实现背包问题

package problem

1．　　问题描述

假设有一个能装入总体积为T的背包和n件体积分别为w1 , w2 , … , wn 的物品，能否从n件物品中挑选若干件恰好装满背包，即使w1 +w2 + … + wn=T，要求找出所有满足上述条件的解。例如：当T=10，各件物品的体积{1，8，4，3，5，2}时，可找到下列4组解：　　　　 （1，4，3，2）、（1，4，5）、（8，2）、（3，5，2）。

2．　　基本要求

读入T、n、w1 , w2 , … , wn

3．提示：

可利用递归方法：若选中w1 则问题变成在w2 , … , wn 中挑选若干件使得其重量之和为T- w1 ，若不选中w1，则问题变成在w2 , … , wn 中挑选若干件使得其重量之和为T 。依次类推。

也可利用回溯法的设计思想来解决背包问题。首先将物品排成一列，然后顺序选取物品装入背包，假设已选取了前i 件物品之后背包还没有装满，则继续选取第i+1件物品，若该件物品“太大”不能装入，则弃之而继续选取下一件，直至背包装满为止。但如果在剩余的物品中找不到合适的物品以填满背包，则说明“刚刚”装入背包的那件物品“不合适”，应将它取出“弃之一边”，继续再从“它之后”的物品中选取，如此重复，，直至求得满足条件的解，或者无解。



注：没压缩密码-knapsack problem achieve a package problem. Problem descr iption one would assume that the total volume of loaded backpack and T n size pieces of w1, w2, ..., wn items Can n items from the selected pieces were just filled with backpacks, even w1 w2 ... wn = T, asked to identify all of the above conditions are met solution. For example : when T = 10, the volume of items (1,8,4,3,5,2), may find the following four solutions : (1,4,3,2), (1,4,5), (8,2), (3,5,2). 2. Basic requirements read T, n, w1, w2, ..., wn 3. Tip : Recursive methods can be used : If the problem were selected w1 into the w2, ..., wn selected several pieces make its weight and as a T-w1, if selected w1, w2 issue into the .... wn selected several pieces make its weight and as T. Renumbered accordingly. Retrospective can also u