Complete Binary Tree

If the array has holes in it then it is not a complete binary tree.

Heap

The complete binary tree with heap order is called a heap.
This heap order (in case of min heap) is defined such that if k is the keys of nodes then \(k_p \le k_c\)
Where subscript p stands for parent node and c stands for child nodes.

Max Heap

max heap follows \(k_p \ge k_c\).

Insertion in a Heap

If inserting a new element violates the min heap order then it replaces positions with the arrow's(pointed in the array) head and tail