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If each node additionally records the size of its subtree ( including itself and its descendants ), then the nodes can be retrieved by index in O ( log n ) time as well.

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## Some Related Sentences

If and each

__If__

**the**Union conceded this to them,

**the**same right must

**be**conceded to

__each__remaining state whenever it saw fit to secede: This would destroy

**the**federal balance between it

**and**

**the**states,

**and**

**in**

**the**end sacrifice to

**the**sovereignty

**of**

**the**states all

**the**liberty

**the**citizens had gained

**by**their Union

**.**

__If__

**the**railroads, for example, regularly slaughtered 25,000 passengers

__each__year,

**the**high priests

**of**

**the**cult would have cause to tremble for their personal safety, for such a holocaust would excite demands for

**the**hanging

**of**every railroad president

**in**

**the**United States

**.**

__If__a branch extended out too far,

__each__man held it back for

**the**next,

**and**if they met a low overhang,

__each__warned

**the**other

**.**

__If__coffee is sold at

**the**cafeteria, let a few workers

**in**

__each__department get it for

**the**whole group

**.**

__If__no specific organization plan exists limiting

**the**number

**of**scientists at

__each__salary level,

**the**result is a department top-heavy with high-level, high-salaried personnel ''

**.**

__If__Af are

**the**projections associated with

**the**primary decomposition

**of**T,

**then**

__each__Af is a polynomial

**in**T,

**and**accordingly if a linear operator U commutes with T

**then**U commutes with

__each__

**of**

**the**Af, i.e.,

__each__subspace Af is invariant under U

**.**

__If__

__each__text form is marked when matched with a dictionary form,

**the**text forms not contained

**in**

**the**dictionary

**can**

**be**identified when all dictionary forms have been read

**.**

__If__cell Af is an information cell, it

**and**any information cells

**in**

**the**Y-region that have been linked to Af

__each__contain an address

**in**

**the**W-region where a potentially matching form is stored

**.**

__If__

**the**bottom name

**in**

__each__column did not have a responsible executive identified,

**the**next name above which identified such a responsible executive was substituted

**.**

__If__

**the**wedding party lasted late,

**and**

**the**travel schedule means there are only a few hours before resuming

**the**trip or making an early start,

**the**husband may forestall tensions

**and**uncertainties

**by**confiding to his bride that lying

**in**

__each__other's arms will

**be**bliss enough for these few hours

**.**

__If__he is not told which

**of**four or five readings was meant for him, he

**can**more readily assess

__each__item

**in**a larger frame: `` Does that statement really sound

**as**if it were for me, significant

**in**my particular life??

__If__laborers are merely commodities competing against

__each__other

**in**a market place like so many bags

**of**wheat

**and**corn

**(**unsupported,

**by**

**the**way,

**by**any agricultural subsidy

**)**,

**then**they may

**be**pardoned for reacting with complete antagonism to a system that imposes such status upon them

**.**

__If__

**the**method is applied to an infinite sequence

**(**X < sub > i </ sub >: i ∈ ω

**)**

**of**nonempty sets, a function is obtained at

__each__finite stage, but there is no stage at which a choice function for

**the**entire family is constructed,

**and**no " limiting " choice function

**can**

**be**constructed,

**in**general,

**in**ZF without

**the**axiom

**of**choice

**.**

__If__we try to choose an element from

__each__set,

**then**, because X is infinite, our choice procedure will never come to an end,

**and**consequently, we will never

**be**able to produce a choice function for all

**of**X

**.**

__If__a particle

**and**antiparticle are

**in**

**the**appropriate quantum states,

**then**they

**can**annihilate

__each__other

**and**produce other particles

**.**

__If__

**the**square mile is divided into quarters,

__each__quarter has a side length

**of**mile

**(**880 yards

**)**

**and**is square mile

**in**area, or 160 acres

**.**

__If__

**the**domain

**of**F is a disjoint union

**of**two or more intervals,

**then**a different constant

**of**integration may

**be**chosen for

__each__

**of**

**the**intervals

**.**

__If__a water absorbing swale for

__each__yard is combined with permeable concrete streets, storm drains

**can**

**be**omitted from

**the**neighbourhood

**.**

__If__

**the**candidate relies on sponsors,

**the**celebrant asks them if they will raise

**the**child

**in**"

**the**Christian faith

**and**life "

**(**ECUSA BCP

**),**

**and**will raise

**the**child through " prayers

**and**witness to grow into

**the**full stature

**of**Christ " to which

**the**parents will state to

__each__, " I will, with God's help

**.**

__If__

**the**dealer does not bust,

__each__remaining bet wins if

**its**hand is higher than

**the**dealer's,

**and**loses if it is lower

**.**

__If__all four players pass

**in**

**the**first round,

**the**deal is not played ;

**in**rubber bridge

**the**deal is not scored

**and**

**the**hand is redealt

**by**

**the**original dealer, while

**in**duplicate

**the**score is recorded

**as**zero for

__each__pair

**and**returned to

**the**board

**.**

If and node

*

__If__**the**balance factor**of**P is-2**then****the**right**subtree**outweighs**the**left**subtree****of****the**given__node__,**and****the**balance factor**of****the**right child**(**R**)**must**be**checked**.**
*

__If__**the**balance factor**of**P is 2,**then****the**left**subtree**outweighs**the**right**subtree****of****the**given__node__,**and****the**balance factor**of****the**left child**(**L**)**must**be**checked**.**__If__a

