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the array and linked representations of binary trees, as well as different methods for traversing binary trees:

Array Representation of Binary Trees:

In an array representation, you store the binary tree in an array, where each node’s position in the array corresponds to its position in the binary tree. This representation is particularly useful for complete binary trees.

For a node at index i:

  • Its left child is at index 2*i + 1.
  • Its right child is at index 2*i + 2.

However, in this representation, you may waste memory space for sparse trees, as not all indices may be filled.

Linked Representation of Binary Trees:

In a linked representation, each node of the binary tree is represented using a node structure. Each node contains pointers or references to its left and right children.

python
class Node:

def __init__(self, value):

self.value = value

self.left = None

self.right = None

Using the Node class, you can construct the binary tree by linking nodes together.

Traversing Binary Trees:

Traversing a binary tree means visiting all the nodes of the tree in a specific order. There are three common methods for traversing binary trees:

  1. Inorder Traversal: In this traversal, nodes are visited in the order of left subtree, root, and then right subtree. It’s commonly used for binary search trees to visit nodes in sorted order.

    python
    def inorder_traversal(node):

    if node:

    inorder_traversal(node.left)

    print(node.value)

    inorder_traversal(node.right)

  2. Preorder Traversal: In this traversal, nodes are visited in the order of root, left subtree, and then right subtree.

    python
    def preorder_traversal(node):

    if node:

    print(node.value)

    preorder_traversal(node.left)

    preorder_traversal(node.right)

  3. Postorder Traversal: In this traversal, nodes are visited in the order of left subtree, right subtree, and then root.

    python
    def postorder_traversal(node):

    if node:

    postorder_traversal(node.left)

    postorder_traversal(node.right)

    print(node.value)

These traversals can be implemented recursively or iteratively, depending on your preference and requirements. Each traversal order has its own use cases and advantages.