To traverse a binary tree means to visit each node of the tree exactly once in a systematic fashion. Binary tree is non-linear data structure. Hence, we can’t traverse it like a linked list is a sequential manner but it requires a different approach. We mainly have three algorithms for traversing binary tree. The difference in them is when they visit which nodes.

1.Pre-order traversal

• To traverse a non-empty binary tree by pre-order method, the following operations are performed recursively until all nodes are visited:

  i. Visit the root node.

  ii. Traverse the left sub-tree fully.

  iii. Traverse the right sub-tree.

• Consider the example beside. The pre-order traversal of the tree is A,Q,W,Z,C,H,G,D
• As we see, we traverse the root node first, then the left sub-tree, then move to right sub-tree.
• The keyword ‘pre’ here means that the root node is accessed the very first.
• It is also known as depth first traversal.
• The pre-order traversal is used to extract a prefix notation from an expression tree.

2.In-order traversal

• To traverse a non-empty binary tree by in-order method, the following operations are performed recursively until all nodes are visited:

  i. Traverse the left sub-tree.

  ii. Now, visit the root node.

  iii. Then, finally traverse the right sub-tree.

• Consider the example above. The in-order traversal of the tree is Q, Z, W, C, A, H, D, G
• As we see, we traverse the left sub-tree first, then we moved to the root node and finally the right sub tree.
• The keyword ‘in’ specifies that the root node is accessed between left and right node.
• In-order traversal is used to display the elements of a binary search tree.

3.Post-Order traversal.

• To traverse a non-empty binary tree by post-order method, the following operations are performed recursively until all nodes are visited:

  i. Traverse the left sub-tree.

  ii. Now, move to the right sub tree

  iii. Then, finally visit the root node.

• Consider the example above. The post-order traversal of the tree is Z, C, W, Q, D, G, H, A

• As we see, we traverse the left sub-tree first, then the right sub-tree and finally we visit the root node.
• The keyword ‘post specifies that the root node is accessed after we visit the left and right sub-trees.
• They are used to extract post fix notation from an expression tree