Place k mailboxes on a line to minimize the sum of distances from each house to its nearest mailbox; optimal placement partitions the sorted houses into k contiguous groups served by a mailbox at each group's median, solvable by dynamic programming with precomputed interval costs.
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Given the array houses where houses[i] is the location of the ith 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. LC: https://leetcode.com/problems/allocate-mailboxes/
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