Right Side View of Binary Tree in DSA C++ - Time & Space Complexity

Time Complexity: Right Side View of Binary Tree

O(n)

Understanding Time Complexity

We want to understand how the time needed to find the right side view of a binary tree changes as the tree grows.

How does the number of nodes affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void rightSideViewHelper(TreeNode* root, int level, vector& view) {
    if (!root) return;
    if (level == view.size())
        view.push_back(root->val);
    rightSideViewHelper(root->right, level + 1, view);
    rightSideViewHelper(root->left, level + 1, view);
}

vector rightSideView(TreeNode* root) {
    vector view;
    rightSideViewHelper(root, 0, view);
    return view;
}
    

This code visits nodes to collect the rightmost node at each level of the tree.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Recursive calls visiting each node once.
• How many times: Each node in the tree is visited exactly one time.

How Execution Grows With Input

As the number of nodes increases, the function visits each node once, so the work grows directly with the number of nodes.

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

Pattern observation: The work grows linearly as the tree size grows.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the right side view grows directly with the number of nodes in the tree.

Common Mistake

[X] Wrong: "Since we only look at the right side, the time is less than visiting all nodes."

[OK] Correct: The code still visits every node to check if it is the rightmost at its level, so all nodes are processed.

Interview Connect

Understanding this time complexity helps you explain how tree traversal works and shows you can analyze recursive solutions clearly.

Self-Check

"What if we changed the traversal to visit the left child before the right child? How would the time complexity change?"