Boundary Traversal of Binary Tree in DSA C - Time & Space Complexity

Time Complexity: Boundary Traversal of Binary Tree

O(n)

Understanding Time Complexity

We want to know how the time to do a boundary traversal changes as the tree gets bigger.

Specifically, how many steps does it take to visit the edges of the tree?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void printBoundary(Node* root) {
    if (!root) return;
    if (root->left || root->right) printf("%d ", root->data);
    printLeftBoundary(root->left);
    printLeaves(root);
    printRightBoundary(root->right);
}

void printLeftBoundary(Node* node) {
    if (!node || (!node->left && !node->right)) return;
    printf("%d ", node->data);
    if (node->left) printLeftBoundary(node->left);
    else printLeftBoundary(node->right);
}

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

void printRightBoundary(Node* node) {
    if (!node || (!node->left && !node->right)) return;
    if (node->right) printRightBoundary(node->right);
    else printRightBoundary(node->left);
    printf("%d ", node->data);
}
    

This code prints the boundary nodes of a binary tree in anti-clockwise order: left edge, leaves, then right edge.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Recursive traversal of nodes to print left boundary, leaves, and right boundary.
• How many times: Each node is visited at most once during these traversals.

How Execution Grows With Input

As the number of nodes (n) grows, the code visits each node once in worst case.

Input Size (n)	Approx. Operations
10	About 10 visits
100	About 100 visits
1000	About 1000 visits

Pattern observation: The number of steps grows roughly in direct proportion to the number of nodes.

Final Time Complexity

Time Complexity: O(n)

This means the time to do the boundary traversal grows linearly with the number of nodes in the tree.

Common Mistake

[X] Wrong: "The boundary traversal only visits the boundary nodes, so it must be faster than visiting all nodes."

[OK] Correct: The code still visits many internal nodes to find leaves and boundaries, so it touches most nodes anyway.

Interview Connect

Understanding this traversal helps you practice tree recursion and careful node visits, skills useful in many tree problems.

Self-Check

"What if we changed the tree to be a linked list (all nodes only have one child)? How would the time complexity change?"

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