How do you solve Kth Largest Sum in a Binary Tree on LeetCode?

Kth Largest Sum in a Binary Tree (LeetCode #2583) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log k) time complexity and O(k) space complexity. Key insight: Using a heap can significantly optimize the retrieval of the k-th largest element.

What is the brute force solution for Kth Largest Sum in a Binary Tree?

The brute force approach for Kth Largest Sum in a Binary Tree is Brute Force, with O(n²) time complexity and O(n) space complexity. In this approach, we traverse the binary tree level by level, calculating the sum of node values at each level. We then sort these sums and retrieve the k-th largest sum. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log k).

What algorithm or data structure is used to solve Kth Largest Sum in a Binary Tree?

Kth Largest Sum in a Binary Tree uses the following concepts: Tree, Breadth-First Search, Sorting, Binary Tree. The recommended patterns to study are: Heap, Tree Traversal.

What are the interview tips for Kth Largest Sum in a Binary Tree?

Explain your thought process clearly during the traversal. Discuss the trade-offs between different approaches. Practice writing code on a whiteboard or in an online editor.

What are common mistakes when solving Kth Largest Sum in a Binary Tree?

Not handling the case where there are fewer than k levels. Forgetting to maintain the heap size while inserting sums.

#2583

Kth Largest Sum in a Binary Tree

Medium

TreeBreadth-First SearchSortingBinary TreeHeapTree Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log k)
Space	O(n)	O(k)

💡

Intuition

Time O(n log k)Space O(k)

This approach uses a priority queue (min-heap) to efficiently keep track of the top k largest level sums while traversing the tree. This avoids the need for sorting the entire list of sums, making it faster.

⚙️

Algorithm

4 steps

1Step 1: Perform a level-order traversal of the binary tree using a queue.
2Step 2: For each level, calculate the sum of the node values.
3Step 3: Use a min-heap to keep track of the top k largest sums. If the size of the heap exceeds k, remove the smallest sum.
4Step 4: After processing all levels, if the heap has fewer than k elements, return -1; otherwise, return the root of the heap.

solution.py22 lines

1# Full working Python code
2import heapq
3from collections import deque
4
5def kthLargestLevelSum(root, k):
6    if not root:
7        return -1
8    level_sums = []
9    queue = deque([root])
10    while queue:
11        level_sum = 0
12        for _ in range(len(queue)):
13            node = queue.popleft()
14            level_sum += node.val
15            if node.left:
16                queue.append(node.left)
17            if node.right:
18                queue.append(node.right)
19        heapq.heappush(level_sums, level_sum)
20        if len(level_sums) > k:
21            heapq.heappop(level_sums)
22    return level_sums[0] if len(level_sums) == k else -1

ℹ

Complexity note: The time complexity is O(n log k) because we process each node once and maintain a heap of size k, which takes log k time for each insertion. The space complexity is O(k) for storing the k largest sums.

1Using a heap can significantly optimize the retrieval of the k-th largest element.
2Level-order traversal is essential for calculating sums at each level.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.