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Problem Brief

Find Minimum Dist. 😉

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note - See the Problem Source at the vely bottom of the page for the original problem description~

In a realm where data centers and servers flourished along a mystical one-dimensional line, a wise ruler sought to optimize their connections. Each data center needed to establish a bond with a server, minimizing the lag defined as the absolute distance between their coordinates. Tasked with this quest, the ruler gathered the bravest minds to decipher the best pairings from the enchanted positions of the data centers and servers. Together, they embarked on a journey to forge connections that would ensure the smallest lag possible, bringing harmony to the kingdom's network and enhancing its magical efficiency.

❀⊱ 🌺 Credit to Tong and txr and aikay! 🌺 ⊰❀

1Example 1

Input
center = [1, 2, 2], destination = [5, 2, 4]
Output
6
Explanation
In a land where three connections needed to be forged, the positions of the data centers were as follows: center = [1, 2, 2], while the server destinations were located at: destination = [5, 2, 4]. To achieve the most efficient deliveries, the following connections were made: a. The data center at location 1 established its first bond with the server at location 2. b. The data center at location 2 then connected to the server at location 4. c. Lastly, the other data center at location 2 formed a connection with the server at location 5. The minimum total lag for these connections was calculated as follows: abs(1 - 2) + abs(2 - 4) + abs(2 - 5) = 1 + 2 + 3 = 6. Thus, the quest for optimization was successful, with a total lag of 6 uniting the realm of data centers and servers.

2Example 2

Input
center = [3, 1, 6, 8, 9], destination = [2, 3, 1, 7, 9]
Output
5
Explanation
In a land filled with data centers and server destinations, a new set of connections needed to be established. The positions of the data centers were as follows: center = [1, 3, 6, 8, 9], and the server destinations were located at: destination = [1, 2, 3, 7, 9]. To create the most efficient connections, the following pairings were made: The data center at location 1 connected perfectly with the server at location 1. The data center at location 3 established a bond with the server at location 2. The data center at location 6 formed a connection with the server at location 3. The data center at location 8 connected to the server at location 7. Finally, the data center at location 9 paired with the server at location 9. The total distance for these connections was calculated as: abs(1 - 1) + abs(3 - 2) + abs(6 - 3) + abs(8 - 7) + abs(9 - 9) = 0 + 1 + 3 + 1 + 0 = 5. Thus, the quest for optimizing connections was accomplished with a minimum total distance of 5, ensuring harmony in the network of data centers and servers.

Constraints

Limits and guarantees your solution can rely on.

  • 1 <= n <= 105
  • 1 <= center[i], destination[i] <= 109
    • public long findMinimumDist(int[] center, int[] destination) {
 // write your code here
}
    Input

    center

    [1, 2, 2]

    destination

    [5, 2, 4]

    Output

    6

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