分支限界法题目.doc

第一题：用分支限界法解决最优装载问题（主要学习思想）二、问题描述给定 2n 个方格组成的一行方格。除了两个相邻的空方格外，其余每个方格中都放入了一枚金币或一枚银币。共有 n-1 枚金币和 n-1 枚银币。任何两个非空方格中的钱币可以移动到两个相邻的空格中，但不能改变线币的排列顺序。金币变换问题要求用最少移动次数将所有金币移到所有银币的左边。编程任务对于给定的 n-1 枚金币和 n-1 枚银币的初始排列，设计一个分支限界法，计算满足要求的最少移动次数。数据输入第一行有一个正整数 T ，表示有 T 组测试数据。每组测试数据包括两行，第一行是一个整数 n ，第二行是 n-1 枚金币，n-1 枚银币和两个空方格的初始排列,字母 a 表示金币，字母 b 表示银币，字符.表示空方格。0 T 1002 n 10数据输出对于每组测试数据，输出一行一个整数，表示最少需要移动的次数；如果无解，请输出一行“No Solution”。输入文件示例 输出文件示例输入33abab.5abba.abab6a.babbababa输出No Solution34 三、Description （此题比较难，符合竞赛题目的难度）N gangsters are going to a restaurant. The i-th gangster comes at the time Ti and has the prosperity Pi. The door of the restaurant has K+1 states of openness expressed by the integers in the range 0, K. The state of openness can change by one in one unit of time; i.e. it either opens by one, closes by one or remains the same. At the initial moment of time the door is closed (state 0). The i-th gangster enters the restaurant only if the door is opened specially for him, i.e. when the state of openness coincides with his stoutness Si. If at the moment of time when the gangster comes to the restaurant the state of openness is not equal to his stoutness, then the gangster goes away and never returns. The restaurant works in the interval of time 0, T. The goal is to gather the gangsters with the maximal total prosperity in the restaurant by opening and closing the door appropriately. Input The first line of the input file contains the values N, K, and T, separated by spaces. (1 = N = 100 ,1 = K = 100 ,0 = T = 30000 ) The second line of the input file contains the moments of time when gangsters come to the restaurant T1, T2, ., TN, separated by spaces. ( 0 = Ti = T for i = 1, 2, ., N) The third line of the input file contains the values of the prosperity of gangsters P1, P2, ., PN, separated by spaces. ( 0 = Pi = 300 for i = 1, 2, ., N) The forth line of the input file contains the values of the stoutness of gangsters S1, S2, ., SN, separated by spaces. ( 1 = Si = K for i = 1, 2, ., N) All values in the input file are integers. Output Print to the output file the single integer ?the maximal sum of prosperity of gangsters in the restaurant. In case when no gangster can enter the