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Adaptive Frequency Balance 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 adaptive frequency balance according to the target algorithm rules. Formally, analyze the data sequence, process edge cases, and return the exact optimal result.

Example 1
Input
arr = [3, 2, 11, 10]
Output
28

Explanation: By processing the sequence using Depth-First Search, the computed optimal value is 28.

Example 2
Input
arr = [10, 10]
Output
11

Explanation: Minimal sequence evaluated to 11.

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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