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.
Types of nodes and their representations:
- Single node in the Heap:
- Parent – Child relationship between nodes:
- Sibling relationship between nodes:
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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