The final state of the parking center can easily be determined by sorting the input list of car types. This can be done in linear time (~\mathcal O(M+N)~). ~\mathcal O(N^2)~ and ~\mathcal O(N \log N)~ methods may be too slow for larger ~N~.

A greedy approach to construct successive rounds will work, since in each round it can be guaranteed that at least ~W-1~ cars are put into their final position. Hence, the number of rounds needed by this greedy algorithm is ~\left\lceil \frac{D}{W-1} \right\rceil~, where ~D~ is the number of displaced cars in the initial state for the input. In general, finding the minimum number of rounds is NP-complete. Even reducing the number of rounds for the greedy algorithm by just one round is, in general, as hard as finding the minimum (compare to bin packing: you need to find cycles that add up in length to ~W~, for otherwise one worker is not doing useful work).

The greedy algorithm can be implemented in ~\mathcal O(N+M)~ space and ~\mathcal O(N)~ time. However, a more naive implementation may use ~\mathcal O(N)~ space and ~\mathcal O(N^2)~ time. The test data has been designed to distinguish linear solutions from less efficient ones.