【bzoj】1010: [HNOI2008]玩具装箱toy （斜率优化，模板题）

 https://www.cnblogs.com/Paul-Guderian/p/7259491.html#4009803 看链接

#include <bits/stdc++.h>
#define mem(x,v) memset(x,v,sizeof(x)) 
#define rep(i,a,b)  for (int i = a; i <= b; i++)
#define per(i,a,b)  for (int i = a; i >= b; i--)
using namespace std;
typedef long long LL;
const double EPS = 1e-10;
const int INF = 0x3f3f3f3f;
const int N = 1e5+10;
int n,m,Q[N];
LL a[N],sum[N],f[N];
double X(LL i){return sum[i];}
double Y(LL i){return f[i] + (sum[i] + m)*(sum[i] + m); }
double Rate(LL i, LL k){return (Y(k) - Y(i))/(X(k) - X(i)); }
int main(){
	scanf("%d%d",&n,&m); m++;
	rep(i,1,n) {scanf("%lld",&sum[i]);sum[i]+= sum[i-1]; }
	rep(i,1,n) sum[i] += i;
	int tail = 1,head = 1;	Q[1] = 0;
	rep(i,1,n){
		while(tail > head && Rate(Q[head],Q[head+1]) < 2*sum[i]) head++;
		int j = Q[head]; f[i] = f[j] + (sum[i] - sum[j] - m)*(sum[i]-sum[j]-m);
		while(tail > head && Rate(Q[tail - 1],Q[tail])>Rate(Q[tail],i)) tail--;
			Q[++tail] = i;
	}

    printf("%lld\n",f[n]);
return 0;
}