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Quantum Network Stream Evaluator Solution

Problem Statement

Given a high-dimensional input dataset or state graph of length $N$, calculate the optimal result using the **Heavy-Light Decomposition** algorithm. Formally, implement an optimal sub-linear or $O(N \log N)$ solution capable of satisfying strict time and space complexity limits under maximum competitive edge cases.

Example 1
Input
arr = [7, 19, 11, 23]
Output
40

Explanation: By applying Heavy-Light Decomposition, the optimal hard constraint value evaluates to 40.

Example 2
Input
arr = [1, 5]
Output
5

Explanation: Minimal edge input evaluates to 5.

Constraints

  • 1 <= N <= 2 * 10^5
  • -10^9 <= arr[i] <= 10^9
  • Time Complexity: O(N log N) or O(N log^2 N)
  • Space Complexity: O(N)

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