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)
Famous quotes containing the words comparison of, comparison, bounds and/or variants:
“When we reflect on our past sentiments and affections, our thought is a faithful mirror, and copies its objects truly; but the colours which it employs are faint and dull, in comparison of those in which our original perceptions were clothed.”
—David Hume (1711–1776)
“I have travelled a good deal in Concord; and everywhere, in shops, and offices, and fields, the inhabitants have appeared to me to be doing penance in a thousand remarkable ways.... The twelve labors of Hercules were trifling in comparison with those which my neighbors have undertaken; for they were only twelve, and had an end; but I could never see that these men slew or captured any monster or finished any labor.”
—Henry David Thoreau (1817–1862)
“What comes over a man, is it soul or mind
That to no limits and bounds he can stay confined?
You would say his ambition was to extend the reach
Clear to the Arctic of every living kind.
Why is his nature forever so hard to teach
That though there is no fixed line between wrong and right,
There are roughly zones whose laws must be obeyed?”
—Robert Frost (1874–1963)
“Nationalist pride, like other variants of pride, can be a substitute for self-respect.”
—Eric Hoffer (1902–1983)