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Calculated Interval Partition 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 calculated interval partition according to the target algorithm rules. Formally, analyze the data sequence, process edge cases, and return the exact optimal result.

Example 1
Input
arr = [2, 7, 12, 7]
Output
29

Explanation: By processing the sequence using Priority Crate Allocation, the computed optimal value is 29.

Example 2
Input
arr = [6, 12]
Output
14

Explanation: Minimal sequence evaluated to 14.

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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