**Min and Max heaps** are complete binary trees with some unique properties.

# Binary Tree

A Binary Tree is a tree data structure wherein each node has at most two "children."

A node in the binary tree typically contains the following properties:

- Reference to the left child.
- Reference to the right child.
- Data

> A **complete Binary Tree** is a binary tree in which every level, except possibly the last, is filled.



### Min-Heap

- The root node has the **minimum** value.

- The value of each node is equal to or greater than the value of its parent node.

- A complete binary tree.


### Max-Heap

- The root node has the **maximum** value.

- The value of each node is equal to or less than the value of its parent node.
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- A complete binary tree.

# How are Min/Max Heaps represented?

A Min/Max heap is typically represented as an array.

> - Arr[0] Returns the root node.
> - Arr[(i-1)/2] Returns the parent node.
> - Arr[(2*i)+1] Returns the left child node.
> - Arr[(2*i)+2] Returns the right child node.


# Time Complexity of Min/Max Heap



- **Get Max or Min Element**

     * The Time Complexity of this operation is O(1).

- **Remove Max or Min Element**

     * The time complexity of this operation is O(Log n) because we need to maintain the max/mix at their root node, which takes Log n operations.

- **Insert an Element**

     * Time Complexity of this operation is O(Log n) because we insert the value at the end of the tree and traverse up to remove violated property of min/max heap.

Min Heap vs. Max Heap

Min and Max heaps are complete binary trees with some unique properties. Binary Tree A Binary Tree is a tree data structure wherein each node has at most two “children.” A node in the binary tree typically contains the following properties:  Reference to the left child. Reference to the right child. Data   A complete Binary Tree is a binary tree in which every level, except possibly the last, is filled.  