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Amazon Online Assessment: Optimal Warehouse Placement Problem

Amazon has recently established nnn distribution centers in a new location. They want to set up 2 warehouses to serve these distribution centers. Note that the centers and warehouses are all built along a straight line. A distribution center has its demands met by the warehouse that is closest to it. A logistics team wants to choose the location of the warehouses such that the sum of the distances of the distribution centers to their closest warehouses is minimized.

Given an array dist_centers, that represent the positions of the distribution centers, return the minimum sum of distances to their closest warehouses if the warehouses are positioned optimally.


Suppose dist_centers = [1, 2, 3]

One optimal solution is to position the 2 warehouses at x1=1x_1 = 1x1​=1 and x2=2x_2 = 2x2​=2.

Distances to
the nearest 0 0 1

O - Warehouse
• - Distribution center

The minimum sum of the distances between distribution centers and the warehouses closest to them is 0+0+1=10 + 0 + 1 = 10+0+1=1.

Function Description

Complete the function getMinTotalDistance in the editor below.

getMinTotalDistance has the following parameter:

  • int dist_centers[n]: the locations of the distribution centers


  • int: the minimum sum of the given expression


Sample Input For Custom Testing

Sample Case 0

rust复制代码STDIN           FUNCTION
2               -> n = 2
1 6             -> dist_centers = [1, 6]

Sample Output



Place one warehouse at x1=1x_1 = 1x1​=1 and the other at x2=6x_2 = 6x2​=6. Each center is 0 distance from its nearest warehouse.

Sample Case 1

4 -> n = 4
1 2 5 6 -> dist_centers = [1, 2, 5, 6]

Sample Output



One optimal solution is to place the warehouses at x1=1x_1 = 1x1​=1 and x2=6x_2 = 6x2​=6. Distances to the nearest warehouse for centers at [1, 2, 5, 6] are [0, 0, 1, 0].

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