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2. Heap (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Heap_(mathematics)

   Theorem: A semiheap with a biunitary element e may be considered an involuted semigroup with operation given by ab = [a, e, b] and involution by a –1 = [e, a, e]. [1]: 76 When the above construction is applied to a heap, the result is in fact a group. [1]: 143 Note that the identity e of the group can be chosen to be any element of the heap.

3. Heap (data structure) - Wikipedia

   en.wikipedia.org/wiki/Heap_(data_structure)

   Example of a binary max-heap with node keys being integers between 1 and 100. 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.

4. Pairing heap - Wikipedia

   en.wikipedia.org/wiki/Pairing_heap

   A pairing heap is either an empty heap, or a pairing tree consisting of a root element and a possibly empty list of pairing trees. The heap ordering property requires that parent of any node is no greater than the node itself. The following description assumes a purely functional heap that does not support the decrease-key operation.

5. Binary heap - Wikipedia

   en.wikipedia.org/wiki/Binary_heap

   and we want to add the number 15 to the heap. We first place the 15 in the position marked by the X. However, the heap property is violated since 15 > 8, so we need to swap the 15 and the 8. So, we have the heap looking as follows after the first swap: However the heap property is still violated since 15 > 11, so we need to swap again:

6. Ternary tree - Wikipedia

   en.wikipedia.org/wiki/Ternary_tree

   Height - Length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node (the root) has a height of zero. In the example diagram, the tree has height of 2. Sibling - Nodes that share the same parent node. A node p is an ancestor of a node q if it exists on the path from q to the root. The node q is then ...

7. Self-balancing binary search tree - Wikipedia

   en.wikipedia.org/wiki/Self-balancing_binary...

   Most operations on a binary search tree (BST) take time directly proportional to the height of the tree, so it is desirable to keep the height small. A binary tree with height h can contain at most 2 0 +2 1 +···+2 h = 2 h+1 −1 nodes. It follows that for any tree with n nodes and height h: + And that implies:

8. Heapsort - Wikipedia

   en.wikipedia.org/wiki/Heapsort

   The heapsort algorithm can be divided into two phases: heap construction, and heap extraction. The heap is an implicit data structure which takes no space beyond the array of objects to be sorted; the array is interpreted as a complete binary tree where each array element is a node and each node's parent and child links are defined by simple arithmetic on the array indexes.

9. Fibonacci heap - Wikipedia

   en.wikipedia.org/wiki/Fibonacci_heap

   Figure 1. Example of a Fibonacci heap. It has three trees of degrees 0, 1 and 3. Three vertices are marked (shown in blue). Therefore, the potential of the heap is 9 (3 trees + 2 × (3 marked-vertices)). A Fibonacci heap is a collection of trees satisfying the minimum-heap property, that is, the key of a child is always greater than or equal to ...