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Dynamic Stream Minimum 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 dynamic stream minimum according to the target algorithm rules. Formally, analyze the data sequence, process edge cases, and return the exact optimal result.

Example 1
Input
arr = [8, 7, 6, 5]
Output
23

Explanation: By processing the sequence using Min Capacity Target, the computed optimal value is 23.

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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