DP单调队列--斜率优化P3195

Posted 2020-11-23 --hpy-7m

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

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

  1 #define ios ios_base::sync_with_stdio(0); cin.tie(0);
  2 #include <cstdio>//sprintf islower isupper
  3 #include <cstdlib>//malloc  exit strcat itoa system("cls")
  4 #include <iostream>//pair
  5 #include <fstream>//freopen("C:\Users\13606\Desktop\Input.txt","r",stdin);
  6 #include <bitset>
  7 //#include <map>
  8 //#include<unordered_map>
  9 #include <vector>
 10 #include <stack>
 11 #include <set>
 12 #include <string.h>//strstr substr strcat
 13 #include <string>
 14 #include <time.h>// srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
 15 #include <cmath>
 16 #include <deque>
 17 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
 18 #include <vector>//emplace_back
 19 //#include <math.h>
 20 #include <cassert>
 21 #include <iomanip>
 22 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
 23 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
 24 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
 25 //******************
 26 clock_t __START,__END;
 27 double __TOTALTIME;
 28 void _MS(){__START=clock();}
 29 void _ME(){__END=clock();__TOTALTIME=(double)(__END-__START)/CLOCKS_PER_SEC;cout<<"Time: "<<__TOTALTIME<<" s"<<endl;}
 30 //***********************
 31 #define rint register int
 32 #define fo(a,b,c) for(rint a=b;a<=c;++a)
 33 #define fr(a,b,c) for(rint a=b;a>=c;--a)
 34 #define mem(a,b) memset(a,b,sizeof(a))
 35 #define pr printf
 36 #define sc scanf
 37 #define ls rt<<1
 38 #define rs rt<<1|1
 39 typedef pair<int,int> PII;
 40 typedef vector<int> VI;
 41 typedef unsigned long long ull;
 42 typedef long long ll;
 43 typedef double db;
 44 const double E=2.718281828;
 45 const double PI=acos(-1.0);
 46 const ll INF=(1LL<<60);
 47 const int inf=(1<<30);
 48 const double ESP=1e-9;
 49 const int mod=(int)1e9+7;
 50 const int N=(int)1e6+10;
 51 
 52 int n,L;
 53 int a[N];
 54 db dp[N],sum[N];
 55 db A(int x)
 56 {
 57     return sum[x]+x;
 58 }
 59 db B(int x)
 60 {
 61     return sum[x]+x+L+1;
 62 }
 63 db X(int x)
 64 {
 65     return B(x);
 66 }
 67 db Y(int x)
 68 {
 69     return dp[x]+B(x)*B(x);
 70 }
 71 double slope(int a,int b)
 72 {
 73     return 1.0*(Y(a)-Y(b))/(1.0*(X(a)-X(b)));
 74 }
 75 
 76 class mydeque{
 77 public:
 78     int len=1000000;
 79     int p[N];
 80     int l,r,tot;
 81     void init()
 82     {
 83         l=1;r=1;
 84         tot=1;
 85     }
 86     int size()
 87     {
 88         return tot;
 89     }
 90     int pos(int x)
 91     {
 92         return (x+len)%len;
 93     }
 94     int f()
 95     {
 96         return p[l];
 97     }
 98     int b()
 99     {
100         return p[r];
101     }
102     void pf(int x)
103     {
104         tot++;
105         l=pos(l-1);
106         p[l]=x;
107     }
108     void pb(int x)
109     {
110         tot++;
111         r=pos(r+1);
112         p[r]=x;
113     }
114     void popf()
115     {
116         p[l]=0;
117         l=pos(l+1);
118         tot--;
119     }
120     void popb()
121     {
122         p[r]=0;
123         r=pos(r-1);
124         tot--;
125     }
126 }q;
127 
128 int main()
129 {
130     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
131     sc("%d%d",&n,&L);
132     for(int i=1;i<=n;++i)sc("%d",&a[i]),sum[i]=a[i]+sum[i-1];
133     for(int i=1;i<=n;++i)
134     {
135         while(q.l<q.r&&slope(q.f(),q.p[q.pos(q.l+1)])<2.0*A(i))q.popf();
136         dp[i]=dp[q.f()]+(A(i)-B(q.f()))*(A(i)-B(q.f()));
137         while(q.l<q.r&&slope(q.p[q.pos(q.r-1)],q.b())>slope(q.p[q.pos(q.r-1)],i))q.popb();
138         q.pb(i);
139     }
140     pr("%lld
",(ll)dp[n]);
141     return 0;
142 }
143 
144 /**************************************************************************************/