Maximum Level Sum of a Binary Tree

Maximum Level Sum of a Binary Tree

What is this problem about?

The Maximum Level Sum of a Binary Tree coding problem asks you to find the level (depth) of a binary tree with the maximum sum of node values. Level 1 is the root. You need to return the smallest level number in case of ties. This is a classic BFS traversal problem with a simple aggregation at each level.

Why is this asked in interviews?

Meta, Amazon, and Google include this problem to test BFS/level-order traversal proficiency. It is straightforward in concept but requires clean implementation of level-order traversal with sum tracking. Interviewers use it as a warm-up or as a basis for follow-up questions about DFS alternatives for level-sum computation.

Algorithmic pattern used

BFS (level-order traversal): Use a queue. For each level, process all nodes currently in the queue (the level's nodes), sum their values, and enqueue their children. Track the maximum sum and the corresponding level. Return the level with maximum sum (smallest level on tie). Time: O(n), Space: O(n) for the queue.

DFS alternative: Maintain an array level_sums where level_sums[depth] accumulates values. After DFS, return the index+1 of the maximum. This uses O(h) call stack + O(h) array where h is tree height.

Example explanation

Tree:

       1
      / \
     7   0
    / \   \
   7  -8   9

• Level 1: sum = 1
• Level 2: sum = 7 + 0 = 7
• Level 3: sum = 7 + (-8) + 9 = 8

Maximum sum = 8 at level 3. Answer = 3.

BFS processes level by level, so at level 3 the queue contains [7, -8, 9], sum = 8.

Common mistakes candidates make

• Not tracking level number: Computing the max sum but returning a sum value instead of the level index.
• Confusing 0-indexed vs 1-indexed levels: The problem typically counts levels starting at 1. An off-by-one returns the wrong level.
• Handling ties incorrectly: The problem asks for the smallest level on tie. Process levels in order 1, 2, 3, ... and only update the answer when strictly greater, not greater-or-equal.

Interview preparation tip

For the Breadth-First Search Depth-First Search Binary Tree Tree interview pattern, know both BFS and DFS implementations for level-sum problems. BFS is more natural and intuitive for level-based problems. When asked "can you do it without a queue?", the DFS with a depth-indexed array is the go-to answer. Both are O(n) — the difference is implementation style.