Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Q&A
Questions
Unanswered
Tags
Subjects
Users
Ask
Previous Years
Blogs
New Blog
Exams
Dark Mode
Recent questions tagged discrete-mathematics
0
votes
0
answers
151
Kenneth Rosen Edition 7 Exercise 8.2 Question 7 (Page No. 524)
In how many ways can a $2 \times n$ rectangular checkerboard be tiled using $1 \times 2 \:\text{and}\: 2 \times 2$ pieces?
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
163
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
0
answers
152
Kenneth Rosen Edition 7 Exercise 8.2 Question 6 (Page No. 524)
How many different messages can be transmitted in $n$ microseconds using three different signals if one signal requires $1$ microsecond for transmittal, the other two signals require $2$ microseconds each for transmittal, and a signal in a message is followed immediately by the next signal?
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
187
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
0
answers
153
Kenneth Rosen Edition 7 Exercise 8.2 Question 5 (Page No. 524)
How many different messages can be transmitted in $n$ microseconds using the two signals described in question $19$ in Section $8.1?$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
123
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
0
answers
154
Kenneth Rosen Edition 7 Exercise 8.2 Question 4 (Page No. 524)
Solve these recurrence relations together with the initial conditions given. $a_{n} = a_{n-1}+ 6a_{n-2} \:\text{for}\: n \geq 2, a_{0} = 3, a_{1} = 6$ $a_{n} = 7a_{n-1}− 10a_{n-2} \:\text{for}\: n \geq 2, a_{0} = 2, a_{1} = 1$ ... $a_{n+2} = −4a_{n+1} + 5a_{n} \:\text{for}\: n \geq 0, a_{0} = 2, a_{1} = 8$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
171
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
155
Kenneth Rosen Edition 7 Exercise 8.2 Question 3 (Page No. 524)
Solve these recurrence relations together with the initial conditions given. $a_{n} = 2a_{n−1}\:\text{for}\: n \geq 1, a_{0} = 3$ $a_{n} = a_{n−1} \:\text{for}\: n \geq 1, a_{0} = 2$ ... $a_{n} = a_{n−2} /4 \:\text{for}\: n \geq 2, a_{0} = 1, a_{1} = 0$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
222
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
156
Kenneth Rosen Edition 7 Exercise 8.2 Question 2 (Page No. 524)
Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are. $a_{n} = 3a_{n-2}$ $a_{n} = 3$ $a_{n} = a^{2}_{n−1}$ $an = a_{n−1} + 2a_{n−3}$ $an = a_{n−1}/n$ $an = a_{n−1} + a_{n−2} + n + 3$ $a_{n} = 4a_{n−2} + 5a_{n−4} + 9a_{n−7}$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
236
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
1
answer
157
Kenneth Rosen Edition 7 Exercise 8.2 Question 1 (Page No. 524)
Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are. $a_{n} = 3a_{n−1} + 4a_{n−2} + 5a_{n−3}$ $a_{n} = 2na_{n−1} + a_{n−2}$ $a_{n} = a_{n−1} + a_{n−4}$ $a_{n} = a_{n−1} + 2 $ $a_{n} = a^{2}_{n−1} + a_{n−2} $ $a_{n} = a_{n−2}$ $a_{n} = a_{n−1} + n$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
2.3k
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
0
answers
158
Kenneth Rosen Edition 7 Exercise 8.1 Question 57 (Page No. 512)
Dynamic programming can be used to develop an algorithm for solving the matrix-chain multiplication problem introduced in Section $3.3.$ This is the problem of determining how the product $A_{1}A_{2} \dots A_{n}$ can be computed ... algorithm from part $(D)$ has $O(n^{3})$ worst-case complexity in terms of multiplications of integers.
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
136
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
159
Kenneth Rosen Edition 7 Exercise 8.1 Question 56 (Page No. 512)
In this question, we will develop a dynamic programming algorithm for finding the maximum sum of consecutive terms of a sequence of real numbers. That is, given a sequence of real numbers ... worst-case complexity in terms of the number of additions and comparisons of your algorithm from part $(C)$ is linear.
