Kth Largest Sum in a Binary Tree

Kth Largest Sum in a Binary Tree - Problem

You are given the root of a binary tree and a positive integer k.

The level sum in the tree is the sum of the values of the nodes that are on the same level.

Return the kth largest level sum in the tree (not necessarily distinct). If there are fewer than k levels in the tree, return -1.

Note that two nodes are on the same level if they have the same distance from the root.

Input & Output

Example 1 — Basic Tree

$ Input: root = [5,8,9,2,1,3,7], k = 2

› Output: 13

💡 Note: Level sums: Level 0 = 5, Level 1 = 8+9 = 17, Level 2 = 2+1+3+7 = 13. Sorted: [17,13,5]. 2nd largest is 13.

Example 2 — Not Enough Levels

$ Input: root = [1,2,null,3], k = 3

› Output: 1

💡 Note: Level sums: Level 0 = 1, Level 1 = 2, Level 2 = 3. Sorted: [3,2,1]. 3rd largest is 1.

Example 3 — Single Node

$ Input: root = [1], k = 1

› Output: 1

💡 Note: Only one level with sum = 1. 1st largest level sum is 1.

Constraints

The number of nodes in the tree is in the range [1, 10⁵]
1 ≤ Node.val ≤ 10⁶
1 ≤ k ≤ 10⁵

Visualization

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Asked in

M Meta 15 a Amazon 12 G Google 8 M Microsoft 6

The key insight is to use BFS to traverse the tree level by level and calculate sums efficiently. Best approach uses BFS + Min-Heap to track only the k largest sums without sorting. Time: O(n + L log k), Space: O(n + k).

Common Approaches

✓ Bit Manipulation

⏱️ Time: N/A Space: N/A

BFS + Min-Heap

⏱️ Time: O(n + L log k) Space: O(n + k)

Calculate level sums using BFS and maintain a min-heap of size k containing the k largest sums seen so far. This avoids storing all level sums and eliminates the sorting step.

BFS + Sort All Sums

⏱️ Time: O(n + L log L) Space: O(n + L)

Use breadth-first search to traverse the tree level by level, calculate the sum for each level, store all sums in an array, sort the array in descending order, and return the kth element.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

⚡ Linearithmic

Space Complexity

⚡ Linearithmic Space

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Medium Frequency

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Smart Actions

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