Consider a binary tree T with 100 nodes.
Qualcomm technical mcq question, verified with a worked answer. Free to practise - no sign-up.
Consider a binary tree T with 100 nodes. What will be the maximum number of nodes at 2nd level of T?
**
Show answer & explanation
Answer: B. 4
In a binary tree, each node can have at most 2 children. Level 0 (root) has at most 1 node, level 1 has at most 2 nodes, and level 2 has at most 2 × 2 = 4 nodes. Since the tree has 100 total nodes, there are enough nodes to fill level 2 completely with 4 nodes.
Step-by-step Derivation:
In a binary tree:
- Level 0 (root): max 2^0 = 1 node
- Level 1: max 2^1 = 2 nodes
- Level 2: max 2^2 = 4 nodes
General formula: Maximum nodes at level k = 2^k
For level 2: 2^2 = 4 nodes
Since the tree has 100 nodes total (more than enough to fill level 2), the maximum at level 2 is 4.