Question 1: Minimum Time to Synchronize Distributed Data

Developers at Amazon have deployed an application with a distributed database. The database is stored on total_servers different servers numbered from 1 to total_servers that are connected in a circular fashion, i.e., 1 is connected to 2, 2 is connected to 3, and so on until total_servers connects back to 1.

A subset of servers is represented by an array servers of size n integers. These servers need to transfer data to each other to stay synchronized. Data transfer from one server to its direct neighbor takes 1 unit of time. Starting from any server, find the minimum amount of time required to transfer the data to all the other servers.

Example:

• Input:
  • total_servers = 8
  • n = 3
  • servers = [2, 6, 8]

Two possible paths are shown, but there can be many more:

1. Path goes from 2 to 6 to 8, taking 6 units of time.
2. Path goes from 2 to 8 to 6, taking 4 units of time.

Return the shorter path length, which is 4.

Function Description:

Complete the function getMinTime in the editor below.

Parameters:

• total_servers (integer): The number of servers in the system.
• servers (array of integers): The servers to share the data with.

Returns:

• Integer: The minimum time required to transfer the data on all the servers.

Constraints:

• The value of total_servers and n satisfies:
  • 1 <= total_servers, n <= 1,000,000,000.

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Question 2: Sorting Points on the X-Axis

Developers at Amazon are working on a new sorting algorithm for points on the x-axis of the coordinate system.

There are n points. The i-th point initially has a weight of weight[i] and is located at position i on the x-axis. In a single operation, the i-th point can be moved to the right by a distance of dist[i].

Objective:

Given weight and dist, find the minimum number of operations required to sort the points by their weights.

Example:

• Input:
  • n = 4
  • weight = [3, 6, 5, 1]
  • dist = [4, 3, 2, 1]

Explanation:

1. Perform operation on point 1: Move it twice, increasing position by 2 * dist[0] = 8.
2. Perform operation on point 2: Move it twice, increasing position by 2 * dist[1] = 6.
3. Perform operation on point 3: Move it twice, increasing position by 2 * dist[2] = 4.

Thus, the total number of operations required is 1 + 2 + 2 = 5.

Function Description:

Complete the function getMinOperations in the editor below.

Parameters:

• weights (array of integers): The weights of the points.
• dist (array of integers): The distances the points can move.

Returns:

• Integer: The minimum number of operations required to sort the points.

Constraints:

• The number of points, n, satisfies:
  • 1 <= n <= 100,000.
• Each weight and distance satisfies:
  • 1 <= weights[i], dist[i] <= 1,000,000,000.

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