# Fibonacci heaps

## Basic idea

A heap of rooted trees with lazy consolidation. Achieves $O(1)$ amortised for insert and decrease-key, making Dijkstra and Prim run in $O(E + V\log V)$. Heavy hidden constants make it more theoretical than practical.

## Key formulas

* insert, find-min, merge, decrease-key: $O(1)$ amortised
* delete-min, delete: $O(\log n)$ amortised
* Max degree of any node: $D(n) \le \log\_\phi n$


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