bzoj1010: [HNOI2008]玩具装箱toy

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define rep(i,n) for(int i=1;i<=n;i++)
#define clr(x,c) memset(x,c,sizeof(x))
#define ll long long
const int nmax=50005;
const int inf=0x7f7f7f7f;
ll read(){
	ll x=0;char c=getchar();bool f=true;
	while(!isdigit(c)){
		if(c==‘-‘) f=false;c=getchar();
	}
	while(isdigit(c)) x=x*10+c-‘0‘,c=getchar();
	return f?x:-x;
}
ll sum[nmax],f[nmax],dp[nmax],c,n;
int q[nmax];
void init(){
	n=read(),c=read();c++;
	rep(i,n) sum[i]=read(),sum[i]+=sum[i-1],f[i]=sum[i]+i;
}
ll S(int x,int y) {
	return 2*(f[x]-f[y]);
}
ll G(int x,int y){
	return dp[x]-dp[y]+(f[x]+c)*(f[x]+c)-(f[y]+c)*(f[y]+c);
}
void work(){
	int h=1,t=2;q[1]=0;
	rep(i,n){
		while(h<t-1&&G(q[h+1],q[h])<=S(q[h+1],q[h])*f[i]) h++;
		dp[i]=dp[q[h]]+(f[i]-f[q[h]]-c)*(f[i]-f[q[h]]-c);
		while(h<t-1&&G(i,q[t-1])*S(q[t-1],q[t-2])<=G(q[t-1],q[t-2])*S(i,q[t-1])) t--;
		q[t++]=i;
	}
	printf("%lld\n",dp[n]);
}
int main(){
	init();work();return 0;
}