Lecture9Backtracking复件程序.ppt

例n＝6，M＝30和W(1：6)＝(5，10，12，13，15，18)。S=0,r=73 ,k=1 0,1,73 5,2,68 15,3,58 15,4,46 15,5,33 X(1)=1 X(2)=1 X(3)=0 X(4)=0 X(5)=1 5, 3,58 17,4,46 17, 5,33 (1,0,1,1) (1,1,0,0,1) 0,2,68 10,3,58 0,3,58 10,4,46 10,5,33 12,4,46 12,5,33 12,6,18 (0,0,1,0,0,1) ……. X(1)=0 0,4,46 * 1.回溯法要求问题P的状态能表达为n元组(x1，…，xn)，要求xi?Si，i=1,2,…n， Si是有穷集，对于给定关于n元组中的分量的一个约束集D，满足D 的全部约束条件的所有n元组为问题P的解。 2.从k=1开始构造k元组，如果k元组满足隐约束， 则 k=k+1，即向下扩展有哪些信誉好的足球投注网站；如果试探了X(k)的所有选择X(k-1)的值，则向上回溯。这种扩展回溯的有哪些信誉好的足球投注网站方法可以表示为状态空间树上的带约束条件的深度优先的有哪些信誉好的足球投注网站。 回溯法小结 * * * Example: 0/1 knapsack problem with n=3, W=[16,15,15], P=[45,25,25],M=30. At first, A is a “live node”, and also an “extension node”, then move deeper to B, B to D, D is a “dead node”( why?) A B D H I E J K C F L M G N O 1 1 1 0 0 1 0 0 0 1 1 0 1 0 * Move back to the nearest “live node” B, extend to E(E is a “live node” now, until J. J is a “dead node”, then returns to E, and extends to K (feasible solution with value 45). Move back to E. E could not be extended any more, and becomes a “dead node”. A B D H I E J K C F L M G N O 1 1 1 0 0 1 0 0 0 1 1 0 1 0 * Move back to B, and B becomes a “dead node”. Move back to A, and extends to C (“live node”), until F, L…. A B D H I E J K C F L M G N O 1 1 1 0 0 1 0 0 0 1 1 0 1 0 * Basic steps using Backtracking （1）Based on the problem given, define solution space of problem. （2）Define the structure of the solution space, and organize it in specific data structure( Tree). （3）search solution space by depth-first method, and use constraint function to avoid useless search. * n-queen problem n皇后问题:要在n*n的国际象棋棋盘中放n个皇后，使任意两个皇后都不能互相吃掉。规则：皇后能吃掉同一行、同一列、同一对角线的任意棋子。求所有的解。 How to solve it? systematically generate every possible arrangement test each one to see if it is a valid solution * n-queen problem if we were smart, we could greatly reduce the search space e.g., any board arrangement with a queen at (1,1) and (2,1) is invalid no point in looking at the other queens, so can eliminate 12 boards from consideration if a ch