Find value on most distinct levels
Company: IXL Learning
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Technical Screen
Given a binary tree whose nodes store values (e.g., characters), find the value that appears on the greatest number of distinct depth levels. For example, for the tree:
A
/ \
A B
/ \
C C
the answer is 'A' because it appears on two different levels (levels 1 and
2). Describe an algorithm, justify its correctness, and analyze its time and space complexity.
Quick Answer: This question evaluates a candidate's understanding of binary tree structures, level-wise aggregation and frequency analysis, along with algorithm design and complexity reasoning.
Given a binary tree whose nodes store character values, find the value that appears on the greatest number of distinct depth levels.
The tree is provided as a level-order (breadth-first) array `tree`, where `tree[i]` is a node value (a single-character string) or `None` to indicate a missing node. The array uses complete-tree indexing: the node at index `i` has its left child at index `2*i + 1` and its right child at index `2*i + 2`. The root is at depth 0.
For each value, count how many *distinct* depth levels it appears on (multiple occurrences on the same level count once). Return the value that appears on the largest number of distinct levels. If several values tie for the maximum, return the one that is smallest in sorted (lexicographic) order. If the tree is empty, return `None`.
Example:
```
A (level 0)
/ \
A B (level 1)
/ \
C C (level 2)
```
Input: `["A", "A", "B", "C", "C"]`. `A` appears on levels {0, 1} (2 distinct levels), `B` on {1}, `C` on {2}. Answer: `"A"`.
Constraints
- 0 <= number of nodes <= 10^4
- Each present node value is a non-empty single-character string.
- The input array uses complete-tree indexing: index i has children at 2*i+1 and 2*i+2.
- Missing nodes are represented by None (Python) / null (JS) / "" (C++); a missing index never has descendants.
- On a tie for the most distinct levels, return the lexicographically smallest value.
- Return None / null / "" for an empty tree.
Examples
Input: (["A", "A", "B", "C", "C"],)
Expected Output: "A"
Explanation: A is on levels {0,1} (2 distinct levels), B on {1}, C on {2}. A wins with 2 distinct levels.
Input: (["X"],)
Expected Output: "X"
Explanation: Single-node tree: X appears only on level 0, so it is trivially the answer.
Hints
- Do a traversal that knows each node's depth (BFS naturally tracks levels, or DFS carrying a depth argument). The depth of the root is 0.
- For each value, keep a SET of the depths it appears on, not a count of occurrences — two nodes with the same value on the same level should add nothing.
- After the traversal, the answer is the value whose depth-set is largest. Resolve ties deterministically by iterating values in sorted order and keeping the first that reaches the maximum size.
- When using array indexing, only descend into children of indices that actually hold a node, so that gaps (None entries) don't generate phantom levels.