DP单调队列--斜率优化P3195

题意：https://www.luogu.com.cn/problem/P3195

思路：https://www.luogu.com.cn/problemnew/solution/P3195

 #define IOS ios_base::sync_with_stdio(0); cin.tie(0);
 #include <cstdio>//sprintf islower isupper
 #include <cstdlib>//malloc  exit strcat itoa system("cls")
 #include <iostream>//pair
 #include <fstream>//freopen("C:\\Users\\13606\\Desktop\\Input.txt","r",stdin);
 #include <bitset>
 //#include <map>
 //#include<unordered_map>
 #include <vector>
 #include <stack>
 #include <set>
 #include <string.h>//strstr substr strcat
 #include <string>
 #include <time.h>// srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
 #include <cmath>
 #include <deque>
 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
 #include <vector>//emplace_back
 //#include <math.h>
 #include <cassert>
 #include <iomanip>
 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
 //******************
 clock_t __START,__END;
 double __TOTALTIME;
 void _MS(){__START=clock();}
 void _ME(){__END=clock();__TOTALTIME=(double)(__END-__START)/CLOCKS_PER_SEC;cout<<"Time: "<<__TOTALTIME<<" s"<<endl;}
 //***********************
 #define rint register int
 #define fo(a,b,c) for(rint a=b;a<=c;++a)
 #define fr(a,b,c) for(rint a=b;a>=c;--a)
 #define mem(a,b) memset(a,b,sizeof(a))
 #define pr printf
 #define sc scanf
 #define ls rt<<1
 #define rs rt<<1|1
 typedef pair<int,int> PII;
 typedef vector<int> VI;
 typedef unsigned long long ull;
 typedef long long ll;
 typedef double db;
 const double E=2.718281828;
 const double PI=acos(-1.0);
 const ll INF=(1LL<<);
 const int inf=(<<);
 const double ESP=1e-;
 const int mod=(int)1e9+;
 const int N=(int)1e6+;

 int n,L;
 int a[N];
 db dp[N],sum[N];
 db A(int x)
 {
     return sum[x]+x;
 }
 db B(int x)
 {
     return sum[x]+x+L+;
 }
 db X(int x)
 {
     return B(x);
 }
 db Y(int x)
 {
     return dp[x]+B(x)*B(x);
 }
 double slope(int a,int b)
 {
     return 1.0*(Y(a)-Y(b))/(1.0*(X(a)-X(b)));
 }

 class mydeque{
 public:
     int len=;
     int p[N];
     int l,r,tot;
     void init()
     {
         l=;r=;
         tot=;
     }
     int size()
     {
         return tot;
     }
     int pos(int x)
     {
         return (x+len)%len;
     }
     int f()
     {
         return p[l];
     }
     int b()
     {
         return p[r];
     }
     void pf(int x)
     {
         tot++;
         l=pos(l-);
         p[l]=x;
     }
     void pb(int x)
     {
         tot++;
         r=pos(r+);
         p[r]=x;
     }
     void popf()
     {
         p[l]=;
         l=pos(l+);
         tot--;
     }
     void popb()
     {
         p[r]=;
         r=pos(r-);
         tot--;
     }
 }q;

 int main()
 {
     q.init();//初始化有dp[0](l=r=1而不是l=1,r=0,tot=0),因为要用到
     sc("%d%d",&n,&L);
     for(int i=;i<=n;++i)sc("%d",&a[i]),sum[i]=a[i]+sum[i-];
     for(int i=;i<=n;++i)
     {
         while(q.l<q.r&&slope(q.f(),q.p[q.pos(q.l+)])<2.0*A(i))q.popf();
         dp[i]=dp[q.f()]+(A(i)-B(q.f()))*(A(i)-B(q.f()));
         while(q.l<q.r&&slope(q.p[q.pos(q.r-)],q.b())>slope(q.p[q.pos(q.r-)],i))q.popb();
         q.pb(i);
     }
     pr("%lld\n",(ll)dp[n]);
     return ;
 }

 /**************************************************************************************/