hdu 3842 Machine Works(cdq分治维护凸壳)

题目链接：hdu 3842 Machine Works

详细题解： HDU 3842 Machine Works cdq分治 斜率优化

细节比较多，好好体会一下。

在维护斜率的时候要考虑x1与x2是否相等，这里要处理一下。

#include<bits/stdc++.h>
#define F(i,a,b) for(int i=a;i<=b;i++)
using namespace std;
typedef long long ll;
typedef pair<int,ll>P;

const int N=1e5+7;
int n,c,d,cas;
ll dp[N];
struct node{
    int D,P,R,G;
    bool operator < (const node &b)const{return D<b.D;}
}a[N];
P A[N],Q[N];

ll h(int j){return dp[j]-a[j].P-(ll)(a[j].D+1)*a[j].G+a[j].R;}
inline void up(ll &a,ll b){if(a<b)a=b;}

int check(P a,P b,P c)
{
    ll y1=b.second-a.second,y2=c.second-b.second;
    ll x1=b.first-a.first,x2=c.first-b.first;
    return (double)x1*y2>=(double)x2*y1;
}

void cdq(int l=0,int r=n)
{
    if(l==r)return;
    int mid=l+r>>1;
    cdq(l,mid);
    int head=1,tail=0,ed=0;
    F(i,l,mid)if(dp[i]>=a[i].P)A[++ed]=P(a[i].G,h(i));
    sort(A+1,A+1+ed);
    F(i,1,ed)
    {
        while(head<tail&&check(Q[tail-1],Q[tail],A[i]))tail--;
        Q[++tail]=A[i];    
    }
    F(i,mid+1,r)
    {
        while(head<tail&&Q[head+1].second-Q[head].second>=-(ll)a[i].D*(Q[head+1].first-Q[head].first))head++;
        up(dp[i],(ll)Q[head].first*a[i].D+Q[head].second);
    }
    
    cdq(mid+1,r);
}

int main()
{
    while(scanf("%d%d%d",&n,&c,&d),n+c+d)
    {
        F(i,1,n)scanf("%d%d%d%d",&a[i].D,&a[i].P,&a[i].R,&a[i].G);
        sort(a+1,a+1+n);
        a[++n].D=d+1,a[n].G=a[n].P=a[n].R=0;
        F(i,0,n)dp[i]=c;
        cdq();
        printf("Case %d: %lld
",++cas,dp[n]);
    }
    return 0;
}