Summary: In this tutorial, we will learn what is Inorder, Preorder and Postorder traversal method and how to implement these methods in C++ and Java.
A Tree which is a hierarchical (non-linear) data structure can be traversed in multiple ways unlike the linear data structure eg array, linked list, etc which can be traversed only in a linear fashion.
The basic two ways using which we can traverse a tree are:
- Depth First Traversal
- Inorder
- Preorder
- Postorder
- Breadth First Traversal
In-order, pre-order, and post-order are three forms of depth-first search traversal method i.e. each method explores as far as possible along each branch before backtracking.
So let’s see how they differ form each other in context of depth-first traversal.
Inorder Traversal
- Left subtree.
- Root.
- Right subtree.
In the Inorder Traversal method, we first visit the left subtree then the root and after that to the right subtree of the tree.
Preorder Traversal
- Root.
- Left subtree.
- Right subtree.
In the Preorder traversal method, we start from the root, then we go the left subtree and finally to the right subtree.
Preorder Traversal
- Left subtree.
- Right subtree.
- Root.
In the Postorder tree traversal method, we first visit the left subtree and then the right subtree and finally the root.
Trick: Whichever method you use always remember that the left subtree always comes before the right subtree.
To implement these traversal methods we will use recursion because each part of the tree whether left or right is itself a tree (i.e. subtree).
In recursion, we treat each node as the root of the underlying subtree.
Here is the implementation of Pre-order, In-order, and Post-order traversal in C++ and Java.
Java
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | class Node{ int value; Node left; Node right; //Constructor to initialize value to node Node(int value){ this.value = value; left = right = null; } //Function to insert data i.e to form binary tree public void insert(int v){ if(v < value){ if(left == null){ left = new Node(v); } else { left.insert(v); } } else { if(right == null){ right = new Node(v); } else{ right.insert(v); } } } //Function to perform Pre-Order Travesal public void preOrder(){ //1. Root System.out.print(value+" "); //2. Left subtree if(left != null){ left.preOrder(); } //3. Right subtree if(right != null){ right.preOrder(); } } //Function to perform Post-Order Travesal public void postOrder(){ //1. Left subtree if(left != null){ left.postOrder(); } //2. Right subtree if(right != null){ right.postOrder(); } //3. Root System.out.print(value+" "); } //Function to perform In-Order Travesal public void inOrder(){ //1. Left subtree if(left != null){ left.inOrder(); } //2. Root System.out.print(value+" "); //3. Right subtree if(right != null){ right.inOrder(); } } } class Main { public static void main(String[] args) { Node root = new Node(25); root.insert(20); root.insert(31); root.insert(19); root.insert(23); root.insert(26); root.insert(36); System.out.print("\n Inorder: "); root.inOrder(); System.out.print("\n Preorder: "); root.preOrder(); System.out.print("\n Postorder: "); root.postOrder(); } } |
C++
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 | #include <iostream> using namespace std; //Class TreeNode represent each node class TreeNode{ public: int data; TreeNode *leftNode {nullptr}; TreeNode *rightNode {nullptr}; TreeNode(); TreeNode(int d); void insertData(int d); void inorderTraverse(); void preorderTraverse(); void postorderTraverse(); }; //Implementing TreeNode class prototypes function. TreeNode::TreeNode(int d){ data = d; } //Inserting node as a left child if it is smaller than the current node //else it will be inserted as the right child // Assuming no two numbers/nodes are same void TreeNode::insertData(int d){ if(d < data){ if(leftNode == nullptr){ leftNode= new TreeNode(d); } else { leftNode->insertData(d); } } else { if(rightNode == nullptr){ rightNode = new TreeNode(d); } else { rightNode->insertData(d); } } } // Inorder traversal algorithm void TreeNode::inorderTraverse(){ //1.Left subtree if(leftNode != nullptr){ leftNode->inorderTraverse(); } //2. Root cout << data << " "; //3. Right subtree if(rightNode != nullptr){ rightNode->inorderTraverse(); } } // Preorder traversal algorithm void TreeNode::preorderTraverse(){ //1. Root cout << data << " "; //2.Left subtree if(leftNode != nullptr){ leftNode->preorderTraverse(); } //3. Right subtree if(rightNode != nullptr){ rightNode->preorderTraverse(); } } // Postorder Traversal Algorithm void TreeNode::postorderTraverse(){ //1.Left subtree if(leftNode != nullptr){ leftNode->postorderTraverse(); } //2. Right subtree if(rightNode != nullptr){ rightNode->postorderTraverse(); } //3. Root cout << data << " "; } int main() { //Taking root node as 25 TreeNode *root= new TreeNode(25); //inserting data into the binary tree root->insertData(20); root->insertData(31); root->insertData(19); root->insertData(23); root->insertData(26); root->insertData(36); //Calling inorder traversal function from root object cout << "\n Inorder: "; root->inorderTraverse(); cout << "\n Preorder: "; root->preorderTraverse(); cout << "\n Postorder: "; root->postorderTraverse(); return 0; } |
Output:
1 2 3 | Inorder: 19 20 23 25 26 31 36 Preorder: 25 20 19 23 31 26 36 Postorder: 19 23 20 26 36 31 25 |
In the above program, we have implemented the node as a class and linked other nodes using the insert method on the root.
By doing this we formed a Binary tree, then traversed it using the tree traversal methods.
In this tutorial, we learned what In-order, Pre-order and Post-order traversal are and how to implement them in C++ and Java programming languages.