BZOJ 1010 玩具装箱

Posted 2020-08-04 ziliuziliu

斜率优化。

事实上是选一个大于某个数的最小斜率。维护下凸壳。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define maxn 50050
using namespace std;
long long n,c,s[maxn],dp[maxn],q[maxn],l=1,r=0;
double slop(long long j,long long k)
{
    return (dp[k]-dp[j]+(s[k]+c)*(s[k]+c)-(s[j]+c)*(s[j]+c))/(2.0*(s[k]-s[j]));
}
void dps()
{
    q[++r]=0;
    for (long long i=1;i<=n;i++)
    {
        while ((l<r) && (slop(q[l],q[l+1])<s[i])) l++;
        long long t=q[l];
        dp[i]=dp[t]+(s[i]-s[t]-c)*(s[i]-s[t]-c);
        while ((l<r) && (slop(q[r-1],i)<slop(q[r-1],q[r]))) r--;
        q[++r]=i;
    }
}
int main()
{
    scanf("%lld%lld",&n,&c);c++;
    for (long long i=1;i<=n;i++) scanf("%lld",&s[i]);
    for (long long i=1;i<=n;i++) s[i]+=s[i-1];
    for (long long i=1;i<=n;i++) s[i]+=i;
    dps();
    printf("%lld\n",dp[n]);
    return 0;
}