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Problem Brief

Find Machine Count

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There are n regions where servers are hosted. The number of machines in the i-th region is given by machineCount[i], where 0 <= i < n. Managing all these regions can be challenging, so the team decided to move some machines to exactly 3 regions. The number of machines in the i-th of these 3 target regions is given by finalMachineCount[i], where 0 <= i < 3.

There are two operations that can be performed:

  • Add or Remove Machines: Add or remove a machine from any existing region. The number of machines in that server should be non-zero before and after the operation. This operation costs 1 unit.
  • Move All Machines: Move all machines from one region to another existing region at a cost of shiftingCost units. The now-empty region is destroyed in this operation.

    • Objective: Find the minimum cost to shift the machines so that any 3 regions have the counts required in finalMachineCount.

    Note: It is possible that there are additional machines left at the end apart from the ones placed in the final 3 regions.

    Function Description

    Complete the function getMinimumCost in the editor.

    getMinimumCost has the following parameters:

    1. int machineCount[]: The initial number of machines in the regions.
    2. int finalMachineCount[]: The final number of machines required in the 3 regions.
    3. int shiftingCost: The cost to move all machines from one region to another.

    Returns

    int: The minimum cost to move machines into 3 regions.

    1Example 1

    Input
    machineCount = [2, 3, 5, 7], finalMachineCount = [5, 10, 5], shiftingCost = 2
    Output
    5
    Explanation

    1. Increase the number of machines in the 1st and 2nd regions by 1 and 2 machines respectively. The new machineCount = [3, 5, 5, 7]. Total cost for these operations is 1 + 2 = 3.

    2. Move all the machines from the 4th region to the 1st region, which takes shiftingCost = 2. The new machineCount = [10, 5, 5]. The cost of this operation is 2.

    Total Cost = 3 + 2 = 5

    2Example 2

    Input
    machineCount = [2, 4, 5, 3], finalMachineCount = [4, 4, 4], shiftingCost = 5
    Output
    2
    Explanation

    Increase the number of machines in the 4th region by 1 and decrease the number of machines in the 3rd region by 1. The new machineCount = [2, 4, 4, 4]. Total cost for these operations is 1 + 1 = 2. Use the 2nd, 3rd, and 4th regions as the required servers, leaving behind the 1st region.

    3Example 3

    Input
    machineCount = [5, 10, 15, 20, 25], finalMachineCount = [20, 20, 20], shiftingCost = 3
    Output
    8
    Explanation

    On increasing the number of machines of the 5th region by 5, the new machineCount = [5, 10, 15, 20, 20]. Total cost required for these operations = 5.

    Now, moving all the machines from the 3rd region to the 1st region, which takes shiftingCost(3) dollars, the new machineCount = [20, 10, 20, 20]. Total cost required for these operations = 3.

    Use the 1st, 3rd, and 4th regions as required regions, leaving behind the 2nd region. The total cost = 5 + 3 = 8.

    Constraints

    Limits and guarantees your solution can rely on.

    • 3 <= n <= 10^8
    • 1 <= machineCount[i], finalMachineCount[i] <= 10^6
    • 1 <= shiftingCost <= 10^6
    public int getMinimumCost(int[] machineCount, int[] finalMachineCount, int shiftingCost) {
  // write your code here
}
    Input

    machineCount

    [2, 3, 5, 7]

    finalMachineCount

    [5, 10, 5]

    shiftingCost

    2

    Output

    5

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