bzoj1010: [HNOI2008]玩具装箱toy

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
const int maxn = 50000 + 10;

int n;
long long L;
int c[maxn],q[maxn];
long long s[maxn],f[maxn];

double slop(int j,int k) {
    return (f[k]-f[j]+(s[k]+L)*(s[k]+L)-(s[j]+L)*(s[j]+L))/(2.0*(s[k]-s[j]));
}

void dp() {
    int l=0,r=0;
    q[r++]=0;
    for(int i=1;i<=n;i++) {
        while(l<r-1 && slop(q[l],q[l+1]) <= s[i]) l++;
        int t=q[l];
        f[i]=f[t]+(s[i]-s[t]-L)*(s[i]-s[t]-L);
        while(l<r-1 && slop(q[r-1],i) < slop(q[r-2],q[r-1])) r--;
        q[r++]=i;
    }
}

int main() {
    scanf("%d%lld\n",&n,&L);
    L++;
    for(int i=1;i<=n;i++) {
        scanf("%d",&c[i]);
        s[i]=(long long)s[i-1]+c[i]+1;
    }
    dp();
    printf("%lld\n",f[n]);
    return 0;
}