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Segmented 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 segmented 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
8

Explanation: By processing the sequence using Min-Heap Extraction, the computed optimal value is 8.

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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