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.

* 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 the node is a leaf or has only one child, remove it.

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 data is found, it is cached on each node along the path.

If the color of node is not equal to target-color, return.

If the color of node is not equal to target-color, return.

If the color of the node to the north of n is target-color, add that node to Q.

If the color of the node to the south of n is target-color, add that node to Q.

If a search request turns up a result, the node that has the result contacts the searcher.

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 the checksum is bad, the routing node discards the packet.

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 the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If F and G are ( covariant ) functors between the categories C and D, then a natural transformation η from F to G associates to every object X in C a morphism in D such that for every morphism in C, we have ; this means that the following diagram is commutative:

If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of A is not zero.

If we view the DFT as just a coordinate transformation which simply specifies the components of a vector in a new coordinate system, then the above is just the statement that the dot product of two vectors is preserved under a unitary DFT transformation.

If there is an additional magnitude of value or a loss of value after transformation compared with before then the relation between values ( proportional to labor ) and prices ( proportional to total capital advanced ) is incomplete.

If the unitary transformation is chosen correctly, several components of the combined system will evolve into approximate copies of the original system.

If the Sex Pistols ' breakup the previous year had marked the end of the original UK punk scene and its promise of cultural transformation, for many the death of Vicious signified that it had been doomed from the start.

If this is the case, then the transformation of whole lineages should be rare, as the fossil record indicates.

If two theories are related by a duality transformation, it means that the first theory can be transformed in some way so that it ends up looking just like the second theory.

If an index transforms like a vector with the inverse of the basis transformation, it is called contravariant and is traditionally denoted with an upper index, while an index that transforms with the basis transformation itself is called covariant and is denoted with a lower index.

If every object X < sub > i </ sub > of C admits a initial morphism to U, then the assignment and defines a functor V from C to D. The maps φ < sub > i </ sub > then define a natural transformation from 1 < sub > C </ sub > ( the identity functor on C ) to UV.

If an origin is also chosen, this can be decomposed as an affine transformation that sends, namely

If there is a fixed point, we can take that as the origin, and the affine transformation reduces to a linear transformation.

If the categories C and D have all limits of type J then lim is a functor and the morphisms τ < sub > F </ sub > form the components of a natural transformation

If this object is a class of transformations ( such as " isomorphism " or " permutation "), it implies the equivalence of objects one of which is the image of the other under such a transformation.

If F and G are functors between the categories C and D, then a natural transformation η from F to G associates to every object X in C a morphism between objects of D, called the component of η at X, such that for every morphism we have:

If η is a natural transformation from F to G, we also write or.

If and are natural transformations between functors, then we can compose them to get a natural transformation.

If is a natural transformation between functors and is a natural transformation between functors, then the composition of functors allows a composition of natural transformations.

If is a natural transformation between functors, and is another functor, then we can form the natural transformation by defining

If on the other hand is a functor, the natural transformation is defined by