Summary of Running Times
| Common Operations | Effect | Unsorted Linked List | Self-balancing binary search tree | Binary heap | Binomial heap | Fibonacci heap | Brodal queue | Pairing heap |
|---|---|---|---|---|---|---|---|---|
| insert(data,key) | Adds data to the queue, tagged with key | O(1) | O(log n) | O(log n) | O(log n) | O(1) | O(1) | O(1) |
| findMin -> key,data | Returns key,data corresponding to min-value key | O(n) | O(log n) or O(1) (**) | O(1) | O(log n) | O(1) | O(1) | O(1) |
| deleteMin | Deletes data corresponding to min-value key | O(n) | O(log n) | O(log n) | O(log n) | O(log n)* | O(log n) | O(log n)* |
| delete(node) | Deletes data corresponding to given key, given a pointer to the node being deleted | O(1) | O(log n) | O(log n) | O(log n) | O(log n)* | O(log n) | O(log n)* |
| decreaseKey(node) | Decreases the key of a node, given a pointer to the node being modified | O(1) | O(log n) | O(log n) | O(log n) | O(1)* | O(1) | Unknown but bounded: * |
| merge(heap1,heap2) -> heap3 | Merges two heaps into a third | O(1) | O(m log(n+m)) | O(m + n) | O(log n)*** | O(1) | O(1) | O(1) |
(*)Amortized time
(**)With trivial modification to store an additional pointer to the minimum element
(***)Where n is the size of the larger heap
Read more about this topic: Fibonacci Heap
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