单调队列优化DP，多重背包

Posted 2020-08-10 youmi

 单调队列优化DP：http://www.cnblogs.com/ka200812/archive/2012/07/11/2585950.html

单调队列优化多重背包：http://blog.csdn.net/flyinghearts/article/details/5898183

传送门：hdu 3401 Trade

/**************************************************************
    Problem:hdu 3401 Trade
    User: youmi
    Language: C++
    Result: Accepted
    Time:171MS
    Memory:17368K
****************************************************************/
//#pragma comment(linker, "/STACK:1024000000,1024000000")
//#include<bits/stdc++.h>
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <map>
#include <stack>
#include <set>
#include <sstream>
#include <cmath>
#include <queue>
#include <deque>
#include <string>
#include <vector>
#define zeros(a) memset(a,0,sizeof(a))
#define ones(a) memset(a,-1,sizeof(a))
#define sc(a) scanf("%d",&a)
#define sc2(a,b) scanf("%d%d",&a,&b)
#define sc3(a,b,c) scanf("%d%d%d",&a,&b,&c)
#define scs(a) scanf("%s",a)
#define sclld(a) scanf("%I64d",&a)
#define pt(a) printf("%d\\n",a)
#define ptlld(a) printf("%I64d\\n",a)
#define rep(i,from,to) for(int i=from;i<=to;i++)
#define irep(i,to,from) for(int i=to;i>=from;i--)
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
#define lson (step<<1)
#define rson (lson+1)
#define eps 1e-6
#define oo 1e9
#define TEST cout<<"*************************"<<endl
const double pi=4*atan(1.0);

using namespace std;
typedef long long ll;
template <class T> inline void read(T &n)
{
    char c; int flag = 1;
    for (c = getchar(); !(c >= \'0\' && c <= \'9\' || c == \'-\'); c = getchar()); if (c == \'-\') flag = -1, n = 0; else n = c - \'0\';
    for (c = getchar(); c >= \'0\' && c <= \'9\'; c = getchar()) n = n * 10 + c - \'0\'; n *= flag;
}
ll Pow(ll base, ll n, ll mo)
{
    ll res=1;
    while(n)
    {
        if(n&1)
            res=res*base%mo;
        n>>=1;
        base=base*base%mo;
    }
    return res;
}
//***************************

int T,P,w;
const int maxn=2000+10;
const ll mod=1000000007;
int dp[maxn][maxn];
int ap[maxn],bp[maxn];
int as[maxn],bs[maxn];
struct node
{
    int val,p;
};
node q[maxn];
int head,tail;
int main()
{
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    #endif
    int T_T;
    scanf("%d",&T_T);
    for(int kase=1;kase<=T_T;kase++)
    {
        sc3(T,P,w);
        rep(i,1,T)
        {
            sc2(ap[i],bp[i]);//buy,sell,money
            sc2(as[i],bs[i]);//buy,sell,number
        }
        rep(i,0,T)
            rep(j,0,P)
                dp[i][j]=-oo;
        dp[0][0]=0;
        rep(i,1,T)
        {
            if(i<=w+1)
            {
                rep(j,0,min(P,as[i]))
                    dp[i][j]=-ap[i]*j;
            }
            rep(j,0,P)
                dp[i][j]=max(dp[i][j],dp[i-1][j]);
            if(i<=w+1)
                continue;
            head=tail=0;
            for(int j=P;j>=0;j--)
            {
                int temp=dp[i-w-1][j]+bp[i]*j;
                while(tail>head&&temp>q[tail-1].val) tail--;
                q[tail].val=temp,q[tail].p=j,tail++;
                while(tail>head&&q[head].p-bs[i]>j)  head++;
                temp=q[head].val;
                dp[i][j]=max(dp[i][j],temp-bp[i]*j);
            }
            tail=head=0;
            rep(j,0,P)
            {
                int temp=dp[i-w-1][j]+ap[i]*j;
                while(tail>head&&temp>q[tail-1].val)  tail--;
                q[tail].val=temp,q[tail].p=j,tail++;
                while(tail>head&&q[head].p+as[i]<j) head++;
                temp=q[head].val;
                dp[i][j]=max(dp[i][j],temp-ap[i]*j);
            }
        }
        int ans=0;
        rep(i,0,P)
            ans=max(ans,dp[T][i]);
        pt(ans);
    }
    return 0;
}

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