Search results
Results from the WOW.Com Content Network
A strict Fibonacci heap with no loss. Nodes 5 and 2 are active roots. Their active subtrees are binomial trees. A strict Fibonacci heap is a single tree satisfying the minimum-heap property. That is, the key of a node is always smaller than or equal to its children. As a direct consequence, the node with the minimum key always lies at the root.
A binomial heap is implemented as a set of binomial trees that satisfy the binomial heap properties: [1] Each binomial tree in a heap obeys the minimum-heap property: the key of a node is greater than or equal to the key of its parent. There can be at most one binomial tree for each order, including zero order.
A Fibonacci heap is thus better than a binary or binomial heap when is smaller than by a non-constant factor. It is also possible to merge two Fibonacci heaps in constant amortized time, improving on the logarithmic merge time of a binomial heap, and improving on binary heaps which cannot handle merges efficiently.
Examples of mergeable heap data structures include: Binomial heap; Fibonacci heap; Leftist tree; Pairing heap; Skew heap; A more complete list with performance comparisons can be found at Heap (data structure) § Comparison of theoretic bounds for variants. In most mergeable heap structures, merging is the fundamental operation on which others ...
Vuillemin invented the binomial heap [2] and Cartesian tree data structures. [3] With Ron Rivest, he proved the Aanderaa–Rosenberg conjecture, according to which any deterministic algorithm that tests a nontrivial monotone property of graphs, using queries that test whether pairs of vertices are adjacent, must perform a quadratic number of adjacency queries. [4]
Skew binomial heap containing numbers 1 to 19, showing trees of ranks 0, 1, 2, and 3 constructed from various types of links Simple, type a skew, and type b skew links. A skew binomial heap is a forest of skew binomial trees, which are defined inductively: A skew binomial tree of rank 0 is a singleton node.
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.
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.