Comparison of Theoretic Bounds For Variants
The following time complexities are amortized (worst-time) time complexity for entries marked by an asterisk, and regular worst case time complexities for all other entries. O(f) gives asymptotic upper bound and Θ(f) is asymptotically tight bound (see Big O notation). Function names assume a min-heap.
| Operation | Binary | Binomial | Fibonacci | Pairing | Brodal*** | RP |
|---|---|---|---|---|---|---|
| find-min | Θ(1) | Θ(1) | Θ(1) | Θ(1) | Θ(1) | Θ(1) |
| delete-min | Θ(log n) | Θ(log n) | O(log n)* | O(log n)* | O(log n) | O(log n)* |
| insert | Θ(log n) | O(log n) | Θ(1) | Θ(1)* | Θ(1) | Θ(1) |
| decrease-key | Θ(log n) | Θ(log n) | Θ(1)* | O(log n)* | Θ(1) | Θ(1)* |
| merge | Θ(n) | O(log n)** | Θ(1) | Θ(1)* | Θ(1) | Θ(1) |
(*)Amortized time
(**)Where n is the size of the larger heap
(***)Brodal and Okasaki later describe a persistent variant with the same bounds except for decrease-key, which is not supported. Heaps with n elements can be constructed bottom-up in O(n).
Read more about this topic: Heap (data Structure)
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