Thought is seed of action, since current to future; the knowledge is most influential that can be rocks the world, what is your ideal ultimate goal? We know Imagination is source of creation. So there is never alone accompanied by noble knowledge.
A New Technology for Your Creation of Quick Designing and Fast Constructing
Anonymous subject: Rating Networks
Exemplar: The Key Words To Help People Composite Their Arts.
Following noun cluster and verb phrase come from Introduction to Algorithms, Second Edition chapter27: Sorting Networks. I wish you would be enjoy its convenience please. Good luck.
Part Overview: ________Examined Into a Matter
This principle ____is aim for access ai technology.
computers ________allow
random________be executed
machines________investigate
RAM's________based complementary metal oxide semiconductor.
operation ________can be performed
time________differ
chapter________respects
rating algorithms ________can
comparison________perform
network model ________sort
computation________see
comparison operations ________be implemented
simultaneously________Second
Comparison networks ________occur
RAM's ________is
comparisons________shall see
Thus________allows
algorithm ________values
counting ________begin
Section ________give
cannot ________proves
comparison network________eases
RAM model________shall design is
operations ________will have
serially________steps
another________presents
comparison network ________design
same time________will be
characteristic ________block
construction ________modify
sublinear time________produce
defining comparison networks ________can merge
definition ________sorted
terms ________assemble
depth ________can sort
network________are
greatly ________inputs
task ________makes sense
analyzing ________is composed
correctness ________wires
rating network ________shown
essentially ________Figure
version ________is
merge________performs
sorter ________function
basic building ________inputs
bitonic sorter slightly ________drawn
merging network ________line
sequences ________are shown
sequence________shall adopt
merging networks ________lines
Comparison networks________Inputs appear
Rating networks ________left
discussion ________input value
characteristics________think
solely ________shall assume
comparators________operates
comparator________assume
device ________input values
outputs________wire transmits
comparator ________value
outputs x' ________place
same comparator________Wires can connect
min________input
max________input wires
pictorial representation ________wires
bulky ________contains
purposes________be sorted enter
convention ________results computed
drawing comparators ________shall speak
outputs ________use
smaller ________name
appearing ________wire
output ________carries
larger ________will
bottom output________be clear
thus ________shows
rating ________set
words________draw
time ________lines
appearance ________stretched
production ________Note
otherwise ________line does not represent
network ________wire
network output ________line
n output ________represents
sequence 〈a1________input wire
output sequence 〈b1________connects
bn〉________comes
referring ________input is connected
same ________is connected
intention ________be
context________trace
comparators interconnected ________given
collection ________input
comparators ________cycle back
vertically________go
sequence ________can draw
connecting various comparators________move
example________input values shown appear
connecting ________input wires
comparator C________values shown appear
network's n ________have
Similarly________values
comparator output ________do not
network's n output ________produces
requirement ________input values are
interconnecting comparators ________suppose
graph ________appears
interconnections ________requires
acyclic________compute
path ________values are shown
etc________not
same comparator ________operate
network outputs ________connect
data ________carry
4________has
output comparison network________values are carried
fact ________complete
rating network________takes
c________can define
comparators C ________receive
D________input wires receive
b1 ________number
b4 ________can pass
b2 ________travels
b3 ________define
comparator E________follows
sequence 〈________wires have
B ________cycles
Assuming ________wire is
time unit ________defined
resulting ________value
E________produce values
D ________observe
comparator C ________input values has been produced
bottom output ________remains is
comparator D ________ensure
b4________values occupy
respectively________correct
comparator E ________happens
b3________specifies
output sequence 〈________occur
assumption ________depends
unit time________shall
Informally________develop
largest ________specify
element ________is named
formally________Exercises
depths dx ________Show
depth max________appear
comparator depths________is given
equivalently________Let
depth d ________construct
time d________carries
equals ________input value
output sequence ________take
monotonically increasing ________add
course________is not
comparator B________does not sort
symmetrical argument ________Prove
comparator D________inputs has
output positions________Consider
procedure ________describe
comparisons ________structure is related
size________Exercise
contains________can represent
actually ________list
describing ________pairs
goal ________range
chapter ________pairs contain
family SORTER ________order
family ________is determined
output rating network ________list
SORTER________introduce
power ________convert
output comparison network ________uses
depth lg n ________total
way ________is correct
resulting network ________says
permutation________works
insertion ________input is drawn
c comparators ________input numbers
integers ________numbers can be
integer ________ordered set
representation________will allow
determining ________focus
addition ________have constructed
bottom ________proved
upside________shall appeal
ones________sorts
conversion method ________relies
zero________function
principle________transforms
correctly ________claim
integers________claim
reals________lower
linearly ________apply
sequences consisting solely ________is shown
sequences________yields
properly ________implies
proof ________completes
notion ________can use
Lemma ________result
output sequence b ________wire assumes
sequence f ________is applied
output sequence f________assumes
outputs f________is applied
induction ________wires are included
lemma________will prove
output________result follows
monotonically increasing________input wire carries
Consequently________step
identities________carry values
stronger ________is proved
statement ________repeated
sequence f________applied
statement________result
proving ________inputs sorts
