动态规划（算法竞赛、蓝桥杯）--斜率优化DP打印文章

1、B站视频链接：E51【模板】斜率优化DP 打印文章_哔哩哔哩_bilibili

题目链接：Problem - 3507

#include <bits/stdc++.h> 
using namespace std;
typedef long long LL;
const int N=500010;
int n,m,q[N];
LL s[N],f[N];

double sl(int i,int j){
	return (double)(f[i]+s[i]*s[i]-f[j]-s[j]*s[j])
				/(s[i]==s[j]?1e-9:s[i]-s[j]);
}
int main(){
	while(~scanf("%d%d",&n,&m)){
		for(int i=1;i<=n;i++){
			scanf("%lld",&s[i]);
			s[i]+=s[i-1];
		}
	}
	int h=1,t=0;
	for(int i=1;i<=n;i++){
		while(h<t&&sl(i-1,q[t])<=sl(q[t],q[t-1]))t--;
		q[++t]=i-1;
		while(h<t&&sl(q[h+1],q[h])<=2*s[i])h++;
		int j=q[h];
		f[i]=f[j]+(s[i]-s[j])*(s[i]-s[j])+m;
	}
	printf("%lld\n",f[n]);
	return 0;
}