Heap

 A heap is a special tree-based data structure that satisfies two rules:

---

1. Heap Property

Depending on the type of heap:

Min-Heap

• Every parent node is less than (≤) it's children.

• The smallest element is always at the root.

Max-Heap

• Every parent node is ≥ its children.

• The largest element is always at the root.

It does not require a fully sorted structure, only the parent/child relationship must follow the rule.

---

2. Complete Binary Tree Property

A heap is always a complete binary tree, meaning:

• It is filled level by level, from left to right.

• No gaps are allowed except possibly at the last level.

This makes it easy to store a heap inside an array without needing pointers.

---

How a Heap Is Stored in an Array

For a node at index i:

• Left child = index 2i

• Right child = index 2i + 1

• Parent = index i // 2

This mapping is why heaps work efficiently inside arrays.

Heap Insert

Insert/Create Heap

Heap Deletion

Delete 2 

Python Syntax:

import heapq

nums=[5 3, 8, 1]

heapq.heapify(nums)

heapq.heappush(nums,2)

smallest = heapq.heappop(nums)

#Max heap (negation)

maxheap=[]

heapq.heappush(maxheap, -1 * 5 )

heapq.heappush(maxheap, -1 * 2 )

largest = -1 * heapq.heappop(maxheap)