Problem: Get Minimum Connection Cost

In Amazon's highly efficient logistics network, minimizing operational overhead and optimizing package routing is crucial to ensure smooth deliveries across various regions.

The network consists of n warehouses, numbered from 1 to n, each strategically positioned at its corresponding index. Each warehouse has a specific storage capacity, given by warehouseCapacity, where warehouseCapacity[i] represents the capacity of the warehouse located at position i (assuming 1-based indexing).

These warehouses are organized in a non-decreasing order of their storage capacities, meaning each warehouse's storage capacity is greater than or equal to the one before it. Each warehouse must establish a connection to a distribution hub positioned at a location greater than or equal to its own. This means that a warehouse at position i can only connect to a hub at position j, where j >= i.

To optimize inventory routing, Amazon has placed a central high-capacity distribution hub at the last warehouse, located at position n. This hub serves as the main connection point for all warehouses if necessary. The cost of establishing a connection from warehouse i to a hub at position j is given by warehouseCapacity[j] - warehouseCapacity[i].

Given a series of queries of the form (hubA, hubB), where two additional high-performance distribution hubs are deployed at warehouses hubA and hubB (1 <= hubA < hubB < n), the goal is to calculate the minimum total connection cost for all warehouses, considering the nearest available distribution hub at or beyond each warehouse's position.

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Notes:

1. The problem statement assumes 1-based indexing for the warehouseCapacity array.
2. Each query is independent, i.e., the changes made do not persist for subsequent queries.
3. Each warehouse connects to the nearest hub at or beyond its position (either hubA, hubB, or the central hub at n) to minimize the overall connection cost.

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Function Description

Complete the function getMinConnectionCost as described below.

Function Parameters:

• int warehouseCapacity[n]: A non-decreasing array of integers representing the storage capacities of the warehouses.
• int additionalHubs[q][2]: A 2D array where each element denotes the positions of two additional distribution hubs installed for a query.

Returns:

• long int[q]: The minimum total connection costs for each query.

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Examples

Example 1:

Input:
warehouseCapacity = [3, 6, 10, 15, 20],
q = 1,
additionalHubs = [[2, 4]]

Output:
[8]

Explanation:

• Additional hubs are installed at positions 2 and 4.
• For each warehouse:
  1. Warehouse 1 connects to hub 2 with cost 6 - 3 = 3.
  2. Warehouse 2 is itself a hub, so cost is 0.
  3. Warehouse 3 connects to hub 4 with cost 15 - 10 = 5.
  4. Warehouses 4 and 5 are themselves hubs, so costs are 0.

Total cost: 3+0+5+0+0=83 + 0 + 5 + 0 + 0 = 8.

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Example 2:

Input:
warehouseCapacity = [0, 2, 5, 9, 12, 18],
q = 2,
additionalHubs = [[2, 5], [1, 3]]

Output:
[12, 18]

Explanation:

Query 1: Hubs at positions 2 and 5:

• Warehouse 1 connects to hub 2, cost 2 - 0 = 2.
• Warehouse 2 is itself a hub, cost 0.
• Warehouse 3 connects to hub 5, cost 12 - 5 = 7.
• Warehouse 4 connects to hub 5, cost 12 - 9 = 3.
• Warehouses 5 and 6 are hubs, costs 0.

Total cost: 2+0+7+3+0+0=122 + 0 + 7 + 3 + 0 + 0 = 12.

Query 2: Hubs at positions 1 and 3:

• Warehouse 1 is a hub, cost 0.
• Warehouse 2 connects to hub 3, cost 5 - 2 = 3.
• Warehouse 3 is a hub, cost 0.
• Warehouse 4 connects to hub 6, cost 18 - 9 = 9.
• Warehouse 5 connects to hub 6, cost 18 - 12 = 6.
• Warehouse 6 is a hub, cost 0.

Total cost: 0+3+0+9+6+0=180 + 3 + 0 + 9 + 6 + 0 = 18.

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Constraints:

• 1 <= n <= 10^5
• 1 <= q <= 100
• 1 <= warehouseCapacity[i] <= 10^9
• warehouseCapacity is sorted in non-decreasing order.
• 1 <= hubA < hubB < n

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