CS 218 : Design and Analysis of Algorithms
Lecture 13: Knapsack
Lecturer: Sundar Vishwanathan
Computer Science & Engineering
1
Indian Institute of Technology, Bombay
Knapsack
1.1
Introduction
Given a set of elements with a value and a weight for each elem
CS 218 : Design and Analysis of Algorithms
Lecture 11: Dynamic Programming: Order and Method. Weighted Interval
Scheduling.
Lecturer: Sundar Vishwanathan
Computer Science & Engineering
1
Indian Institute of Technology, Bombay
Weighted Interval Scheduling
CS 218 : Design and Analysis of Algorithms
Lecture 3: Analysis of Algorithms
Lecturer: Sundar Vishwanathan
Computer Science & Engineering
1
Indian Institute of Technology, Bombay
The Model of Computation
There are two parameters of interest for any algori
CS 218 : Design and Analysis of Algorithms
Lecture 4: Basic Principles of Algorithm Design
Lecturer: Sundar Vishwanathan
Computer Science & Engineering
Indian Institute of Technology, Bombay
We begin with the problem of finding a minimum element in an arr
CS 218 : Design and Analysis of Algorithms
Lecture 12: Array Partitioning Problems
Lecturer: Sundar Vishwanathan
Computer Science & Engineering
1
Indian Institute of Technology, Bombay
Writing Recursive Procedures
This section is only for those students h
CS 218 : Design and Analysis of Algorithms
Lecture 7: Integer Multiplication
Lecturer: Sundar Vishwanathan
Computer Science & Engineering
1
1.1
Indian Institute of Technology, Bombay
Integer Multiplication
Problem Statement
We wish to multiply two n-bit n
mathematics at the newly-establisheduniversity of London,
which is the same institution as that now known as Uni1 His life has been written by his widow S. E. De Morgan. London,.
1882.
THE ANALYTICAL SCHOOL. 133
versity College. There (except for five yea
usual during most of this period.
The professorialsystem was already well established. The
regius chairs and others founded at a later time, brought
eminent men to the university,and it would be difficult to
overrate the influence thus exerted ; but as a
14. Determine the position of a line drawn from a given point to a
given inclined plane, through which the body will fall in the same time
as through the given plane.
15. The equation y? - 5x2 + Sx - 4 = 0 has two equal roots. " Find them.
16. Find the su
proof,which contains numerous assumptions, is not worth prer-oducing.
In this treatise he also appliedthe calculus to various
physicalproblems, and in particularto the theory of the tverarnsesvibrations
of strings.
Regarded as mathematicians, Whiston, Lau
ratio.
12. Compare the time of a revolution about the center of a given
ellipse,with that about its focus.
13. Find the attraction of a corpuscle placed in the axis of a
cylindrical superficies,whose particles attract in an inverse duplicate
ratio of the
attributed much of his future distinction. His medical career
was not particularlysuccessful,and his favorite maxim that a
medical diagnosisis only a balance of probabilitieswas not
appreciatedby his patients,who looked for certaintyin return
for their fe
The letter to which I have just referred was sent by Sir
Frederick Pollock in July, 1869, to Prof. De Morgan in
answer to a request for a trustworthy account, which would
be of historical value, about the mathematical reading of men
at the beginning of th
1837 published the Mechanical Euclid. Most of the older
text-books in hydrostaticswere superseded by Eland's Emelen-ts
of hydrostatics, publishedin 1824.
In 1823 Henry Coddington, of Trinity College(who was
senior wrangler in 1820 and died at Rome on Marc
Plutarch's Life of Nicias. By the same Editor. Price $s.
Sophocles."OedipusTyrannus. School Edition,with Introduction
and Commentary by R. C. JEBB, Litt.D., LL.D. 4*. 6d.
Thucydides.Book VII. By H. R. TOTTENHAM, M.A. [Inthe Press.
Xenophon" Agesilaus.By H
finished, the second opponent followed and urged three jobe-ctions
against the first proposition and one against each of
the others. His place was then taken by the third opponent,
of whom but one argument againsteach question was required.
Finally,the re
they still afforded a test by which public opinion as to the
abilities of men was largelyinfluenced.
The moderators's book for 1778 has been preserved and is
in the libraryof Trinity. It may be interestingif I describe
brieflythe way in which it is arrang
illustrative of his home training, and are sufficientlyiten-resting
to deserve repetition. One day when playing in
the garden he asked his father what was the oldest thing
with which he was acquainted. His father repliedin Socratic
manner by asking what t
Illustrations oi Comparative Anatomy, Vertebrate and Ibnraveter.teSecond Edition. Demy 8vo. is. 6d.
A Catalogueof Australian Fossils. By R. ETHERIDGE, Jun.,F.G.S.
Demy 8vo. IQJ. 6d.
The Fossils and FalseontologicalAffinities of the Neocomian
Deposits of U
monopoly to make extortionate charges;and almost the first
act of the university of which we know anything was to atet-mpt
to find a remedy for the evils and dangers to which the
lads who nocked to the universitywere thus exposed. In 1231
a rule was made
H. A. BULL, M.A., late Master at WellingtonCollege. Price is.
La Jeune Siberienne. Le Lepreux de la Cite D'Aoste. Tales by
COUNT XAVIER DE MAISTRE. By GUSTAVE MASSON, B.A. Price is.
La Picciola. By X. B. SAINTINE. The Text, with Introduction,
Notes and Ma
Cambridge philosophicaltransactions for 1839. He died at
Cambridge in 1841. A collected edition of his works was
publishedin 1871.
The senior wrangler in 1841 was George Gabriel Stokes, of
Pembroke College,who was born in Sligo on Aug. 13, 1819,
and in 18
.
a+x
9. To find the fluxion of the mth power of the Logarithm of x.
10. Of right-angled Triangles containing a given Area to find that
whereof the sum of the two legs AB + BC shall be the least possible.
[This and the two following questions are illustra
and the commentary of Duns Scotus. The fourth year
was given up to rhetoric : this meant certain parts of Atorites-lian
philosophy,as derived from Arabic sources.
Instruction in these subjects was given by the cursory
lectures of students in their fifth,s
of any possibilityof episcopal interference that any official
or nominee of the bishop was absolutely ineligiblefor the
office.
The other officers of the university were the taxors, who
fixed the rent of hostels and lodgings,and in conjunction with
two bu
of research,for it is now known that Newton used the fluxional
calculus in the first instance in finding some of the theorems
(especiallythose towards the end of book i. and in book IL),
and then gave geometricalproofs of his results. This tiraonslaof
num
Ai_^ (II).
Therefore from (I)and (II),by multiplication,
Thus, if h and h both change in any way the change in the product hh
is proportionateto the change in A and therefore A varies as hh,or the
area varies as the productof (themeasures of)the base and