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
197
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
160
Kenneth Rosen Edition 7 Exercise 8.1 Question 55 (Page No. 512)
For each part of question $54,$ use your algorithm from question $53$ to find the optimal schedule for talks so that the total number of attendees is maximized. $20, 10, 50, 30, 15, 25, 40.$ $100, 5, 10, 20, 25, 40, 30. $ $2, 3, 8, 5, 4, 7, 10. $ $10, 8, 7, 25, 20, 30, 5.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
97
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
161
Kenneth Rosen Edition 7 Exercise 8.1 Question 54 (Page No. 512)
Use Algorithm $1$ to determine the maximum number of total attendees in the talks in Example $6$ if $w_{i},$ the number of attendees of talk $i, i = 1, 2,\dots, 7,$ is $20, 10, 50, 30, 15, 25, 40.$ $100, 5, 10, 20, 25, 40, 30. $ $2, 3, 8, 5, 4, 7, 10. $ $10, 8, 7, 25, 20, 30, 5.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
110
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
162
Kenneth Rosen Edition 7 Exercise 8.1 Question 53 (Page No. 512)
Construct the algorithm described in the text after Algorithm $1$ for determining which talks should be scheduled to maximize the total number of attendees and not just the maximum total number of attendees determined by Algorithm $1.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
88
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
163
Kenneth Rosen Edition 7 Exercise 8.1 Question 52 (Page No. 512)
Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ ... The resulting equation involving the sequences and its differences is called a difference equation.
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
100
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
164
Kenneth Rosen Edition 7 Exercise 8.1 Question 51 (Page No. 512)
Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ is $\triangledown a_{n} = a_{n} − a_{n−1}.$ ... $a_{n}, \triangledown a_{n},\: \text{and}\: \triangledown^{2}a_{n}.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
78
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
165
Kenneth Rosen Edition 7 Exercise 8.1 Question 50 (Page No. 512)
Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ is $\triangledown a_{n} = a_{n} − a_{n−1}.$ ... expressed in terms of $a_{n}, \triangledown a_{n}, \triangledown ^{2}a_{n},\dots, \triangledown^{k}a_{n}.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
75
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
166
Kenneth Rosen Edition 7 Exercise 8.1 Question 49 (Page No. 512)
Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ is $\triangledown a_{n} = a_{n} − a_{n−1}.$ ... $a_{n−2} = a_{n} − 2\triangledown a_{n} + \triangledown^{2}a_{n}.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
74
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
167
Kenneth Rosen Edition 7 Exercise 8.1 Question 48 (Page No. 512)
Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ is $\triangledown a_{n} = a_{n} − a_{n−1}.$ ... $a_{n−1} = a_{n} − \triangledown a_{n}.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
90
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
168
Kenneth Rosen Edition 7 Exercise 8.1 Question 47 (Page No. 512)
Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ is $\triangledown a_{n} = a_{n} − a_{n−1}.$ The $(k + 1)^{\text{st}}$ ... $a_{n} = 4.$ $a_{n} = 2n.$ $a_{n} = n^{2}.$ $a_{n} = 2^{n}.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
64
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
169
Kenneth Rosen Edition 7 Exercise 8.1 Question 46 (Page No. 512)
Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ is $\triangledown a_{n} = a_{n} − a_{n−1}.$ The $(k + 1)^{\text{st}}$ ... $a_{n} = 4.$ $a_{n} = 2n.$ $a_{n} = n^{2}.$ $a_{n} = 2^{n}.$
Lakshman Patel RJIT
asked
in
Combinatory
May 3, 2020
by
Lakshman Patel RJIT
71
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
170
Kenneth Rosen Edition 7 Exercise 8.1 Question 45 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ to peg $4$ so that no ... how the disks are moved. Show that $R(n)\: \text{is}\: O(\sqrt{n}2^{\sqrt{2n}}).$
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
91
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
171
Kenneth Rosen Edition 7 Exercise 8.1 Question 44 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ ... number of moves required to solve the Reve's puzzle for all integers $n$ with $1 \leq n \leq 25.$
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
70
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
172
Kenneth Rosen Edition 7 Exercise 8.1 Question 43 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ to peg $4$ so that no disk is ... then $R(n) = \displaystyle{}\sum_{i = 1}^{k} i2^{i−1} − (t_{k} − n)2^{k−1}.$
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
75
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
173
Kenneth Rosen Edition 7 Exercise 8.1 Question 42 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ to peg $4$ so that no disk is ... that if $k$ is as chosen in question $41,$ then $R(n) − R(n − 1) = 2^{k−1}.$
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
61
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
174
Kenneth Rosen Edition 7 Exercise 8.1 Question 41 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ to peg $4$ so that no disk is ever on top ... $R(0) = 0\:\text{and}\: R(1) = 1.$
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
98
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
175
Kenneth Rosen Edition 7 Exercise 8.1 Question 40 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ to peg $4$ ... $5$ disks. $6$ disks. $7$ disks. $8$ disks.
