# Memory representation of Binomial Heap

**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
- Key
- Degree
- 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())
- Array Representation Of Binary Heap
- Stack vs Heap Memory Allocation
- Heap Sort for decreasing order using min heap
- Convert min Heap to max Heap
- Difference between Byte Addressable Memory and Word Addressable Memory
- K-ary Heap
- K’th Least Element in a Min-Heap
- Max Heap in Java
- Skew Heap
- Convert BST to Max Heap
- Pairing Heap
- Binary 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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