“Tree Traversal Algorithms” define the systematic process of visiting each node in a tree data structure exactly once to perform a specific operation. Before understanding these algorithms, it is important to understand the meaning of the term traversal.
According to the dictionary, traversal means to explore or move through every part of an area. For example, traversing a forest involves visiting different locations within it.
Similarly, in computer science, tree traversal refers to the process of visiting all nodes of a tree in a well-defined order and executing predefined operations such as searching, printing, or evaluating data.
TL;DR: Tree Traversal Algorithms
Aspect | Summary |
Traversal Basics | A tree is a non-linear data structure made of nodes and branches, starting from a root node. Traversal means systematically visiting every node in the tree. |
Meaning of Traversal | Traversal means exploring every part of a structure, just like roaming through a forest. In programming, it refers to visiting all tree nodes in a defined order. |
Purpose of Tree Traversal | Tree traversal allows programmers to search, print, evaluate, or process all nodes efficiently. Non-linear structures cannot be accessed in a simple linear way. |
Types of Traversal | Depth-first traversals include inorder, preorder, and postorder, each differing by when the root node is processed. Breadth-first traversal visits nodes by level. |
Performance & Importance | All tree traversal algorithms have a time complexity of O(n) since every node is visited once. |
What Is Tree Traversal In Data Structures?
A tree or a binary tree is a non-linear data structure that originates from a root node or parent node and then gets divided into two subtrees. These are the left subtree and the right subtree. Both subtrees have children or child nodes.
Tree traversal generally means to traverse or visit each node in the tree. We have different methods to perform this. You must select the method carefully, considering the time complexity and the space complexity.
In the following section, I will tell you about the various types of traversal algorithms that you can perform on your binary tree or binary search tree.
But before we explore it, let us get to know why traversing a tree is crucial. Read below to know!
Why Tree Traversal Feels Unclear To Beginners?
When students first learn tree traversal, the logic often feels invisible. Unlike arrays or loops, nothing moves step by step in front of your eyes. Most confusion starts because traversal happens mentally, not physically.
1) Students Don’t Understand What Traversal Is Actually Doing:
Many beginners think tree traversal is about changing the tree or rearranging nodes. In reality, traversal is only about visiting nodes in a specific order, not modifying the structure.
void preorder(Node root)
{
if(root == null)
return; // stop at empty node
System.out.print(root.data); // visit current node
preorder(root.left); // go left
preorder(root.right); // go right
}
The tree remains exactly the same before and after traversal. Students get confused because “visit” sounds like an action that changes data—but it doesn’t.
2) Same Tree But Different Orders Feels Counter-Intuitive:
Students struggle when they see that the same tree produces different outputs depending on the traversal method. They expect one correct answer, not three.
void inorder(Node root)
{
if(root == null)
return;
inorder(root.left); // left first
System.out.print(root.data); // then root
inorder(root.right); // then right
}
Nothing about the tree has changed. Only the order of visiting nodes has changed. This disconnect between structure and output is where confusion usually starts.
3) Recursion Hides The Actual Visiting Order:
Traversal algorithms rely on recursion, and students often cannot track when a node is printed during recursive calls.
void postorder(Node root)
{
if(root == null)
return;
postorder(root.left); // visit left subtree
postorder(root.right); // visit right subtree
System.out.print(root.data); // visit node last
}
Students expect the node to print as soon as it’s reached. They don’t realize that recursion delays printing until the child calls finish, which breaks their mental flow.
Types Of Tree Traversal Algorithm:
There are mainly three types of Tree Traversal Algorithms. Depending upon the situation, programmers use any of them. So, let us get to know what tree traversal techniques are. First, we will see the three main techniques of Depth-first traversal. These are:
- Inorder Traversal
- Preorder Traversal
- Postorder Traversal
Let us know each of the methods briefly, one by one.
Still want to learn more about types of tree traversal, then you can check out our article, we’ve written a detailed article on it.
Also, if you’re curious to know about types of constraints in linear programming, then you can check out our blog section.
