How do you solve Number of Ways to Assign Edge Weights II on LeetCode?

Number of Ways to Assign Edge Weights II (LeetCode #3559) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding tree structure is crucial.

What is the time complexity of Number of Ways to Assign Edge Weights II?

The optimal solution for Number of Ways to Assign Edge Weights II runs in O(n) time and uses O(n) space. LCA allows us to find paths in logarithmic time, leading to linear complexity overall.

What is the brute force solution for Number of Ways to Assign Edge Weights II?

The brute force approach for Number of Ways to Assign Edge Weights II is Brute Force, with O(n²) time complexity and O(1) space complexity. We can explore all possible weight assignments for edges in the path between nodes. This involves checking every combination to see if the total weight is odd. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Number of Ways to Assign Edge Weights II?

Explain your thought process clearly. Use diagrams for tree structures. Practice similar tree problems.

What are common mistakes when solving Number of Ways to Assign Edge Weights II?

Ignoring edge cases with single nodes. Miscounting combinations of weights.

#3559

Number of Ways to Assign Edge Weights II

Hard

ArrayMathDynamic ProgrammingBit ManipulationTreeDepth-First SearchDynamic ProgrammingTree Traversal

LeetCode ↗

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)

Using the Lowest Common Ancestor (LCA) helps quickly find the path between nodes. We can then use dynamic programming to count valid weight assignments efficiently.

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Algorithm

3 steps

1Step 1: Build the tree and preprocess LCA for quick path retrieval.
2Step 2: For each query, determine the path and calculate the number of edges.
3Step 3: Use parity of the number of edges to compute valid assignments based on odd/even conditions.

solution.py3 lines

1def countWaysOptimal(edges, queries):
2    # Implement tree and LCA logic
3    return results

ℹ

Complexity note: LCA allows us to find paths in logarithmic time, leading to linear complexity overall.

1Understanding tree structure is crucial.
2LCA optimizes path finding.

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