Mergeable heap

In computer science, a mergeable heap (also called a meldable heap) is an abstract data type, which is a heap supporting a merge operation.

Definition

A mergeable heap supports the following operations:^[1]

Make-Heap(), creating an empty heap.
Insert(H,x), inserting an element x into the heap H.
Min(H), returning the minimum element, or Nil if no such element exists.
Extract-Min(H), extracting and returning the minimum element, or Nil if no such element exists.
Merge(H1,H2), combining the elements of H1 and H2.

Trivial implementation

It is straightforward to implement a mergeable heap given a simple heap:

Merge(H1,H2):

x ← Extract-Min(H2)
while x ≠ Nil
1. Insert(H1, x)
2. 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.

More efficient implementations

Examples of mergeable heaps include:

A more complete list with performance comparisons can be found here.

See also

Addressable heap

References

↑ Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. 2009, 3rd ed. The MIT Press. ISBN 978-0-262-53305-8.

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