__node__has fewer than two children, some

**of**

**the**child pointers may

**be**set to a special null value, or to a special sentinel

__node__

**.**

__If__a piece

**of**data is not

**retrieved**for some

**time**

**and**a

__node__keeps getting new data, it will drop

**the**old data sometime when

**its**allocated disk space is fully used

**.**

__If__it's not found,

**the**key's hash is turned into another number

**in**

**the**same range,

**and**

**the**request is routed to

**the**

__node__whose location is closest to

**the**key

**.**

__If__

**the**

__node__which has

**the**requested file is not firewalled,

**the**querying

__node__

**can**connect to it directly

**.**

In computer science, a heap is a specialized tree-based data structure that satisfies

**the**heap property:__If__A is a parent__node__**of**B**then**key**(**A**)**is ordered with respect to key**(**B**)**with**the**same ordering applying across**the**heap**.**__If__10

**of**those mutants are viable genotypes that may reproduce

**(**

**and**some

**of**whose offspring or grandchilden may mutate back into AGGT again

**),**we would consider that sequence a well-connected

__node__

**in**

**the**cloud

**.**

__If__

**the**cluster contains two values, however, either one

**can**become

**the**black

__node__

**in**

**the**red – black tree

**(**

**and**

**the**other one will

**be**red ).

__If__

**the**central

__node__is passive,

**the**originating

__node__must

**be**able to tolerate

**the**reception

**of**an echo

**of**

**its**own transmission, delayed

**by**

**the**two-way transmission

**time**

**(**i

**.**e

**.**to

**and**from

**the**central

__node__

**)**plus any delay generated

**in**

**the**central

__node__

**.**

If and additionally

__If__

**the**aging for one

**of**these types

**of**whiskey reaches two years or beyond,

**the**whiskey is

**then**

__additionally__designated

**as**" straight " e

**.**g., " straight rye whiskey ".

__If__we use NC reductions, that is, reductions which

**can**operate

**in**polylogarithmic

**time**on a parallel computer with a polynomial number

**of**processors,

**then**all P-complete problems lie outside NC

**and**so cannot

**be**effectively parallelized, under

**the**unproven assumption that NC ≠ P

**.**

__If__we use

**the**weaker log-space reduction, this remains true, but

__additionally__we learn that all P-complete problems lie outside L under

**the**weaker unproven assumption that L ≠ P

**.**In this latter case

**the**set P-complete may

**be**smaller

**.**

__If__UV / Vis spectrophotometry is used

**in**quantitative chemical analysis

**then**

**the**results are

__additionally__affected

**by**uncertainty sources arising from

**the**nature

**of**

**the**compounds

**and**/ or solutions that are measured

**.**

__If__,

__additionally__,

**the**recipient

**of**

**the**criticism is not

**the**intended target, that is also a factor to consider

**.**

__If__we

__additionally__assume that

**the**image plane is perpendicular to

**the**ground plane

**(**an imaginary plane Tangential to

**the**surface

**of**

**the**Earth

**),**

**and**that

**the**waterfall flows on a plane that is parallel to

**the**image plane, we

**can**estimate

**the**height

**by**measuring

**the**vertical separation

**of**waterfall head

**and**base

**in**

__If__,

__additionally__,

**the**real part

**of**s is positive,

**then**

**the**limit γ

**(**s, u

**)**→ 0 for u → 0 applies, finally arriving at

**the**complex integral definition

**of**γ

__If__not,

**then**

**the**judge must

__additionally__assess

**the**application under

**the**" centralized mode

**of**existence " approach, guided

**by**

**the**non-exhaustive factors set out

**in**Koo

**(**Re ).

__If__

**the**poset P

__additionally__is a join-semilattice

**(**i

**.**e., if it has binary suprema

**)**

**then**these conditions are equivalent to

**the**following statement:

__If__a player cannot follow suit, he must play a trump card if able,

**and**

__additionally__,

**the**player is compelled to play a higher trump than any existing trump

**in**

**the**trick if he is able

**(**The " Petit " or 1 is valued lowest,

**and**

**the**" Monde " or 21 is valued highest ).

__If__it were a warship,

**and**repairable, usually

**the**Crown bought it at a fair price ;

__additionally__,

**the**Crown added " head money "

**of**5 pounds per enemy sailor aboard

**the**captured warship

**.**

Their sets included songs spanning Strummer's career to that point,

**including**works from The 101ers**and**The Clash,__additionally__material co written with Mick Jones for Big Audio Dynamite's No**.**10, Upping St**.**album**as****well****as**a cover**of**The Pogues ' famous "__If__I Should Fall From Grace With God**.**__If__

**the**sample is depolarizing

**the**Mueller matrix formalism should

**be**used, because it gives

__additionally__access to

**the**amount

**of**depolarization

**.**

__If__X was

**in**good faith,

**and**

__additionally__was

**in**legal possession

**of**

**the**house,

**then**any vindicatio brought

**by**Y could

**be**defeated

**by**X using

**the**defence

**of**fraud

**(**exceptio dolus malus

**)**until Y paid X for

**the**materials

**.**

__If__

**the**two vertices are

__additionally__connected

**by**a path

**of**length 1, i

**.**e

**.**

**by**a single edge,

**the**vertices are called adjacent

**.**

__If__police

__additionally__have reasonable suspicion that a person so detained may

**be**armed, they may " frisk "

**the**person for weapons, but not for contraband like drugs

**.**

__If__

**the**officer

__additionally__has reasonable suspicion that

**the**person is armed,

**the**officer may perform a search

**of**

**the**person's outer garments for weapons

**.**

__If__abstract

**index**notation is used also for spinors

**then**these will carry a spinorial

**index**

**and**

**the**Dirac gamma will carry one Lorentzian

**and**two spinorian indices, but it is more common to regard spinors

**as**column matrices

**and**

**the**Dirac gamma

**as**a matrix which

__additionally__carries a Lorentzian

**index**

**.**

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