Explanation
- A **Fibonacci Heap** is a collection of heap-ordered trees where each tree follows the heap property. It is used to optimize priority queues and supports very efficient **decrease-key** and **delete-min** operations.
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- It is often used in algorithms like **Dijkstra's shortest path algorithm** and **Prim's minimum spanning tree algorithm**.
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Steps:
- Insert: Insert a new element by creating a new tree with the element and adding it to the root list.
- Minimum: The minimum element is easily accessible from the root list.
- Decrease Key: The decrease key operation is optimized by cutting and reattaching nodes.
- Meld: Two Fibonacci heaps can be merged efficiently by merging their root lists.
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Time Complexity:
- Insertion: O(1) (amortized)
- Find Min: O(1)
- Decrease Key: O(1) (amortized)
- Delete Min: O(log n) (amortized)