Lecture 03
A common waay to prove amortized bounds is to use the potential function method.
Define potential function $\Phi(x)$ as the function that returns the value of the potential at a point $x$.
Fibonacci Heap
Time complexity of operations for various heaps
| Operation | Binary Heap | Binomial Heap | Fibonacci Heap |
|---|
| Find Min | $O(1)$ | $O(\log{n})$ | $O(1)$ |
| Insert | $O(\log{n})$ | $O(\log{n})$ | $O(1)$ |
| Extract Min | $O(\log{n})$ | $O(\log{n})$ | $O(\log{n})$ |
| Delete | $O(\log{n})$ | $O(\log{n})$ | $O(\log{n})$ |
| Decrease Key | $O(\log{n})$ | $O(\log{n})$ | $O(1)$ |
| Merge | $O(n)$ | $O(\log{n})$ | $O(1)$ |
| Construct | $O(n)$ | $O(n)$ | $O(n)$ |