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The red subset = {1,2,3,4} has two maximal elements, viz. 3 and 4, and one minimal element, viz. 1, which is also its least element. In mathematics , especially in order theory , a maximal element of a subset S {\displaystyle S} of some preordered set is an element of S {\displaystyle S} that is not smaller than any other element in S ...
The root element is the smallest element in the min-max heap. One of the two elements in the second level, which is a max (or odd) level, is the greatest element in the min-max heap; Let be any node in a min-max heap. If is on a min (or even) level, then . is the minimum key among all keys in the subtree with root .
In computer science, a heap is a tree-based data structure that satisfies the heap property: In a max heap, for any given node C, if P is the parent node of C, then the key (the value) of P is greater than or equal to the key of C. In a min heap, the key of P is less than or equal to the key of C. [1] The node at the "top" of the heap (with no ...
Likewise, a greatest element of a partially ordered set (poset) is an upper bound of the set which is contained within the set, whereas the maximal element m of a poset A is an element of A such that if m ≤ b (for any b in A), then m = b. Any least element or greatest element of a poset is unique, but a poset can have several minimal or ...
Hilbert projection theorem — For every vector in a Hilbert space and every nonempty closed convex , there exists a unique vector for which ‖ ‖ is equal to := ‖ ‖. If the closed subset C {\displaystyle C} is also a vector subspace of H {\displaystyle H} then this minimizer m {\displaystyle m} is the unique element in C {\displaystyle C ...
If T.min = T.max = x then x is the only element stored in the tree and we set T.min = M and T.max = −1 to indicate that the tree is empty. Otherwise, if x == T.min then we need to find the second-smallest value y in the vEB tree, delete it from its current location, and set T.min=y.
In computer science, selection sort is an in-place comparison sorting algorithm.It has a O(n 2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort.
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]