P1776 宝物筛选_NOI导刊2010提高（02）

https://www.luogu.org/problemnew/show/P1776

模版的多重背包,但朴素肯定不行,这里采用单调队列优化

朴素方程式

 变形

(第一维压掉)

 如此,便可以用分mod用单调队列优化啦,代码如下

#include <bits/stdc++.h>
#define up(i,l,r) for(register int i = (l); i <= (r); ++i)
#define dn(i,l,r) for(register int i = (l); i >= (r); --i)
#define ll long long
#define re register
#define _N putchar('
')
using namespace std;

template <typename T> void in(T &x) {
    x = 0; T f = 1; char ch = getchar();
    while(!isdigit(ch)) {if(ch == '-') f = -1; ch = getchar();}
    while( isdigit(ch)) {x = 10 * x + ch - 48; ch = getchar();}
    x *= f;
}

template <typename T> void out(T x) {
    if(x < 0) x = -x , putchar('-');
    if(x > 9) out(x/10);
    putchar(x%10 + 48);
}
//---------------------------------------------------------------

const int N = 40007;

int n,max_w,tmp,ans,f[N],num[N];

struct {
    int pos,v;
}que[N];

int main() {
    freopen("0.in","r",stdin);
    in(n); in(max_w);int v,w,cnt;
    for(int i = 1; i <= n; ++i) {
        in(v); in(w); in(cnt);
        if(!w) {
            tmp += cnt * v; continue;
        }
        int a = min(cnt,max_w/w);
        for(int mod  = 0; mod < w; ++mod) {
            int head = 0,tail = 0,c = (max_w-mod)/w;
            for(int k = 0; k <= c; ++k) {
                int add = f[k*w+mod] - k*v;
                while(head < tail && add >= que[tail-1].v) --tail;
                ++tail; que[tail-1].v = add,que[tail-1].pos = k;
                
                while(head < tail && que[head].pos + a < k) ++head;
                
                f[k*w+mod] = max(f[k*w+mod],que[head].v + k*v);//
                ans = max(ans,f[k*w+mod]);
            }
        }
    }
    out(ans+tmp);
    return 0;
}