Boundary Traversal of Binary Tree in DSA C - Build from Scratch

Boundary Traversal of Binary Tree

📖 Scenario: Imagine you have a family tree represented as a binary tree. You want to visit all the family members who are on the outer edge of the tree, starting from the top ancestor, going down the left side, then the leaves from left to right, and finally up the right side.

🎯 Goal: Build a program in C that performs a boundary traversal of a binary tree. The program will print the nodes on the boundary in the correct order: root, left boundary (excluding leaves), all leaves, and right boundary (excluding leaves) in reverse.

📋 What You'll Learn

Define a binary tree node structure with integer data and left and right pointers

Create a binary tree with the exact nodes and structure given

Implement functions to print the left boundary, leaves, and right boundary

Combine these functions to print the full boundary traversal

Print the boundary traversal nodes in one line separated by spaces

💡 Why This Matters

🌍 Real World

Boundary traversal helps in graphical rendering, printing the outline of tree-like structures, and in certain tree-based algorithms where edge nodes are important.

💼 Career

Understanding tree traversals, including boundary traversal, is essential for software engineers working with hierarchical data, UI trees, and in technical interviews.

1

Create the binary tree structure and nodes

Define a struct called Node with an int data, and two pointers left and right to Node. Then create the following binary tree nodes and link them exactly as shown:
1 as root, 2 as root's left child, 3 as root's right child, 4 as left child of 2, 5 as right child of 2, 6 as left child of 3, and 7 as right child of 3.

DSA C

# Define struct Node and create the binary tree nodes and links
# Your code here

Hint

Start by defining the Node structure. Then write a helper function newNode to create nodes. Finally, create the root and link all children as described.

2

Add helper functions to print left boundary, leaves, and right boundary

Add three functions: printLeftBoundary(Node* root), printLeaves(Node* root), and printRightBoundary(Node* root). Each function should print the node data followed by a space. printLeftBoundary should print all left boundary nodes except leaves, printLeaves should print all leaf nodes from left to right, and printRightBoundary should print all right boundary nodes except leaves in reverse order.

DSA C

#include 
#include 

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

Node* newNode(int data) {
    Node* node = (Node*)malloc(sizeof(Node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return node;
}

// Add printLeftBoundary, printLeaves, and printRightBoundary functions below
// Your code here

int main() {
    Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);
    return 0;
}

Hint

Use recursion to print the left boundary by going down left children first, skipping leaves. For leaves, print nodes with no children. For right boundary, recurse first then print to get reverse order.

3

Combine functions to print the full boundary traversal

In main, after creating the tree, print the root node's data followed by a space. Then call printLeftBoundary with root->left, printLeaves with root->left and root->right, and finally printRightBoundary with root->right. This will print the boundary traversal in order.

DSA C

#include 
#include 

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

Node* newNode(int data) {
    Node* node = (Node*)malloc(sizeof(Node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return node;
}

void printLeftBoundary(Node* root) {
    if (root) {
        if (root->left) {
            printf("%d ", root->data);
            printLeftBoundary(root->left);
        } else if (root->right) {
            printf("%d ", root->data);
            printLeftBoundary(root->right);
        }
    }
}

void printLeaves(Node* root) {
    if (root) {
        printLeaves(root->left);
        if (!root->left && !root->right) {
            printf("%d ", root->data);
        }
        printLeaves(root->right);
    }
}

void printRightBoundary(Node* root) {
    if (root) {
        if (root->right) {
            printRightBoundary(root->right);
            printf("%d ", root->data);
        } else if (root->left) {
            printRightBoundary(root->left);
            printf("%d ", root->data);
        }
    }
}

int main() {
    Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);

    // Print the boundary traversal below
    // Your code here

    return 0;
}

Hint

Start by printing the root data. Then call the three functions in order: left boundary, leaves (left and right), and right boundary.

4

Print the boundary traversal output

Run the program and observe the printed output. It should show the boundary traversal of the binary tree nodes in one line separated by spaces.

DSA C

# Run the program and check the output
# Your code here

Hint

The output should be the boundary nodes in order: root, left boundary (excluding leaves), leaves, and right boundary (excluding leaves) reversed.

Practice

1. What is the main purpose of the Boundary Traversal of Binary Tree?

easy

A. To print all nodes on the boundary of the tree in an anti-clockwise direction

B. To print all nodes in level order

C. To print all leaf nodes only

D. To print nodes in in-order traversal

Solution

1. Step 1: Understand boundary traversal definition

   Boundary traversal prints nodes on the edges of the tree: left boundary, leaves, and right boundary.

2. Step 2: Compare with other traversals

   Level order prints all nodes level-wise, leaf traversal prints only leaves, in-order prints nodes in left-root-right order.

