# Tree Traversals

## Traversing A Binary Tree

• Traversing a binary tree is the process of visiting each and every node in the tree exactly once in a systematic way.
• As we know that a tree is a non-linear data structure in which the elements can be traversed in many different ways.

### Types of traversals

1. Pre-order Traversal
2. In-order Traversal
3. Post-order Traversal

### Pre-order Traversal:-

• To traverse a nonempty binary tree in pre-order, the following operations are performed at each node:
1. Visiting the root node,
2. Traversing the left sub-tree,
3. Traversing the right sub-tree.

Pre-order Traversal: 1 2 4 3  5 7 8 6
• The pre-order traversal of the above tree is 1-2-4-3-5-7-8-6 as we have to traverse from root first, and then left sub-tree, and finally right sub-tree.
• Pre-order traversal is also called depth-first traversal.
• The word 'pre' in the pre-order specifies that the root node is traversed first to any other nodes in the left and right sub-trees.
C++ code for pre-order traversal

//recursive function to perform pre-order traversal of the tree
void preorder(struct node *root)
{
//if the current node is empty
if(root==NULL)
return;

//display the data part of the root node.
cout<<root->data;

//traverse the left sub-tree
preorder(root->left);

//traverse the right sub-tree
preorder(root->right);
}

### In-order Traversal:

• To traverse a nonempty binary tree in in-order, the following operations are performed at each node:
1. Traversing the left sub-tree,
2. Visiting the root node,
3. Traversing the right sub-tree.

In-order Traversal: 4 2 1 7 5 8 3 6

• The in-order traversal of the above tree is 4-2-1-7-5-8-3-6.
• Left sub-tree first, and then root node, and finally the right sub-tree.
• In-order traversal is also called symmetric traversal.
• The word 'in' in the in-order traversal specifies that the root node is accessed in between the left and the right sub-trees.
C++ code for in-order traversal

//recursive function to perform in-order traversal of the tree
void inorder(struct node *root)
{
//if the current node is empty
if(root==NULL)
return;

//traverse the left sub-tree
inorder(root->left);

//display the data part of the root node.
cout<<root->data;

//traverse the right sub-tree
inorder(root->right);
}

### Post-order Traversal:

• To traverse a nonempty binary tree in post-order, the following operations are performed at each node:
1. Traversing the left sub-tree,
2. Traversing the right sub-tree,
Post-order Traversal: 4 2 7 8 5 6 3 1

• The post-order traversal of the above tree is 4-2-7-8-5-6-3-1.
• Left sub-tree first, and then right sub-tree, and finally the root node.
• In this traversal, the left sub-tree is always traversed before the right sub-tree and the root nodes.
• The word 'post' in the post-order traversal specifies that the root node is accessed after the left and the right sub-trees.
C++ code for in-order traversal

//recursive function to perform post-order traversal of the tree
void postorder(struct node *root)
{
//if the current node is empty
if(root==NULL)
return;

//traverse the left sub-tree
postorder(root->left);

//traverse the right sub-tree
postorder(root->right);

//display the data part of the root node.
cout<<root->data;

}