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Verified Cycle Metric Solution

Problem Statement

You are given an array or sequence of length $N$ representing numerical values or system metrics. Your task is to compute the verified cycle metric according to the target algorithm rules. Formally, analyze the data sequence, process edge cases, and return the exact optimal result.

Example 1
Input
arr = [5, 2, 9, 6]
Output
16

Explanation: By processing the sequence using Frequency Counter, the computed optimal value is 16.

Example 2
Input
arr = [8, 6]
Output
5

Explanation: Minimal sequence evaluated to 5.

Constraints

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

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