1. Inorder Traversal:
This is one type of Tree Traversal Algorithm. Here, in this case, the nodes of the tree will be visited in a particular manner. The procedure will be different from the other Algorithms.
Suppose we have a tree where the Root node is ‘N’, the Left Node is ‘L’ & Right Node is ‘R’. So the Tree Traversal Inorder will visit the Root node in the middle of the two sub-nodes. The term ‘Inorder’ represents that the Root node will be inside of those two sub-nodes.
Then the Inorder Traversal sequence will be:
Visit Left Node (L)
Visit Root Node (N)
Visit Right Node (R)
So, the remembering formula will be L-N-R. Remember this formula. This will help to solve many problems in the future.
How students should think about it:
- You should finish the left side first, no matter how deep it goes.
- You can process the current node only after returning from the left child.
- The right subtree is visited only after the root is handled.
Let us have a look at the example tree to understand how in-order traversal works. In the representation, we have a binary tree where the root node is A, and it is then divided into the left subtree and right subtree by its children nodes B and C.
Let us perform the inorder traversal here by using the L-N-R rule. So, we will first travel to the left subtree upto the last left leaf node, i.e., D, and then to its parent node B, and finally to the right node E.
We have now covered the left subtree; thus, we will visit the root node A.
Then we will traverse to the right subtree and move to its left leaf node first, then the parent node, and finally the right leaf node.
In this way, we will traverse the whole tree. Now, we will see that the order of traversal comes out to be:
D-B-E-A-F-C-G
2. Preorder Traversal:
This is another type of Tree Traversal Algorithm. This kind of algorithm is different from the Inorder Traversal Algorithm.
Then the preorder traversal sequence will be:
Visit Root Node (N)
Visit Left Node (L)
Visit Right Node (R)
So, the remembering formula will be N-L-R. Remember this formula. This will help to solve many problems in the future.
How students should think about it:
- As soon as you reach a node, you should record it immediately.
- Children are explored after the parent is processed.
- This traversal helps to rebuild or copy the tree structure.
Again, considering the above example binary tree. Here, we need to follow the N-L-R rule. How will we do it? Let me help you understand.
Here, first we will visit the root node, i.e., A. Next, we will move to the left subtree. After coming here, we will again visit the root node of the left subtree, which is B. Let’s now move to the next level, and towards the left leaf node, i.e D.
Now, it is time to visit the right leaf node, E. We will now come back upwards and go to the right subtree. Visiting its parent node first, i.e., C, then F, and finally G.
Thus, the preorder traversal sequence for the given tree is:
A-B-D-E-C-F-G
3. Postorder Traversal:
This is the third kind of Tree Traversing Algorithm. This is different from the previous two algorithms. Let’s take the same example for understanding purposes.
In this case, Postorder Traversal will first visit the Left Sub Node. Then it will directly visit the Right Sub Node. At last, it will visit the Root Node. The term ‘Postorder’ defines that the Root Node will be visited last in the Tree Traversal Algorithm.
Then the sequence will be:
Visit Left Node (L)
Visit Right Node (R)
Visit Root Node (N)
So, the remembering formula will be L-R-N. Remember this formula. This will help to solve many problems in the future.
How students should think about it:
- You should not touch the root until both children are completely done.
- This feels slow at first, but it is logically safe.
- Parents depend on children, so children must finish first.
Now, it is time to see the postorder traversal of our example tree.
In this technique, we have to first visit the left leaf node, D. Now, moving to the right leaf node, i.e., E, and finally the root node B. Similarly, performing it on the right subtree and finally visiting the root node.
The final order of postorder traversal is-
D-E-B-F-G-C-A
Now, let me tell you how you implement these techniques. Read further to know what traversals are in code.
How Students Should Think About Tree Traversals?
Most of the time, we have seen students make mistakes with Tree Traversals in exams, just because the mental model of it is not clarified. Here, we will share a student’s model to think about it.
