of all integers. Define $A+B=\{a+b:a\in A,b\in B\}$.Prove that $\mid A+B \mid \geq \mid A \mid ...
451
views
asked
May 12, 2019
Set Theory & Algebra
isi2018-pcb-a
set-theory&algebra
descriptive
+
–
1
votes
0
answers
115
ISI2018-PCB-A3
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.
430
views
asked
May 12, 2019
Quantitative Aptitude
isi2018-pcb-a
general-aptitude
quantitative-aptitude
descriptive
+
–
0
votes
2
answers
116
ISI2018-PCB-A2
Let there be a pile of $2018$ chips in the center of a table. Suppose there are two players who could alternately remove one, two or three chips from the pile. At least one chip must be removed, but no more than three chips can be removed in a ... game, that is, whatever moves his opponent makes, he can always make his moves in a certain way ensuring his win? Justify your answer.
Let there be a pile of $2018$ chips in the center of a table. Suppose there are two players who could alternately remove one, two or three chips from the pile. At least o...
711
views
asked
May 12, 2019
Analytical Aptitude
isi2018-pcb-a
general-aptitude
analytical-aptitude
logical-reasoning
descriptive
+
–
1
votes
1
answer
117
ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alp...
510
views
asked
May 12, 2019
Linear Algebra
isi2018-pcb-a
engineering-mathematics
linear-algebra
matrix
descriptive
+
–
0
votes
1
answer
118
ISI2018-MMA-25
The solution of the differential equation $(1 + x^2y^2)ydx + (x^2y^2 − 1)xdy = 0$ is $xy = \log\ x − \log\ y + C$ $xy = \log\ y − \log\ x + C$ $x^2y^2 = 2(\log\ x − \log\ y) + C$ $x^2y^2 = 2(\log\ y − \log\ x) + C$
The solution of the differential equation$(1 + x^2y^2)ydx + (x^2y^2 − 1)xdy = 0$ is$xy = \log\ x − \log\ y + C$$xy = \log\ y − \log\ x + C$$x^2y^2 = 2(\log\ x − \...
545
views
asked
May 11, 2019
Others
isi2018-mma
non-gate
differential-equation
+
–
1
votes
4
answers
119
ISI2018-MMA-28
Consider the following functions $f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ ... at $\pm1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $\pm2$ $h_1$ has discontinuity at $\pm 2$ and $h_2$ has discontinuity at $\pm1$.
Consider the following functions$f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ and $g(x)=\begin{cases} 1, & \te...
1.2k
views
asked
May 11, 2019
Calculus
isi2018-mma
engineering-mathematics
calculus
continuity
+
–
0
votes
1
answer
120
ISI2018-MMA-30
Consider the function $f(x)=\bigg(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots+\frac{x^n}{n!}\bigg)e^{-x}$, where $n\geq4$ is a positive integer. Which of the following statements is correct? $f$ has no local maximum For every $n$, $f$ has a local maximum at $x = 0$ ... at $x = 0$ when $n$ is even $f$ has no local extremum if $n$ is even and has a local maximum at $x = 0$ when $n$ is odd.
Consider the function$f(x)=\bigg(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots+\frac{x^n}{n!}\bigg)e^{-x}$,where $n\geq4$ is a positive integer. Which of the following statemen...
1.0k
views
asked
May 11, 2019
Calculus
isi2018-mma
engineering-mathematics
calculus
maxima-minima
+
–
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