Prerequisites:Fibonacci Heap (Introduction)
Fibonacci Heap is a collection of trees with min-heap or max-heap property. In Fibonacci Heap, trees can can have any shape even all trees can be single nodes (This is unlike Binomial Heap where every tree has to be Binomial Tree).
In this article, we will discuss Insertion and Union operation on Fibonacci Heap.
Insertion: To insert a node in a Fibonacci heap H, the following algorithm is followed:
- Create a new node ‘x’.
- Check whether heap H is empty or not.
- If H is empty then:
- Make x as the only node in the root list.
- Set H(min) pointer to x.
- Insert x into root list and update H(min).
Union: Union of two Fibonacci heaps H1 and H2 can be accomplished as follows:
- Join root lists of Fibonacci heaps H1 and H2 and make a single Fibonacci heap H.
- If H1(min) < H2(min) then:
- H(min) = H1(min).
- H(min) = H2(min).
Following is a program to demonstrate building and inserting in a Fibonacci heap:
The root nodes of Heap are: 1-->2-->3-->4-->7-->5-->10 The heap has 7 nodes Min of heap is: 1
- Fibonacci Heap | Set 1 (Introduction)
- Fibonacci Heap - Deletion, Extract min and Decrease key
- Union-Find Algorithm | (Union By Rank and Find by Optimized Path Compression)
- Heap Sort for decreasing order using min heap
- Convert min Heap to max Heap
- Check if a M-th fibonacci number divides N-th fibonacci number
- AVL Tree | Set 1 (Insertion)
- Kth smallest element after every insertion
- Skip List | Set 2 (Insertion)
- Insertion in Unrolled Linked List
- ScapeGoat Tree | Set 1 (Introduction and Insertion)
- Optimal sequence for AVL tree insertion (without any rotations)
- Klee's Algorithm (Length Of Union Of Segments of a line)
- K-ary Heap
- K’th Least Element in a Min-Heap