Traversal

In a Binary Search Tree (BST), there are several ways to traverse the nodes in a specific order. The most common traversal methods are Inorder, Preorder, Postorder, and Level Order traversals. Here's a detailed explanation of each:

Inorder Traversal

In an inorder traversal, the nodes are visited in the following order: Left subtree -> Root -> Right subtree. This traversal method results in the nodes being visited in ascending order if it's a BST.

Algorithm:

1. Traverse the left subtree recursively.

2. Visit the root node.

3. Traverse the right subtree recursively.

Example: For the following BST:

    4
   / \
  2   6
 / \ / \
1  3 5  7

The inorder traversal would be: 1, 2, 3, 4, 5, 6, 7

Preorder Traversal

In a preorder traversal, the nodes are visited in the following order: Root -> Left subtree -> Right subtree. This traversal method is often used to create a copy of the tree.

Algorithm:

1. Visit the root node.

2. Traverse the left subtree recursively.

3. Traverse the right subtree recursively.

Example: For the same BST:

    4
   / \
  2   6
 / \ / \
1  3 5  7

The preorder traversal would be: 4, 2, 1, 3, 6, 5, 7

Postorder Traversal

In a postorder traversal, the nodes are visited in the following order: Left subtree -> Right subtree -> Root. This traversal method is useful for deleting nodes in a tree.

Algorithm:

1. Traverse the left subtree recursively.

2. Traverse the right subtree recursively.

3. Visit the root node.

Example: For the same BST:

    4
   / \
  2   6
 / \ / \
1  3 5  7

The postorder traversal would be: 1, 3, 2, 5, 7, 6, 4

Level Order Traversal

In a level order traversal, the nodes are visited level by level from left to right. This traversal method is also known as Breadth-First Search (BFS).

Algorithm:

1. Start from the root node.

2. Use a queue to keep track of nodes at each level.

3. Dequeue a node, visit it, and enqueue its left and right children.

4. Repeat the process until the queue is empty.

Example: For the same BST:

    4
   / \
  2   6
 / \ / \
1  3 5  7

The level order traversal would be: 4, 2, 6, 1, 3, 5, 7

These traversal methods allow different ways of accessing and processing all the nodes in a BST, each with its own unique order and use cases.