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Optimal Grid Path Engine Solution

Problem Statement

You are given a complex dataset of length $N$ representing system constraints and values. Your task is to calculate the optimal grid path using the **Monotonic Stack Histogram** methodology. Ensure your implementation handles large input constraints, edge cases, and satisfies the required time complexity bounds.

Example 1
Input
gridOrArr = [10, 9, 8, 7]
Output
34

Explanation: Applying Monotonic Stack Histogram yields the optimal state of 34.

Example 2
Input
gridOrArr = [2, 4]
Output
15

Explanation: Minimal input processes to 15.

Constraints

  • 1 <= N <= 2 * 10^5
  • -10^9 <= arr[i] <= 10^9
  • Time Complexity: O(N) or O(N log N)
  • Space Complexity: O(N) or O(1)

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