What is the time complexity of Minimum Weighted Subgraph With the Required Paths II?

The optimal solution for Minimum Weighted Subgraph With the Required Paths II runs in O(n) time and uses O(n) space. LCA preprocessing takes O(n) time, and each query is resolved in constant time due to precomputed paths.

What is the brute force solution for Minimum Weighted Subgraph With the Required Paths II?

The brute force approach for Minimum Weighted Subgraph With the Required Paths II is Brute Force, with O(n²) time complexity and O(1) space complexity. Explore all possible subtrees to find the minimum weight that connects the required nodes. This method checks every combination, leading to inefficiency. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Minimum Weighted Subgraph With the Required Paths II?

Explain your thought process clearly. Focus on edge cases and constraints. Practice tree-related problems regularly.

What are common mistakes when solving Minimum Weighted Subgraph With the Required Paths II?

Not considering all paths when using brute force. Overlooking the importance of preprocessing for LCA.

#3553

Minimum Weighted Subgraph With the Required Paths II

Hard

ArrayDynamic ProgrammingBit ManipulationTreeDepth-First SearchBinary LiftingDepth-First Search

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Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(n)

Utilize the Lowest Common Ancestor (LCA) to efficiently find paths in the tree. By focusing on the LCA, we minimize the edges needed to connect the nodes.

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Algorithm

3 steps

1Step 1: Preprocess the tree for LCA using binary lifting.
2Step 2: For each query, find the LCA of src1 and src2.
3Step 3: Calculate the total weight from src1 to LCA, src2 to LCA, and LCA to dest.

solution.py3 lines

1def minWeightSubgraph(edges, queries):
2    # Implementation...
3    return results

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Complexity note: LCA preprocessing takes O(n) time, and each query is resolved in constant time due to precomputed paths.

1Understanding LCA is crucial for efficient pathfinding in trees.
2Minimizing the number of edges traversed reduces overall weight.

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