Top View of Binary Tree in DSA C - Build from Scratch

Top View of Binary Tree

📖 Scenario: Imagine you are working with a binary tree that represents a city skyline from left to right. You want to see which buildings are visible when looking from the top, ignoring buildings hidden behind others.

🎯 Goal: Build a program in C that prints the top view of a binary tree. The top view shows nodes visible when the tree is viewed from above, from leftmost to rightmost.

📋 What You'll Learn

Create a binary tree with given nodes and structure

Use a horizontal distance concept to track node positions

Traverse the tree to find the top view nodes

Print the top view nodes from left to right

💡 Why This Matters

🌍 Real World

Top view of a binary tree helps in visualizing hierarchical data from a different perspective, useful in graphics, network routing, and city planning.

💼 Career

Understanding tree traversals and views is important for software engineers working with data structures, algorithms, and system design.

1

Create the Binary Tree Structure

Define a struct Node with int data, struct Node *left, and struct Node *right. Then create nodes to build this exact tree:
1
/ \
2 3
\ \
4 5

DSA C

// Define struct Node and create nodes for the tree
// Your code here

Hint

Start by defining the node structure and a helper function newNode to create nodes. Then build the tree exactly as shown.

2

Set Up Horizontal Distance Tracking

Create a struct QueueNode to hold a struct Node* and its int hd (horizontal distance). Also create a queue with front and rear pointers to hold QueueNode elements for level order traversal.

DSA C

#include 
#include 

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

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

// Define struct QueueNode with struct Node* and int hd
// Define queue front and rear pointers

int main() {
    struct Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->right = newNode(4);
    root->right->right = newNode(5);
    // Your code here
    return 0;
}

Hint

Use a linked list style queue to hold nodes with their horizontal distances for traversal.

3

Implement Top View Logic Using Level Order Traversal

Write code to perform level order traversal using the queue. Track horizontal distances and store the first node at each horizontal distance in an array topViewNodes. Use minHd and maxHd to track the range of horizontal distances. Enqueue left child with hd - 1 and right child with hd + 1. Only store the first node encountered at each horizontal distance.

DSA C

#include 
#include 

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

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

struct QueueNode {
    struct Node* node;
    int hd;
    struct QueueNode* next;
};

struct Queue {
    struct QueueNode *front, *rear;
};

// Implement enqueue and dequeue functions

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

    struct Queue* queue = (struct Queue*)malloc(sizeof(struct Queue));
    queue->front = queue->rear = NULL;

    // Implement top view logic here
    // Your code here

    return 0;
}

Hint

Use a large enough array to store nodes by horizontal distance. Initialize with -1 to mark empty. Enqueue root with a middle index (like 500) to allow negative and positive horizontal distances.

4

Print the Top View Nodes from Left to Right

Use a for loop from minHd to maxHd and print the values in topViewNodes separated by spaces.

DSA C

#include 
#include 

// ... previous code ...

int main() {
    // ... previous code ...

    // Print top view nodes from minHd to maxHd
    // Your code here

    return 0;
}

Hint

Print the stored top view nodes from the smallest horizontal distance to the largest, separated by spaces.

Practice

1. What does the top view of a binary tree represent?

easy

A. Nodes visible when the tree is viewed from the top

B. Nodes visible when the tree is viewed from the left side

C. Nodes visible when the tree is viewed from the right side

D. All leaf nodes of the tree

Solution

1. Step 1: Understand the meaning of top view

   The top view of a binary tree shows nodes visible when looking down vertically from above the tree.

2. Step 2: Compare with other views

   Left or right views show nodes from side angles, and leaf nodes are only the bottom nodes, not the top view.

3. Final Answer:

   Nodes visible when the tree is viewed from the top -> Option A

4. Quick Check:

   Top view = nodes seen from above [OK]

Hint: Top view shows nodes visible from above the tree [OK]

Common Mistakes:

• Confusing top view with left or right view
• Thinking top view includes all leaf nodes
• Assuming top view shows all nodes

2. Which data structure is commonly used to find the top view of a binary tree in C?

easy

A. Stack

B. Queue

C. Hash Map

D. Linked List

Solution

1. Step 1: Identify traversal method for top view

   Top view is found using level order traversal, which uses a queue to process nodes level by level.