All tree traversals work on the same tree structure. Nothing changes in the tree; only when you visit a node does it change. Understanding this timing removes 80% of the confusion.
Instead of thinking about algorithms, students should focus on one simple question: “When am I allowed to process the current node?”
- In order: Root is processed between left and right subtrees
- Preorder: Root is processed before visiting children
- Postorder: Root is processed after both subtrees are done
Same tree and same nodes, only the timing of the root visit changes. This mindset makes traversal predictable instead of confusing during lab exams.
Implementation Of Tree Traversal Algorithm:
Implementation of the Tree Traversal Algorithm is a multistage process. It will go through different functions. Also, one needs to be very clear in the function, structure, and pointer to implement such things. Also, knowing the linked list will be a cherry on the cake.
The tree structure is going to be implemented using the code. The code will first develop the tree. Then it will do Tree Traversal Operations on it. After that, it will provide the result of Tree Traversal.
The above tree will develop after providing value to it. Then the Tree Traversal Algorithms will act on it.
So, first, let us know the steps to implement such algorithms. Here, we are using the C programming language.
Step-1: Create A Tree
Here, we will start our code by creating a tree. For this, we will define our structure and add functions to it that will create new nodes and assign values to them. Let us see how to do it.
Creating The Structure Of Node:
As we know, a tree is built with a value & some pointers. Here, we have taken an integer value for the info purpose. Also, we have taken two pointers of the type of a certain structure. In this way, we have created a tree structure for further use.
// Structure For A Node Of Tree
struct node
{
// Elements Of A Node
int data;
struct node* left;
struct node* right;
};
Implementing A Function to Create & Develop New Nodes:
Here, using a dynamic memory allocation process, we will create a new node. The size of the node will be equal to the size of the structure of the node. Then the data that we have collected will be inserted into the nodes. At last, the address of the node will be returned to the called function.
We use malloc Here to reserve space for the new node; understanding dynamic memory allocation in C is crucial for managing tree structures efficiently.
/ Process To Create A New Node
struct node* createNode(int data)
{
// Allocate Memory Equivalent To Node Structure And Hold Address In Node Pointer
struct node* newNode = malloc(sizeof(struct node));
// Assigning Data To Nodes
newNode -> data = data;
newNode -> left = NULL;
newNode -> right = NULL;
// Returning The Pointer Value
return newNode;
}
Linking Left & Right Sub Nodes with Root:
Here, we will define two different functions. One will add nodes to the Left side of the Root Node. Another will add nodes to the Right side of the Root Node. After that, those functions will return the address of that node to the called function.
// Insert A New Node To Left Of The Given Node
struct node* insertLeft(struct node* root, int data)
{
root -> left = createNode(data);
return root;
}
// Insert A New Node To Right Of The Given Node
struct node* insertRight(struct node* root, int data)
{
root -> right = createNode(data);
return root;
}
Step-2: Function For Implementation Of Inorder Traversal
Here, as we previously discussed, we will follow the LNR rule there. Here, printing the values of the Root Node will be easy. Using the printf() function, we can print the values. But traversing to the Left & Right sub-nodes will be done using the recursive calling of the function.
// Process Of Inorder Traversal
void inorder(struct node* root)
{
if (root == NULL)
return;
// Recursive Calling To Follow LNR Rule
inorder(root -> left);
printf("%d ", root -> data);
inorder(root -> right);
}
Step-3: Function For Implementation Of Preorder Traversal
Here, as we previously discussed, we will follow the NLR rule there. Here, printing the values ofthe Root Node can be done using the printf() function. But traversing to the Left & Right sub-nodes will be done using the recursive calling of the function.
// Process Of Preorder Traversal
void preorder(struct node* root)
{
if (root == NULL)
return;
// Recursive Calling To Follow NLR Rule
printf("%d ", root -> data);
preorder(root -> left);
preorder(root -> right);
}
Step-4: Function For Implementation Of Postorder Traversal
Here, as we previously discussed, we will follow the LRN rule there. Here, printing the values ofthe Root Node can be done using the printf() function. But traversing to the Left & Right sub-nodes will be done using the recursive calling of the function.
