hdu2844 多重背包+二进制优化

最新推荐文章于 2020-08-10 21:44:14 发布

原创最新推荐文章于 2020-08-10 21:44:14 发布 · 385 阅读

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本文探讨了多重背包问题的两种解决方案：直接使用多重背包方法导致超时的问题，以及通过二进制优化来提高效率的方法。文章提供了详细的代码实现，并对比了优化前后的不同。

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直接用多重背包，超时

#include<iostream>
#include<algorithm>
#define INF 1000
using namespace std;
int main()
{
	int n,m;
	while (cin >> n >> m, m,n)
	{
		int *c= new int[n];
		int *w= new int[n];
		int *num = new int[n];
		for (int i = 0; i < n; i++)
			cin >> c[i], w[i] = c[i];
		for (int i = 0; i < n; i++)
			cin >> num[i];
		int sum = 0;
		for (int i = 0; i < n; i++)
			sum += c[i] * num[i];
		int *dp = new int[m+1];//多开一个单位长度
		for (int i = 0; i <= m; i++)
			dp[i] = -INF;
		dp[0] = 0;		
		for (int i = 0; i <n; i++)
			for (int k = 1; k <=num[i]; k++)
				for (int j = m; j >= c[i]; j--)
					dp[j] = max(dp[j], dp[j - w[i]] + c[i] );
		int cnt = 0;
		for (int i = 1; i <=m; i++)
			if (dp[i] == i)
				cnt++;
		cout << cnt << endl;			
	}
	system("pause");
}

进行二进制优化

#include<iostream>
#include<algorithm>
#define MAX 1000000
using namespace std;
int c[MAX], w[MAX],num[MAX];
int dp[MAX];
int main()
{
	int n, m;
	while (cin >> n >> m, m + n)
	{		
		for (int i = 0; i < n; i++)
			cin >> c[i], w[i] = c[i];
		for (int i = 0; i < n; i++)
			cin >> num[i];
		for (int i = 0; i <= m; i++)
			dp[i] = 0;
		for (int i = 0; i < n; i++)
		{
			for (int k = 1; k <= num[i]; k = 2 * k)
			{
				num[i] -= k;
				for (int j = m; j >= w[i] * k; j--)
					dp[j] = max(dp[j], dp[j - k*w[i]] + k*c[i]);
			}
			if (num[i])
			{
				for (int j = m; j >= w[i] * num[i]; j--)
					dp[j] = max(dp[j], dp[j - w[i] * num[i]] + c[i] * num[i]);
			}
		}
		int cnt = 0;
		for (int i = 1; i <= m; i++)
			if (dp[i] == i)
				cnt++;
		cout << cnt << endl;
	}
}