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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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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.