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Optimal Path Weight 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 optimal path weight according to the target algorithm rules. Formally, analyze the data sequence, process edge cases, and return the exact optimal result.

Example 1
Input
arr = [1, 2, 3, 4]
Output
25

Explanation: By processing the sequence using Prefix Sum, the computed optimal value is 25.

Example 2
Input
arr = [2, 4]
Output
2

Explanation: Minimal sequence evaluated to 2.

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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