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Shortest Path Cost Engine 4 Solution

Problem Statement

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

Example 1
Input
gridOrArr = [11, 3, 10, 17]
Output
10

Explanation: Applying Knapsack State Optimization yields the optimal state of 10.

Example 2
Input
gridOrArr = [2, 12]
Output
3

Explanation: Minimal input processes to 3.

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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