Codeforces 321E Ciel and Gondola - Problem Statement

There are $n$ people in a queue for $k$ gondolas. Some pairs know each other. If two people who know each other share a gondola, they talk (cost $1$). Assign people to gondolas in queue order to reduce total talking. Each gondola needs at least one person.

This is partitioning: split $n$ people into $k$ contiguous groups, reducing sum of pair-costs within groups. Before reading the solution, try to identify the base case and recursive relationship yourself.