ZJOI2007仓库建设

斜率优化

而且完美的双单调

#include<bits/stdc++.h>
using namespace std;
#define N 1000010
#define rep(a,b,c) for(register int (a)=(b);(a)<=(c);++(a))
#define RG register
#define IL inline
#define mst(a,b) memset((a),(b),sizeof((a)))
#define PN printf("\n")
#define PD(a) printf(" %d ",(a))
IL int isitdigit(char c){    return c<='9'&&c>='0';    }
IL int read()
{
    RG int s;RG char c;
    while(!isitdigit(c=getchar()));
    for(s=c-'0';isitdigit(c=getchar());s=(s<<1)+(s<<3)+c-'0');
    return s;
}
int n;
long long k[N],c[N],sum[N],sump[N];
long long f[N];
int head=1,tail=0;
struct point{
    long long  x,y;
    point(long long a=0,long long b=0):x(a),y(b){}
    IL const point operator - (const point another)
    const{    return (point){x-another.x,y-another.y};    }
}que[N];
IL long long det(const point a,const point b)
{    return a.x*b.y-a.y*b.x;    }
IL int judge(const point a,int b)
{    return a.y<b*a.x;    }
int main()
{
    //freopen("thu.in","r",stdin);
    scanf("%d",&n);
    rep(i,1,n) 
    {
        k[i]=read();
        RG int p=read();
        c[i]=read();
        sum[i]=sum[i-1]+p,sump[i]=sump[i-1]+k[i]*p;
    }
    rep(i,0,n)
    {
        while(head<tail&&judge(que[head+1]-que[head],k[i])) head++;
        f[i]=que[head].y-k[i]*que[head].x+c[i]+k[i]*sum[i]-sump[i];
        point now(sum[i],f[i]+sump[i]);
        while(head<tail&&det(que[tail]-que[tail-1],now-que[tail])<=0) tail --;
        que[++tail]=now;
    }
    printf("%lld",f[n]);
    return 0;
}