3. Final Answer:

   To print all nodes on the boundary of the tree in an anti-clockwise direction -> Option A

4. Quick Check:

   Boundary traversal = print edges anti-clockwise [OK]

Hint: Boundary traversal prints edges anti-clockwise [OK]

Common Mistakes:

• Confusing boundary traversal with level order traversal
• Thinking it prints only leaf nodes
• Mixing it up with in-order traversal

2. Which of the following is the correct C function signature to perform boundary traversal on a binary tree node pointer named root?

easy

A. void boundaryTraversal(struct Node* root);

B. int boundaryTraversal(Node root);

C. void boundaryTraversal(Node root);

D. int boundaryTraversal(struct Node* root);

Solution

1. Step 1: Check parameter type for binary tree node

   Binary tree nodes are usually passed as pointers to struct Node in C.

2. Step 2: Check return type for traversal functions

   Traversal functions usually return void as they print nodes or store results externally.

3. Final Answer:

   void boundaryTraversal(struct Node* root); -> Option A

4. Quick Check:

   Pointer parameter + void return = void boundaryTraversal(struct Node* root); [OK]

Hint: Traversal functions usually take pointer and return void [OK]

Common Mistakes:

• Using struct keyword incorrectly
• Passing node by value instead of pointer
• Returning int instead of void

3. Consider the following binary tree:

        1
       / \
      2   3
     / \   \
    4   5   6
       / \  / \
      7  8 9  10

What is the output of the boundary traversal (anti-clockwise) of this tree?

medium

A. [1, 2, 4, 5, 7, 8, 9, 10, 6, 3]

B. [1, 2, 4, 7, 8, 9, 10, 3, 6]

C. [1, 2, 4, 7, 8, 9, 10, 6, 3]

D. [1, 2, 4, 7, 8, 5, 9, 10, 6, 3]

Solution

1. Step 1: Identify left boundary nodes

   Left boundary excluding leaves: 1, 2

2. Step 2: Identify leaf nodes left to right

   Leaves: 4, 7, 8, 9, 10

3. Step 3: Identify right boundary nodes bottom-up excluding leaves

   Right boundary: 6, 3

4. Step 4: Combine in anti-clockwise order

   Boundary traversal: 1, 2, 4, 7, 8, 9, 10, 6, 3

5. Final Answer:

   [1, 2, 4, 7, 8, 9, 10, 6, 3] -> Option C

6. Quick Check:

   Left boundary + leaves + right boundary = [1, 2, 4, 7, 8, 9, 10, 6, 3] [OK]

Hint: Left boundary + leaves + right boundary in order [OK]

Common Mistakes:

• Including leaf nodes twice in boundary
• Wrong order of right boundary nodes
• Missing some leaf nodes

4. The following C code snippet is intended to print the boundary traversal of a binary tree. What is the error?

void printLeftBoundary(Node* root) {
    if (root == NULL) return;
    printf("%d ", root->data);
    if (root->left) {
        printLeftBoundary(root->left);
    } else if (root->right) {
        printLeftBoundary(root->right);
    }
}

medium

A. It does not print the root node

B. It prints leaf nodes which should be excluded in left boundary

C. It does not handle NULL root correctly

D. It prints nodes in bottom-up order instead of top-down

Solution

1. Step 1: Analyze printing condition in left boundary

   Function prints node data before recursive call, so top-down order is correct.

2. Step 2: Check if leaf nodes are excluded

   The printf is before the child checks, so leaf nodes are printed before returning.

3. Step 3: Identify error

   Leaf nodes should not be printed in left boundary function; they are printed separately in leaf traversal.

4. Final Answer:

   It prints leaf nodes which should be excluded in left boundary -> Option B

5. Quick Check:

   Left boundary excludes leaves [OK]

Hint: Exclude leaf nodes in left boundary function [OK]

Common Mistakes:

• Printing leaf nodes in left or right boundary functions
• Not checking for NULL root
• Printing nodes in wrong order

5. Given a binary tree where some nodes have only one child, how should the boundary traversal be adapted to correctly include all boundary nodes without duplicates? Choose the best approach.

hard

A. Traverse all nodes in level order and print only those with one child

B. Traverse left and right boundaries including leaves, then print all leaves

C. Print all nodes in in-order traversal and remove duplicates afterwards

D. Traverse left boundary top-down excluding leaves, then all leaves left to right, then right boundary bottom-up excluding leaves, skipping duplicates

Solution

1. Step 1: Understand boundary traversal with single-child nodes

   Nodes with one child may appear in left or right boundary or as leaves.

2. Step 2: Avoid duplicates by excluding leaves in boundary traversals

   Left and right boundary traversals exclude leaves to avoid duplicates; leaves are printed separately.

3. Step 3: Combine traversals carefully

   Traverse left boundary top-down excluding leaves, then leaves left to right, then right boundary bottom-up excluding leaves, skipping duplicates.

4. Final Answer:

   Traverse left boundary top-down excluding leaves, then all leaves left to right, then right boundary bottom-up excluding leaves, skipping duplicates -> Option D

5. Quick Check:

   Exclude leaves in boundaries, print leaves separately [OK]

Hint: Exclude leaves in boundaries, print leaves separately [OK]

Common Mistakes:

• Including leaves in both boundary and leaf traversals causing duplicates
• Ignoring nodes with single child in boundary
• Printing nodes in wrong order