BZOJ 1010: [HNOI2008]玩具装箱toy | 单调队列优化DP

原题：

http://www.lydsy.com/JudgeOnline/problem.php?id=1010

---

题解：

#include<cstdio>
#include<algorithm>
#include<cstring>
#define N 50005
typedef long long ll;
using namespace std;
ll n,c[N],a[N],b[N],sum[N],f[N],L,q[N],l,r;
ll sq(ll x){return x*x;}
double getD(ll j,ll k)
{
    return 1.0*(f[j]+sq(b[j])-f[k]-sq(b[k]))/(2*(b[j]-b[k]));
}
int main()
{
    scanf("%lld%lld",&n,&L);
    for (ll i=1;i<=n;i++)    
    {
        scanf("%lld",&c[i]);
        sum[i]=sum[i-1]+c[i];
        a[i]=sum[i]+i-1-L;
        b[i]=sum[i]+i;
    }
    for (ll i=1;i<=n;i++)
    {
        while (l<r && getD(q[l],q[l+1])<(double)a[i]) l++;
        ll t=q[l];
        f[i]=f[t]+sq(b[t])-2*a[i]*b[t]+sq(a[i]);
        while (l<r && getD(q[r],i)<getD(q[r-1],q[r])) r--;
        q[++r]=i;
    }
    printf("%lld\n",f[n]);
    return 0;
}