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In order to find the value associated with a given key, a sequential search is used: each element of the list is searched in turn, starting at the head, until the key is found. Associative lists provide a simple way of implementing an associative array , but are efficient only when the number of keys is very small.
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.
In mathematics, a multivalued function, [1] multiple-valued function, [2] many-valued function, [3] or multifunction, [4] is a function that has two or more values in its range for at least one point in its domain. [5]
find the value (if any) that is bound to a given key. The argument to this operation is the key, and the value is returned from the operation. If no value is found, some lookup functions raise an exception, while others return a default value (such as zero, null, or a specific value passed to the constructor).
In the left hand sides of the following identities, L is the L eft most set and R is the R ight most set. Whenever necessary, both L and R should be assumed to be subsets of some universe set X , so that L ∁ := X ∖ L and R ∁ := X ∖ R . {\displaystyle L^{\complement }:=X\setminus L{\text{ and }}R^{\complement }:=X\setminus R.}
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algorithm merge(A, B) is inputs A, B : list returns list C := new empty list while A is not empty and B is not empty do if head(A) ≤ head(B) then append head(A) to C drop the head of A else append head(B) to C drop the head of B // By now, either A or B is empty.
In the F2 schedule, if T1 aborted, T2 has to abort because the value of A it read is incorrect. In both cases, the database is left in a consistent state. Schedule J is unrecoverable because T2 committed before T1 despite previously reading the value written by T1. Because T1 aborted after T2 committed, the value read by T2 is wrong.