 | This article relies on a single source. (May 2024) |
In computer science, a mergeable heap (also called a meldable heap) is an abstract data type, which is a heap supporting a merge operation.
| This article relies on a single source. (May 2024) |
In computer science, a mergeable heap (also called a meldable heap) is an abstract data type, which is a heap supporting a merge operation.
A mergeable heap supports the usual heap operations:
Make-Heap(), create an empty heap.Insert(H,x), insert an element x into the heap H.Min(H), return the minimum element, or Nil if no such element exists.Extract-Min(H), extract and return the minimum element, or Nil if no such element exists.And one more that distinguishes it:
Merge(H1,H2), combine the elements of H1 and H2 into a single heap.It is straightforward to implement a mergeable heap given a simple heap:
Merge(H1,H2):
x ← Extract-Min(H2)while x ≠ Nil
Insert(H1, x)x ← Extract-Min(H2)This can however be wasteful as each Extract-Min(H) and Insert(H,x) typically have to maintain the heap property.
Examples of mergeable heap data structures include:
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 are based. Insertion is implemented by merging a new single-element heap with the existing heap. Deletion is implemented by merging the children of the deleted node.