1478. Allocate Mailboxes

Given the array houses and an integer k. where houses[i] is the location of the ith house along a street, your task is to allocate k mailboxes in the street.

Return the minimum total distance between each house and its nearest mailbox.

The answer is guaranteed to fit in a 32-bit signed integer.

Example 1:

Input: houses = [1,4,8,10,20], k = 3
Output: 5
Explanation: Allocate mailboxes in position 3, 9 and 20.
Minimum total distance from each houses to nearest mailboxes is |3-1| + |4-3| + |9-8| + |10-9| + |20-20| = 5

Example 2:

Input: houses = [2,3,5,12,18], k = 2
Output: 9
Explanation: Allocate mailboxes in position 3 and 14.
Minimum total distance from each houses to nearest mailboxes is |2-3| + |3-3| + |5-3| + |12-14| + |18-14| = 9.

Example 3:

Input: houses = [7,4,6,1], k = 1
Output: 8

Example 4:

Input: houses = [3,6,14,10], k = 4
Output: 0

Constraints:

• n == houses.length
• 1 <= n <= 100
• 1 <= houses[i] <= 10^4
• 1 <= k <= n
• Array houses contain unique integers.