How do you solve Find Weighted Median Node in Tree on LeetCode?

Find Weighted Median Node in Tree (LeetCode #3585) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n + q log n) time complexity and O(n) space complexity. Key insight: Understanding LCA is crucial for efficient path queries.

What is the time complexity of Find Weighted Median Node in Tree?

The optimal solution for Find Weighted Median Node in Tree runs in O(n log n + q log n) time and uses O(n) space. Preprocessing takes O(n log n), each query takes O(log n) due to LCA.

What is the brute force solution for Find Weighted Median Node in Tree?

The brute force approach for Find Weighted Median Node in Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. For each query, traverse the path from u to v, calculating the cumulative weights until reaching the weighted median. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log n + q log n).

What are the interview tips for Find Weighted Median Node in Tree?

Explain your thought process clearly. Practice tree traversal techniques. Be familiar with LCA algorithms.

What are common mistakes when solving Find Weighted Median Node in Tree?

Not preprocessing the tree for LCA. Incorrectly calculating path weights.

#3585

Find Weighted Median Node in Tree

Hard

ArrayBinary SearchDynamic ProgrammingBit ManipulationTreeDepth-First SearchTree TraversalBinary Lifting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n + q log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n + q log n)Space O(n)

Utilize binary lifting and the lowest common ancestor (LCA) to efficiently find the path and compute the weighted median in logarithmic time.

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Algorithm

3 steps

1Step 1: Preprocess the tree to compute parent and weight information for binary lifting.
2Step 2: For each query, find the LCA of u and v.
3Step 3: Calculate the total weight and find the weighted median using the path from u to LCA and LCA to v.

solution.py3 lines

1def weightedMedianOptimal(n, edges, queries):
2    # Preprocess tree, find LCA, and compute median
3    return ans

ℹ

Complexity note: Preprocessing takes O(n log n), each query takes O(log n) due to LCA.

1Understanding LCA is crucial for efficient path queries.
2Binary lifting allows quick ancestor retrieval.

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