BZOJ 1096: [ZJOI2007]仓库建设 动态规划 + 斜率优化

 

#include<bits/stdc++.h>
#define setIO(s) freopen(s".in","r",stdin)
#define maxn 1000004
#define x(i) (a[i])
#define y(i) (f[i]+b[i])
#define ll long long
using namespace std;
ll dis[maxn],p[maxn],cost[maxn],a[maxn],b[maxn],f[maxn];
int q[maxn], tail, head;
double slope(int i,int j)
{
    return (double)(1.0*y(i)-y(j))/(double)(1.0*x(i)-x(j));
}
int main()
{
    // setIO("input");
    int n,i,j;
    scanf("%d",&n);
    for(i=1;i<=n;++i)
    {
        scanf("%lld%lld%lld",&dis[i],&p[i],&cost[i]);
        a[i]=a[i-1]+p[i];
        b[i]=b[i-1]+p[i]*dis[i];
    }
    head=tail=0;
    for(i=1;i<=n;++i)
    {
        while(head<tail && slope(q[head], q[head+1]) < dis[i]) ++head;
        f[i]=f[q[head]] + dis[i]*(a[i]-a[q[head]]) - (b[i]-b[q[head]]) + cost[i];
        while(head<tail && slope(q[tail], i) < slope(q[tail-1], i)) --tail;
        q[++tail]=i;
    }
    printf("%lld\n",f[n]);
    return 0;
}