A decorative fence.pptVIP

问题求解与程序设计 李文新 Problem A decorative fence Table of Contents The problem Solution The problem CENTRAL EUROPEAN OLYMPIAD IN INFORMATICS 30 June – 6 July 2002 Day 1: fence A decorative fence Time limit: 1 s Memory limit: 1 MB The problem Richard just finished building his new house. Now the only thing the house misses is a cute little wooden fence. He had no idea how to make a wooden fence, so he decided to order one. The problem Somehow he got his hands on the ACME1 Fence Catalogue 2002, the ultimate resource on cute little wooden fences. After reading its preface he already knew, what makes a little wooden fence cute. The problem A wooden fence consists of N wooden planks, placed vertically in a row next to each other. A fence looks cute if and only if the following conditions are met: The problem ? The planks have different lengths, namely 1, 2, . . . , N plank length units. ? Each plank with two neighbors is either larger than each of its neighbors or smaller than each of them. (Note that this makes the top of the fence alternately rise and fall.) The problem It follows, that we may uniquely describe each cute fence with N planks as a permutation a1, . . . , aN of the numbers 1, . . . ,N such that (?i; 1 i N) (ai - ai-1) * (ai - ai+1) 0 and vice versa, each such permutation describes a cute fence. The problem It is obvious, that there are many different cute wooden fences made of N planks. The problem To bring some order into their catalogue, the sales manager of ACME decided to order them in the following way: Fence A (represented by the permutation a1, . . . , aN) is in the catalogue before fence B (represented by b1, . . . , bN) if and only if there exists such i, that The problem (?j i) aj = bj and (ai bi). (Also to decide, which of the two fences is earlier in the catalogue, take their corresponding permutations, find the first place on which they differ and compare the values on this place.) The problem All the cute fences with N planks are numbered (