Allocate Mailboxes

arraymathdynamic programming

Problem Statement

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

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

The test cases are generated so that the answer fits in a 32-bit integer.

Examples

Example 1

Input: houses = [1,4,8,10,20], k = 3
Output: 5
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
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.

Constraints

1 <= k <= houses.length <= 100

1 <= houses[i] <= 10 ^4

All the integers of houses are unique .

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicMath