Level Order Traversal Guide in C++ Binary Tree

What Will You Learn in This Guide?

In this guide, you will learn how the Level Order Traversal algorithm works on a Binary Tree.
We will explain the entire process step by step, from calculating the height of the tree to printing the nodes at each level.
This method is based on Breadth-First Search (BFS) logic.

Technical Summary

• Main topic: Level based navigation algorithm in binary tree
• Purpose: To navigate the nodes sequentially from left to right at each level, starting from the root
• Method: Recursively finding the height of the tree → printing it with the print_level() function for each level
• Approach: Recursive method
• Time Complexity: Average O(N²), O(N) in iterative BFS version

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Binary Tree Basics

Binary Tree is a hierarchical data structure in which each node can have at most two child nodes (left and right).
The top node is called the root.

Level:
It is the distance of a node from the root.

• Level of the root 0
• Children of the root 1
• Their children are 2

Height:
It is the longest path from the root to the deepest node.
This value determines how many levels our navigation algorithm will process.

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Logic of the Algorithm

In level-order navigation, nodes are navigated in the following order: Level 0 → Level 1 → Level 2 → ...

Navigation order for the example tree:

10 -> 20 -> 30 -> 40 -> 50

We will use three basic functions to do this:

1. tree_height() → Calculates the height of the tree.
2. print_level() → Prints nodes at the specified level.
3. print_tree_level_order() → Prints all levels on the screen one by one.

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1. Step – Calculating the Height of the Tree

This function calculates the height of all subtrees, starting from the root.
The total tree height is found by adding +1 to the largest height.

// Ağacın yüksekliğini hesaplar.
int tree_height(Node* root) {
    if (root == NULL)
        return 0;
    else {
        int sol_yukseklik = tree_height(root->left);
        int sag_yukseklik = tree_height(root->right);
        return (sol_yukseklik > sag_yukseklik ? sol_yukseklik : sag_yukseklik) + 1;
    }
}

• Description: The height of each branch is calculated separately, the higher one is selected.

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2. Step – Printing Nodes at a Specific Level

The print_level() function works by decreasing the level number until the desired level is reached.

// Belirli bir seviyedeki düğümleri yazdırır.
void print_level(Node* root, int level_no) {
    if (!root)
        return;

    if (level_no == 0)
        printf("%d -> ", root->value);
    else {
        print_level(root->left, level_no - 1);
        print_level(root->right, level_no - 1);
    }
}

• Description: When the level reaches 0, the node value is printed; If not, go down to lower levels.

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3. Step by Step – Navigating All Levels

The print_tree_level_order() function starts at level 0 and calls the print_level() function for each level.

// Tüm seviyeleri sırayla dolaşır.
void print_tree_level_order(Node* root) {
    if (!root)
        return;
    int height = tree_height(root);
    printf("Level Order Traversal: ");
    for (int i = 0; i < height; i++) {
        print_level(root, i);
    }
    printf("\n");
}

Full Code Implementation

The example below is the full C program that includes node creation, height calculation, and level sequential printing.

#include <stdio.h>
#include <stdlib.h>

typedef struct Node {
    int value;
    struct Node* left;
    struct Node* right;
} Node;

// Yeni bir düğüm oluşturur.
Node* create_node(int data) {
    Node* node = (Node*) malloc(sizeof(Node));
    node->value = data;
    node->left = node->right = NULL;
    return node;
}

// Yukarıda tanımlanan diğer fonksiyonlar burada çağrılır (tree_height, print_level, print_tree_level_order)

int main() {
    Node* root = create_node(10);
    root->left = create_node(20);
    root->right = create_node(30);
    root->left->left = create_node(40);
    root->left->right = create_node(50);

    print_tree_level_order(root);
    return 0;
}

Expected Output:

Level Order Traversal: 10 -> 20 -> 30 -> 40 -> 50 ->

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Performance Analysis

Feature	Description
Approach	Recursive
Time Complexity	O(N²)
Alternative Method	Using Queue O(N)
Efficiency	Sufficient for small trees, iterative BFS is recommended for large structures

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Frequently Asked Questions (FAQ)

1. Why can recursive method be slow?

Because the same node is visited multiple times; This increases the processing load.

2. Is there a faster method?

Yes, the iterative solution using the Queue data structure is O(N) fast.

3. In what situations is Level Order Traversal used?

In cases of measuring tree width, operating by levels or graphical visualization.

4. What is the difference between Binary Tree and Binary Search Tree?

Binary Search Tree keeps small values ​​in the left branch and large values ​​in the right branch. This rule does not exist in Binary Tree.

5. How should memory management be done?

All nodes must be freed with free(); otherwise there will be a memory leak.

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Result

In this guide, you learned the Level Order Traversal algorithm in Binary Tree step by step with C/C++. We calculated the height, walked through each level, and ran a full sample code.

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