HDU 2191 多重背包问题

状态转移方程为

if (j < w[i])

dp(i, j) = dp(i - 1, j);

else

dp(i, j) = max(dp(i - 1, j - k * w[i]) + k * v[i])    (j - k * w[i] >= 0)

利用滚动数组计算，代码如下：

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#define MAX_N 1005
#define INF 0x3f3f3f

using namespace std;

typedef long long int ll;
int dp[MAX_N];

void ZeroOnePack(int weight, int value, int V)
{
    for (int i = V; i >= weight; i--)
        dp[i] = max(dp[i], dp[i - weight] + value);
}

void CompletePack(int weight, int value, int V)
{
    for (int i = weight; i <= V; i++)
        dp[i] = max(dp[i], dp[i - weight] + value);
}

int MultiplePack(int n, int* weight, int* value, int* num, int V)
{
    memset(dp, 0, sizeof(dp));
    for (int i = 1; i <= n; i++)
    {
        if (weight[i] * num[i] > V)
            CompletePack(weight[i], value[i], V);
        else
        {
            int k = 1;
            while (k < num[i])
            {
                ZeroOnePack(k * weight[i], k * value[i], V);
                num[i] -= k;
                k <<= 1;
            }
            ZeroOnePack(num[i] * weight[i], num[i] * value[i], V);
        }
    }
    return dp[V];
}

int main()
{
    //freopen("1.txt", "r", stdin);

    int V, n, T;
    int weight[MAX_N], value[MAX_N], num[MAX_N];
    cin >> T;
    while (T--)
    {
        cin >> V >> n;
        for (int i = 1; i <= n; i++)
            scanf("%d%d%d", &weight[i], &value[i], &num[i]);

        cout << MultiplePack(n, weight, value, num, V) << endl;
    }
    return 0;
}