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

     cdq(mid+,r);
 }

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