2. Step 2: Understand role of queue

   Queue helps visit nodes in order from top to bottom and left to right, needed for correct top view.

3. Final Answer:

   Queue -> Option B

4. Quick Check:

   Level order traversal uses queue [OK]

Hint: Use queue for level order traversal in top view [OK]

Common Mistakes:

• Using stack which is for depth-first traversal
• Confusing hash map as traversal structure
• Using linked list instead of queue

3. What is the output top view of the binary tree below?

        1
       / \
      2   3
       \   \
        4   5
         \   \
          6   7

medium

A. [1, 2, 3, 4, 5]

B. [2, 1, 4, 6, 7]

C. [2, 1, 3, 4, 7]

D. [2, 1, 3, 5, 7]

Solution

1. Step 1: Assign horizontal distances

   Assign horizontal distance (HD) from root: root(1) = 0, left child decreases HD by 1, right child increases HD by 1. So, 2 = -1, 3 = 1, 4 = 0, 5 = 2, 6 = 1, 7 = 3.

2. Step 2: Select topmost nodes at each HD

   At HD -1: 2; HD 0: 1 (4 is lower); HD 1: 3 (6 is lower); HD 2: 5; HD 3: 7.

3. Final Answer:

   [2, 1, 3, 5, 7] -> Option D

4. Quick Check:

   Top view nodes by HD = [2,1,3,5,7] [OK]

Hint: Use horizontal distance and pick top nodes [OK]

Common Mistakes:

• Choosing lower nodes instead of top nodes
• Ignoring horizontal distance concept
• Mixing order of nodes in output

4. Consider this C code snippet to print top view of a binary tree:

void topView(Node* root) {
    if (!root) return;
    map topNode;
    queue> q;
    q.push({root, 0});
    while (!q.empty()) {
        auto p = q.front(); q.pop();
        Node* node = p.first;
        int hd = p.second;
        if (topNode.find(hd) == topNode.end())
            topNode[hd] = node->data;
        if (node->left) q.push({node->left, hd - 1});
        if (node->right) q.push({node->right, hd + 1});
    }
    for (auto it : topNode)
        cout << it.second << " ";
}

What is the error in this code?

medium

A. Incorrect horizontal distance calculation

B. Not checking if root is NULL

C. Using C++ STL map and queue in C code

D. Missing return statement in void function

Solution

1. Step 1: Identify language mismatch

   The code uses C++ STL containers like map and queue, but the function is declared in C style which does not support these STL features.

2. Step 2: Check other code parts

   Root NULL check is present, horizontal distance is correctly updated, and void functions do not require return statements.

3. Final Answer:

   Using C++ STL map and queue in C code -> Option C

4. Quick Check:

   C code cannot use C++ STL containers [OK]

Hint: C code can't use C++ STL containers like map or queue [OK]

Common Mistakes:

• Ignoring language differences between C and C++
• Thinking void functions need return
• Assuming horizontal distance logic is wrong

5. You have a binary tree where multiple nodes share the same horizontal distance and level. How should you modify the top view algorithm to always show the leftmost node at that horizontal distance?

hard

A. Store the first node encountered at each horizontal distance during level order traversal

B. Store the last node encountered at each horizontal distance during level order traversal

C. Store nodes with maximum depth at each horizontal distance

D. Store nodes with minimum depth at each horizontal distance but prefer right child first

Solution

1. Step 1: Understand node selection in top view

   Top view shows the first node encountered at each horizontal distance during level order traversal, which naturally picks the leftmost node at that distance.

2. Step 2: Avoid overwriting nodes

   By storing only the first node at each horizontal distance and ignoring later nodes, the leftmost node is preserved.

3. Final Answer:

   Store the first node encountered at each horizontal distance during level order traversal -> Option A

4. Quick Check:

   First node at HD = leftmost node [OK]

Hint: Keep first node per horizontal distance in level order [OK]

Common Mistakes:

• Overwriting with last node instead of first
• Choosing nodes by max depth instead of min
• Preferring right child first breaks leftmost rule