【模板】多重背包(Bounded Knapsack) 题解

思路分析

按题目要求使用对应数据结构与算法模拟/递推求解，注意数据范围边界与时间复杂度。

参考代码

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, m;
    if (!(cin >> n >> m)) return 0;
    vector<long long> dp(m + 1, 0);
    for (int i = 0; i < n; ++i) {
        long long a, v, w;
        cin >> a >> v >> w;
        if (w == 0) {
            for (int j = 0; j <= m; ++j) dp[j] += a * v;
            continue;
        }
        long long cnt = min(a, (long long)(m / w));
        for (long long k = 1; cnt > 0; k <<= 1) {
            long long take = min(k, cnt);
            cnt -= take;
            long long weight = take * w;
            long long val = take * v;
            for (int j = m; j >= weight; --j) {
                dp[j] = max(dp[j], dp[j - weight] + val);
            }
        }
    }
    cout << dp[m] << "\n";
    return 0;
}