Prerequisites: Binomial Heap
Binomial trees are multi-way trees typically stored in the left-child, right-sibling representation, and each node stores its degree. Binomial heaps are collection of binomial trees stored in ascending order of size. The root list in the heap is a linked list of roots of the Binomial heap. The degree of the nodes of the roots increase as on traversing the root list.
The number of binomial trees in a binomial heap can be found with the binary value of the number of nodes in the binomial heap. This article focuses on memory representation of binomial heaps.
Binomial Heap Node:
Fields in each node:
Each node in a binomial heap has 5 fields :
- Pointer to parent
- Pointer to child (leftmost child)
- Pointer to sibling which is immediately to its right
Pointers in each node:
Each node has the following pointers:
- A parent pointer pointing to the immediate parent of the node
- A left pointer pointing to the first child of the node
- A right pointer pointing to the next sibling of the node.
- Single node in the Heap:
- Parent – Child relationship between nodes:
- Sibling relationship between nodes:
- Binomial Heap
- Implementation of Binomial Heap
- Implementation of Binomial Heap | Set - 2 (delete() and decreseKey())
- Convert min Heap to max Heap
- Heap Sort for decreasing order using min heap
- Array Representation Of Binary Heap
- Stack vs Heap Memory Allocation
- Difference between Byte Addressable Memory and Word Addressable Memory
- Applications of Heap Data Structure
- Tournament Tree (Winner Tree) and Binary Heap
- Time Complexity of building a heap
- Why is Binary Heap Preferred over BST for Priority Queue?
- Fibonacci Heap | Set 1 (Introduction)
- Check if a given Binary Tree is Heap
- K-ary Heap
- Heap in C++ STL | make_heap(), push_heap(), pop_heap(), sort_heap(), is_heap, is_heap_until()
- Where is Heap Sort used practically?
- Binary Heap
- Given level order traversal of a Binary Tree, check if the Tree is a Min-Heap
- How to implement stack using priority queue or heap?
Types of nodes and their representations:
Representation of Full binomial heap:
The memory representation of each node of the Binomial heap given above can be illustrated using the following diagram:
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