ZOJ-1149

多重背包，可转化为01背包，但是不能直接用最原始的物品拆分，因为总数太多了，一看这题TLE的数量就知道这么搞不行。。用二进制方式对基础物品进行组合，这样总物品数就大大减少了，具体可见背包九讲

#include<cstdio>
#include<vector>
#include<cstring>

using namespace std;

int main()
{
	int a[6], count = 0;
	vector<int> V;
	bool dp[100001];
	while (true)
	{
		bool flag = false;
		for (int i = 0; i < 6; i++)
		{
			scanf("%d", &a[i]);
			if (a[i])
				flag = true;
		}
		if (!flag)
			break;
		printf("Collection #%d:\n", ++count);
		V.clear();
		int total = 0;
		for (int i = 0; i < 6; i++)
			if (a[i])
			{
				total += a[i] * (i + 1);
				int now = 1, sum = 0;
				while (sum + now < a[i])
				{
					V.push_back(now * (i + 1));
					sum += now;
					now *= 2;
				}
				V.push_back((a[i] - sum) * (i + 1));
			}
		if (total % 2)
		{
			puts("Can't be divided.\n");
			continue;
		}
		memset(dp, 0, sizeof(dp));
		dp[0] = true;
		int max = total / 2;
		bool can = false;
		for (size_t i = 0; i < V.size() && !can; i++)
			for (int j = max; j >= V[i]; j--)
			{
				if (dp[j - V[i]])
					dp[j] = true;
				if (j == max && dp[j])
				{
					puts("Can be divided.\n");
					can = true;
					break;
				}
			}
		if (!can)
			puts("Can't be divided.\n");
	}
	return 0;
}