// Process Of Postorder Traversal
void postorder(struct node* root)
{
if (root == NULL)
return;
// Recursive Calling To Follow LRN Rule
postorder(root -> left);
postorder(root -> right);
printf("%d ", root -> data);
}
Step-5: Implement The Main Function
Here, we just need to send the values of the Root Nodes as an argument to the functions. Then we will just print the sequence of the Tree Traversal Algorithms.
int main()
{
// Assigning Root Value
struct node* root = createNode(4);
// Assigning Other Brach Values
insertLeft(root, 21);
insertRight(root, 13);
insertLeft(root -> left, 34);
insertRight(root -> left, 0);
insertLeft(root -> right, 18);
insertRight(root -> right, 19);
// Printing The Sequence
printf("Inorder traversal of the Tree is : ");
inorder(root);
printf("\n");
printf("Preorder traversal of the Tree is : ");
preorder(root);
printf("\n");
printf("Postorder traversal of the Tree is : ");
postorder(root);
return 0;
}
Output:
As you can see, our traversal algorithms have followed the rules we mentioned above. For Inorder traversal, we used the L-N-R rule. Similarly, N-L-R and L-R-N rules were used for preorder traversal and postorder traversal, respectively.
I hope the above three techniques are clear to you. These techniques are a part of depth-first traversal, which means we reach the leaf node or the deepest level first when traveling.
As a bonus, let me also tell you about another popular traversal technique. The level order traversal, or breadth-first traversal. Let us see what it is and how it is implemented!
What is Level Order Traversal?
The level order traversal is also known as breadth-first traversal or breadth-first search. Here, the nodes on one level are traversed or visited, then we move to the next level or the level below the previous one.
Let us understand this with the help of our example binary search tree. First, we will start with the root node and then move step by step or level by level.
Thus, after visiting A, we will visit nodes B and C. Further, moving downwards, we will visit the leaf nodes, which are D, E, F, and G.
Let us now see how to implement it using the C programming language.
Implementation Of Level Order Traversal
Here, again, we will have to create our tree and write the main function. The code given above will work in the same way in this case as well.
We will only see how to write functions for level order traversal or breadth-first search traversal below. Here, we will use the same tree for implementation that we used in implementing the Depth-first traversal techniques.
Have a look at the code given below!
Tree operations can get complex; if you are struggling to implement traversals in your project, our team offers expert data structure homework assistance.
// declaring functions
void CurrentLevel(struct node* root, int level);
int heightOfTree(struct node* node);
struct node* newNode(int data);
// Function to print level order traversal a tree
void LevelOrderTraversal(struct node* root)
{
int h = heightOfTree(root);
int i;
for (i = 1; i <= h; i++)
CurrentLevel(root, i);
}
// Print nodes at a current level
void CurrentLevel(struct node* root, int level)
{
if (root == NULL)
return;
if (level == 1)
printf("%d ", root->data);
else if (level > 1) {
CurrentLevel(root->left, level - 1);
CurrentLevel(root->right, level - 1);
}
}
// finding tree height
int heightOfTree(struct node* node)
{
if (node == NULL)
return 0;
else {
// Compute the height of each subtree
int lheight = heightOfTree(node->left);
int rheight = heightOfTree(node->right);
// Use the larger one
if (lheight > rheight)
return (lheight + 1);
else
return (rheight + 1);
}
}
So, what is happening here? We first calculate the height of the tree and use it to find the current level. Finally, we are traversing in the level order. For this, we have declared three important functions:
- CurrentLevel()
- heightOfTree()
- LevelOrderTraversal()
In the main function, we are calling the LevelOrderTraversal() function to print the sequence. This can be shown in the output below.
Output:
Let us know the time complexity of these techniques. Read below to know more.
What Is The Time Complexity Of Tree Traversal?
