International Olympiad in Informatics 2005 - tasks and by S.Acedanski, P.Chrzastowski, M.Hiron, Ł.Kowalik, M.Kubica,

By S.Acedanski, P.Chrzastowski, M.Hiron, Ł.Kowalik, M.Kubica, T.Malesinski, A.Niewiarowska, K.Onak, P.Pankov, A.Paterek, J.Pawlewicz, J.Radoszewski, P.Stanczyk, M.Stefaniak, T.Verhoeff, S.Wasik

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At least one dimension is greater than 1 . Moreover, in 50% of test cases the dimensions do not exceed 25. There is also a procedure cut(dir, position), that is called by your program to make moves. Parameters dir and position describe the direction and the position of a cut respectively. The parameter dir must be one of the two values: vertical or horizontal. If dir = vertical then the cut is vertical, and the parameter position specifies the xcoordinate of the cut (see the figure above) and you must ensure that 1 position dimension_x() −1 .

1 0 . . . . . * . . . . . 1 1 . * . * . . . * . . . . . 1 2 . . . . . . * . . . . 1 3 . . . * . . . * . . . . 1 4 . . . . . . . * . . . 1 5 * . * . . * . . . . * . . . 1 6 . . . . . . . . * . . 1 7 . . . . * . . . . * . . 1 8 . . . . . . . . . * . 1 9 . . * . . * . . . . . * . 2 0 . . . . . . . . . . * Fig. 1: A chart depicting winning and losing situations. The latter ones are marked with stars. (a) Let us assume, that after the first cut we have a l × m rectangle, where 2n l < n.

There is also a faster dynamic programming solution, which stores the greatest n < n and m < m for which (n , m) and (n, m ) are losing positions. That way we may find the optimal move for a given position in O(1) time, which results in O(n2 ) time complexity. 35 Łukasz Kowalik Łukasz Kowalik, Tomasz Malesiński Task idea and formulation Analysis Available memory: 32 MB, Maximum running time: 1 s. Rivers Nearly all of the Kingdom of Byteland is covered by forests and rivers. Small rivers meet to form bigger rivers, which also meet and, in the end, all the rivers flow together into one big river.

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