【动态规划】【斜率优化】CDOJ1689 分序列

#include<cstdio>
#include<deque>
using namespace std;
#define EPS 1e-8
typedef long long ll;
deque<int>q;
int n;
ll m,sum[500010],f[500010];
//借鉴了:http://www.cnblogs.com/ka200812/archive/2012/08/03/2621345.html 
ll getDP(int i,int j){
    return f[j]+m+(sum[i]-sum[j])*(sum[i]-sum[j]);
}
ll getUP(int j,int k){//yj-yk，即斜率的分子部分
    return (f[j]+sum[j]*sum[j])-(f[k]+sum[k]*sum[k]);
}
ll getDOWN(int j,int k){//xj-xk，即斜率的分母部分
    return 2ll*(sum[j]-sum[k]);
}
int main(){
	freopen("k.in","r",stdin);
	while(scanf("%d%lld",&n,&m)!=EOF){
		for(int i=1;i<=n;++i){
			scanf("%lld",&sum[i]);
		}
		for(int i=2;i<=n;++i){
			sum[i]+=sum[i-1];
		}
		q.clear();
		q.push_back(0);
		for(int i=1;i<=n;++i){
			while(q.size()>1 && getUP(q[1],q[0])<=sum[i]*getDOWN(q[1],q[0])){
				q.pop_front();
			}
			f[i]=getDP(i,q.front());
			while(q.size()>1 && getUP(i,q.back())*getDOWN(q.back(),q[q.size()-2])<=getUP(q.back(),q[q.size()-2])*getDOWN(i,q.back())){
				q.pop_back();
			}
			q.push_back(i);
		}
		printf("%lld\n",f[n]);
	}
	return 0;
}