basis________numbers
trivially________exists
inductive ________does not
depth d________sort
depth strictly ________places
inductive hypothesis________is input
example ________follows
application ________obtain
same rating network ________fails
remarkable ________numbers
Theorem ________State
's correctly________tree
correctly________Hint
purpose ________handle
contradiction ________contain
〉 containing elements ai ________step
output sequence________increases
sequence 〈f________decreases
〉 correctly________can be
applying ________shifted
sequence 〈n________become
sequences 〈________condition
〈________say
analog ________numbers is
decision________structure
model________form
equality properly________shall construct is
ith ________asks
st ________is called
bitonic rating network________input line
bitonic sequence________is compared
monotonically ________sample
circularly ________values are shown
monotonically decreasing________input is assumed
bitonic________ensures
boundary ________is clean
bitonic ________values are
simple ________derive
monotonically decreasing ________clean
bitonic sorter ________satisfies
bitonic sequences ________compares inputs
half________input is
cleaner________block
stages________falls
cleaner ________occurs
comparison network HALF________is further split
output element ________are shown
halves ________shown
bitonic sequence ________holds
fact________is assumed
clean________can think
consisting ________divided
property ________are compared
properties ________can build
cleaners________consists
properties________can complete
loss ________copies
generality________has been shown
situation ________has been
symmetric________make
cases depending upon ________followed
midpoint n________is shaded
cases ________can be sorted
midpoint ________numbers can be sorted
cases________can be constructed
case ________inputs is not
Subsequences ________will be constructed
gray________sorted input
being ________create
division ________shall prove
subsequence ________can be extended
bitonic sorter________input values
recursively combining half________is based
bitonic sequences________reverse
stage ________second
size ________get
using ________merge
halves recursively________suffices
recursion ________can construct
explicitly________be merged
unrolled ________want
progressively smaller half________effect
cleaners ________compare inputs
remainder ________are reversed compared
recurrence________satisfy
solution ________is transformed
comparison network BITONIC________merges
recursive construction________can be viewed
unrolling ________altered
recursion________are shaded
length n ________be applied
depth bitonic sorter ________verify
bitonic rating networks________be merged are
merging network________lower bound
merging networks________sets
networks ________implement
merging network MERGER________merge sort
intuition________are illustrated
concatenate ________constructed
resulting sequence ________boxes
sequences X ________is indicated
Concatenating X ________are sorted
X concatenated ________merged
MERGER________sorted
modifying ________obtained
reversal ________pass
implicitly________work
sequences 〈a1________merge pairs
bitonically rating ________produce sorted
correspondence________input values is produced
subtlety ________can be shown
bottom outputs ________can analyze
bitonically ________master
Comparing ________wish
monotonic ________can do
bitonic sequences 〈b1________be sorted
resulting merging network ________know
network MERGER________number is
network decomposed ________sorted order
same network ________numbered row
recursion unrolled________order
stages ________are required
Specifically________order should
monotonically increasing sequences ________read
item ________inputs is
items ________levels
monotonic sequences ________connected
Partition ________pattern illustrated
regardless ________can be seen
tools ________figure
rating network SORTER________saw
recursively combining merging networks________shall construct
Replacing ________put
MERGER ________second merges
recursive construction ________combine
elements ________suggests
recursively ________produced
length n________should put
resulting sequences ________produced is
boundary case ________part
element sequence________has switches
element sequence ________switch
lg n stages ________can be set
network SORTER________feed
element sequences ________cross
length ________switches
stage k ________are set
length 2k________realize
stage________Argue
sequence consisting ________replace
rating network recursively________switches
method ________switches have been set
5________performed
lg n ________defined
2n elements 〈a1________sets
n smallest ________switches connected
n largest________be realized
additional depth ________accomplish
separately rating 〈a1________does
k positions ________notes
position ________charts
depth S________were
entries ________explored
m × m matrix ________discovered
repeating ________used
procedure k times________showed
odd________could be used
even________presented
column ________attributes
iterations k ________trees
matrix entries ________question remained open
k iterations ________exists
Problems 27________answer was shown
Transposition rating networks________named
transposition network ________hidden
transposition rating network ________be considered
induction argument analogous ________
depth________
d comparator ________
rating networks actually ________
Batcher's odd________
bitonic rating________
problem________
Otherwise________
elements________
subsequences________
Professor Corrigan ________
recursive merging________
putting ________
counterexample ________
professor ________
mistaken ________
thinking ________
Permutation networks________
permutation network ________
n outputs ________
permutations________
output permutation network P2________
permutation network P2________
ways ________
permutation π ________
permutation network________
permutation π________
output π________
8________
output permutation network P8 ________
recursively________
bottom P4 ________
permutation 〈________
drawing ________
settings ________
permutations ________
Pn recursively ________
manner ________
machine________
element permutation________
machine ________
settings________
including ________
permutation ________
combinations ________
Knuth ________
history________
apparently ________
Armstrong________
Nelson________
O'Connor________
Batcher ________
merging ________
Problem 27________
technique ________
afterward________
Bouricius ________
context ________
decision ________
depth O________
somewhat unsatisfying ________
AKS rating network ________
developers________
Ajtai________
Komlós________
Szemerédi ________
using O________
constants ________
notation ________
thousands