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
51
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
176
Kenneth Rosen Edition 7 Exercise 8.1 Question 39 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ ... disks are moved. Show that the Reve's puzzle with four disks can be solved using nine, and no fewer, moves
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
83
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
177
Kenneth Rosen Edition 7 Exercise 8.1 Question 38 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ to ... are moved. Show that the Reve's puzzle with three disks can be solved using five, and no fewer, moves.
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
98
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
178
Kenneth Rosen Edition 7 Exercise 8.1 Question 37 (Page No. 512)
Question $33-37$ deal with a variation of the $\textbf{Josephus problem}$ described by Graham, Knuth, and Patashnik in $[G_{r}K_{n}P_{a}94].$ This problem is based on an account by the historian Flavius Josephus, who was part of a band of $41$ ... $J (100), J (1000),\: \text{and}\: J (10,000)$ from your formula for $J (n).$
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
77
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
179
Kenneth Rosen Edition 7 Exercise 8.1 Question 36 (Page No. 512)
Question $33-37$ deal with a variation of the $\textbf{Josephus problem}$ described by Graham, Knuth, and Patashnik in $[G_{r}K_{n}P_{a}94].$ This problem is based on an account by the historian Flavius ... induction to prove the formula you conjectured in question $34,$ making use of the recurrence relation from question $35.$
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
84
views
kenneth-rosen
discrete-mathematics
counting
descriptive
0
votes
0
answers
180
Kenneth Rosen Edition 7 Exercise 8.1 Question 35 (Page No. 512)
Question $33-37$ deal with a variation of the $\textbf{Josephus problem}$ described by Graham, Knuth, and Patashnik in $[G_{r}K_{n}P_{a}94].$ This problem is based on an account by the historian Flavius Josephus, who was part of a band of $41$ Jewish rebels ...
Lakshman Patel RJIT
asked
in
Combinatory
May 2, 2020
by
Lakshman Patel RJIT
82
views
kenneth-rosen
discrete-mathematics
counting
descriptive
Page:
« prev
1
2
3
4
5
6
7
8
9
10
11
...
75
next »
Subscribe to GATE CSE 2023 Test Series
Subscribe to GO Classes for GATE CSE 2023
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Life happens, just chill and do hardwork
ISRO RECRUITMENT FOR SCIENTIST B THROUGH GATE
POWER GRID CORPORATION OF INDIA LIMITED
INSTITUTE OF BANKING PERSONNEL SELECTION
GATE Overflow books for TIFR, ISRO, UGCNET and NIELIT
Subjects
All categories
General Aptitude
(2.4k)
Engineering Mathematics
(9.1k)
Digital Logic
(3.2k)
Programming and DS
(5.8k)
Algorithms
(4.5k)
Theory of Computation
(6.6k)
Compiler Design
(2.3k)
Operating System
(4.9k)
Databases
(4.5k)
CO and Architecture
(3.7k)
Computer Networks
(4.5k)
Non GATE
(1.3k)
Others
(2.4k)
Admissions
(648)
Exam Queries
(841)
Tier 1 Placement Questions
(17)
Job Queries
(74)
Projects
(9)
Unknown Category
(854)
Recent questions tagged discrete-mathematics
Recent Blog Comments
Please upload 4th Mock Test, due date was 4th Dec.
The counts of answered, marked etc in the exam...
Tests have been sent and all tests will be...
Maximum age limit changed from 35 yrs. to 28...
Hmm, sir totally getting your point ☺️☺️....