Comparison between Heap and Tree

What is Heap?

A Heap is a special Tree-based data structure in which the tree is a complete binary tree.

Types of Heap Data Structure:

Generally, Heaps can be of two types:

• Max-Heap: In a Max-Heap the key present at the root node must be greatest among the keys present at all of its children. The same property must be recursively true for all sub-trees in that Binary Tree.
• Min-Heap: In a Min-Heap the key present at the root node must be minimum among the keys present at all of its children. The same property must be recursively true for all sub-trees in that Binary Tree.

What is a Tree?

A tree is non-linear and has a hierarchical data structure consisting of a collection of nodes such that each node of the tree stores a value and a list of references to other nodes (the “children”).

Types of Tree data structures:

Usually, the different types of tree data structures are as follows:

• Binary tree: A node of a binary tree can have a maximum of two child nodes.  
• Binary search tree: As the name implies, binary search trees are used for various searching and sorting algorithms. The examples include AVL tree and the red-black tree. It is a non-linear data structure. It shows that the value of the left node is less than its parent, while the value of the right node is greater than its parent.

Comparison between heap and tree:

S.No	Heap	Tree
1	Heap is a kind of Tree itself.	The tree is not a kind of heap.
2	Usually, Heap is of two types, Max-Heap and Min-Heap.	Whereas a Tree can be of various types for eg. binary Tree, BST(Binary Search tree), AVL tree, etc.
3	Heap is ordered.	Binary Tree is not ordered but BST is ordered.
4	Insert and remove will take O(log(N)) time in the worst case.	Insert and remove will take O(N) in the worst case in case the tree is skewed.
5	Finding Min/Max value in Heap is O(1) in the respective Min/Max heap.	Finding Min/Max value in BST is O(log(N)) and Binary Tree is O(N).
6	Heap can also be referred to as Priority Queue.	A tree can also be referred to as a connected undirected graph with no cycle.
7	Heap can be built in linear time complexity.	BST: O(N * log(N)) and Binary Tree: O(N).
8	Applications: Prim’s Algorithm and Dijkstra’s algorithm.	Applications: Spanning Trees, Trie, B+ Tree, BST, Heap.