牛客练习赛43D

转自https://blog.youkuaiyun.com/u013534123/article/details/87560151

#include <bits/stdc++.h>
#define INF 1e18
#define fi first
#define se second
#define LL long long
#define sc(x) scanf("%d",&x)
#define scc(x,y) scanf("%d%d",&x,&y)
#define sccc(x,y,z) scanf("%d%d%d",&x,&y,&z)
using namespace std;
 
const int N = 200010;
 
LL s[N],f[N],w[N];
int a[N],q[N],n;
 
inline LL Y(int x)
{
    return w[x];
}
 
inline LL X(int x)
{
    return x;
}
 
inline bool judge(int j,int k,int i)
{
    return Y(j)-Y(k)>=(X(j)-X(k))*s[i];
}
 
bool maintain(int i,int j,int k)
{
	return (Y(k)-Y(i))*(X(i)-X(j))>(Y(i)-Y(j))*(X(k)-X(i));
}
 
int main()
{
    sc(n);
    for(int i=1;i<=n;i++)
    {
        sc(a[i]);
        s[i]=s[i-1]+a[i];
        f[i]=f[i-1]+(LL)i*a[i];
        w[i]=(LL)i*s[i]-f[i];
    }
    LL ans=-1e18;
    int h=0,t=1;
    for(int i=1;i<=n;i++)
    {
        while (h<t&&judge(q[h+1],q[h],i)) h++;
        while (h>0&&judge(q[h-1],q[h],i)) h--;
        ans=max(ans,f[i]-q[h]*s[i]+w[q[h]]);
        while (t>1&&maintain(q[t],q[t-1],i)) t--;
        q[++t]=i;
    }
    printf("%lld\n",ans);
    return 0;
}