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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 the key of the parent. This implies that the minimum key is always at the root of one of the trees. Compared with binomial heaps, the structure of a Fibonacci heap is more flexible.
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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.
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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.
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A mergeable heap supports the usual heap operations: [1] 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: [1]
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