A binary tree or binary search tree is also considered a graph in data structures. The time complexity of a graph is O(n+m), where n is the number of nodes and m is the number of edges.
The same goes for binary search trees or a binary tree. Here, since 2 edges are connected to one node, the total number of edges becomes n-1.
Thus, O(n+n-1) = O(n) for all cases. Whether it is depth-first search or breadth-first search.
As we progress, why don’t we compare DFS and BFS traversal algorithms? Ready for it? Let’s dive in!
Comparison between Depth-First Traversal and Breadth-Frist Traversal Techniques
Depth-First Traversal | Breadth-First Traversal |
Usually, utilize a stack data structure for traversal. | Utilizes a queue data structure for traversal. |
Node is visited depth-wise and then moved to the same level. | The nodes on the same level are visited, and then we move to the next level. |
Backtracking is possible after visiting the deepest node. | Backtracking does not occur here. |
May or may not find the shortest path. | It is used to find the shortest path or distance between nodes. |
Generally, have lower space complexity as compared to BFS traversal | Generally, have more space complexity as compared to DFS traversal. |
Example: Inorder, preorder, postorder traversal | Example: Level-order traversal |
What Will Be The Preferable Exam Approach For The Tree Traversal Questions?
From our expertise, we can predict that in exams, students rush behind the tree traversal question, and most mistakes happen there. Students don’t need speed; they need a clear process.
That is why, we will here describe a preferable exam approach that can be used both in lab and theory exams to answer the questions on tree traversal. Dry running saves marks, even when the concept feels shaky.
- Draw the tree clearly before writing anything.
- Write the traversal rules like LNR, NLR, or LRN at the top.
- Move node by node, not level by level.
- Write output only when the rule allows it. If confused, pause and ask: “Am I allowed to print the root now?”
Exam-safe tip: Examiners reward the accuracy in traversal questions. So, try to be accurate in the Tree Traversal Questions.
What Are Some Real-World Applications Of Tree Traversal Algorithms?
For a long time, we have been helping students, and we have noticed that students assume that the tree traversal algorithms are only for educational purposes.
But, tree traversals are not just academic concepts; they quietly power many everyday technologies we rely on, helping systems organize, search, and process data efficiently.
- Operating systems use tree traversals to list directories, calculate folder sizes, and search for files in a structured and efficient way.
- Databases traverse trees to quickly insert, delete, and retrieve records, which keeps queries fast even with millions of entries.
- Compilers traverse syntax trees to understand program structure, check errors, and generate optimized machine code.
- Tree traversal techniques help search engines explore links and rank web pages systematically.
- Traversing decision trees allows AI systems to evaluate conditions step-by-step and make accurate predictions or choices.
Conclusion:
As we saw Tree Traversal Algorithm is very important. We should clear the basics of structure, recursion & function calling for learning the Tree Traversal Algorithm.
Remember the short formulas of the Tree Traversal Algorithms for further problem-solving.
So, hope you have liked this piece of article. Share your thoughts in the comments section and let us know if we can improve further.
Takeaways:
- Tree traversal is the technique or process of visiting each node of a binary tree or a binary search tree.
- Depending on your requirements, you can use different approaches.
- The DFS approach includes techniques like in-order, preorder, and postorder traversals.
- The BFS approach includes the level order traversal technique.
- The time complexity for both algorithms is O(n), while the space complexity may differ.
Frequently Asked Questions:
1) Can tree traversal order affect cache performance?
Yes. Traversal order influences memory locality; breadth-first traversal often benefits from better cache usage in array-based trees, while deep recursive DFS may cause more cache misses.
2) Why is Morris Traversal rarely used in production systems?
Although it achieves O(1) space, it temporarily modifies the tree structure, which is risky in concurrent or read-only systems. That is why it is rarely used in productions.
3) Is traversal always O(n) even for balanced trees?
Yes. Every Tree Traversal algorithm must visit every node at least once, so the time complexity remains O(n). This will not change regardless of tree balance.
