Preorder Tree Traversal of Binary Tree in C++

A binary tree is a non-linear hierarchical data structure where each node has at most two children which are referred to as the left child and the right child. As it has non-linear structure it can be traversed in multiple ways one such way is pre-order traversal which is a technique in which nodes are recursively visited in the order: left child, root, right child. 

In this article, we will learn how to implement preorder binary tree traversal in C++, its algorithm and analyze its space and time complexity.

Preorder Traversal of Binary Tree in C++

Preorder traversal is a traversal technique used to visit all the nodes in a specific sequence of the binary tree. This process involves visiting the root node first, then the left subtree, and finally the right subtree.

Steps for Preorder Traversal:

1. Visit the root node.
2. Recursively perform a preorder traversal of the left subtree.
3. Recursively perform a preorder traversal of the right subtree.

Consider the following example:

For preorder traversal of the above binary tree:

1. Start with the root node, which is 1.
2. Move to the left child, which is 2.
3. Visit the left child of 2, which is 4.
4. Move back to 2 and visit its right child, which is 5.
5. Move back to the root node and visit the right child, which is 3.

So, the preorder traversal of the tree is: 1, 2, 4, 5, 3.

Algorithm for Pre-order Binary Tree Traversal

Below is the algorithm for the preorder binary tree traversal:

preorder(TreeNode* root) {
    if (root == NULL)
        return;
    cout << root->val << " ";
    preorder(root->left);
    preorder(root->right);
}

C++ Program to Implement Preorder Traversal of the Binary Tree

The following program demonstrates how we can implement the Preorder traversal in a binary tree in C++.

// C++ Program for Preorder Traversal in a Binary Tree

#include <iostream>
using namespace std;

//  BINARY TREE IMPLEMENTATION

// Class definition for a binary tree node
class Node {
public:
    int data;
    Node* left;
    Node* right;

    // Constructor to create a new node
    Node(int data)
    {
        this->data = data;
        this->left = nullptr;
        this->right = nullptr;
    }
};

// Class definition for a binary tree
class BinaryTree {
public:
    Node* root;

    // Constructor to initialize the root
    BinaryTree() { root = nullptr; }

    // PREORDER TRAVERSAL

    // Function to perform preorder traversal
    void preorderTraversal(Node* node)
    {
        if (node != nullptr) {
            cout << node->data << " ";
            preorderTraversal(node->left);
            preorderTraversal(node->right);
        }
    }
};

int main()
{
    // Initialize a binary tree
    BinaryTree btree;

    // Create the binary tree
    btree.root = new Node(1);
    btree.root->left = new Node(2);
    btree.root->right = new Node(3);
    btree.root->left->left = new Node(4);
    btree.root->left->right = new Node(5);
    btree.root->right->left = new Node(6);
    btree.root->right->right = new Node(7);

    // Perform the preorder traversal
    cout << "Preorder traversal of the binary tree is:"
         << endl;
    btree.preorderTraversal(btree.root);
    cout << endl;

    return 0;
}

Preorder traversal of the binary tree is:
1 2 4 5 3 6 7 

Time Complexity: O(N) where N is the total number of nodes as it traverses all the nodes at least once.
Auxiliary Space: 

• O(1) if no recursion stack space is considered. 
• Otherwise, O(h) where h is the height of the tree
• In the worst case, h can be the same as N (when the tree is a skewed tree)
• In the best case, h can be the same as logN (when the tree is a complete tree)

Applications of Preorder Traversal

Following are some common applications of the preorder traversal:

• It is used to evaluate or print the prefix notation of an expression.
• It is used to create a deep copy of a tree by visiting each node before it's children.
• It is used for the serialization and deserialization of a tree.
• It is also used in operating systems to list the contents of a directory in a hierarchical order.

Related Articles

You can also go through these articles to improve your knowledge about the binary tree and it's traversals:

• Types of Tree traversals
• Binary Tree Traversal
• Preorder Traversal of Binary Tree
• Iterative Preorder Traversal
• Morris traversal for Preorder