HDU 1059 Dividing(多重背包+二进制优化)_push_back0_新浪博客

HDU 1059 Dividing(多重背包+二进制优化)_push_back0_新浪博客

Problem Description

Marsha and Bill own a collection of marbles. They want to split the collection among themselves so that both receive an equal share of the marbles. This would be easy if all the marbles had the same value, because then they could just split the collection in half. But unfortunately, some of the marbles are larger, or more beautiful than others. So, Marsha and Bill start by assigning a value, a natural number between one and six, to each marble. Now they want to divide the marbles so that each of them gets the same total value.
Unfortunately, they realize that it might be impossible to divide the marbles in this way (even if the total value of all marbles is even). For example, if there are one marble of value 1, one of value 3 and two of value 4, then they cannot be split into sets of equal value. So, they ask you to write a program that checks whether there is a fair partition of the marbles.

 

Input

Each line in the input describes one collection of marbles to be divided. The lines consist of six non-negative integers n1, n2, ..., n6, where ni is the number of marbles of value i. So, the example from above would be described by the input-line ``1 0 1 2 0 0''. The maximum total number of marbles will be 20000.

The last line of the input file will be ``0 0 0 0 0 0''; do not process this line.

 

Output

For each colletcion, output ``Collection #k:'', where k is the number of the test case, and then either ``Can be divided.'' or ``Can't be divided.''.

Output a blank line after each test case.

 

Sample Input

1 0 1 2 0 0

1 0 0 0 1 1

0 0 0 0 0 0

 

Sample Output

Collection #1:

Can't be divided.

Collection #2:

Can be divided.

 

分析：多重背包问题，但是如果按照题目给的数据量用多重背包的三重for循环做的话必然会超时，所以要在多重背包的基础上做二进制优化，降低时间复杂度。

二进制优化：例如数13，二进制可以划分为0001 0010 0100 1000，即1 2 4 5（8）来表示，因为1->13之间的任意一个数都可以用这4个数求和得到，即2^0,2^1,2^2，....,2^N...且要满足最后一个数一定满足13-2^n>=0,此时n=3，所以得到5。这样4个数的总和就是13.

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