luogu3628 特别行动队 (斜率优化dp)

推出来式子以后斜率优化水过去就完事了

 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<vector>
 #include<queue>
 #include<cmath>
 #define inf 0x3f3f3f3f
 #define LL long long int
 using namespace std;
 const int maxn=;

 inline LL rd(){
     LL x=;char c=getchar();int neg=;
     while(c<''||c>''){if(c=='-') neg=-;c=getchar();}
     while(c>=''&&c<='') x=x*+c-'',c=getchar();
     return x*neg;
 }

 int N;
 LL f[maxn],x[maxn],s[maxn],A,B,C;
 int q[maxn],head,tail;

 inline LL pw2(LL x){return x*x;}

 inline bool judge1(int j1,int j2,int i){
     return (f[j1]+A*pw2(s[j1])-f[j2]-A*pw2(s[j2]))>*A*s[i]*(s[j1]-s[j2]);
 }
 inline bool judge2(int j1,int j2,int j3,int i){
     return (f[j1]+A*pw2(s[j1])-f[j2]-A*pw2(s[j2]))*(s[j2]-s[j3])<
            (f[j2]+A*pw2(s[j2])-f[j3]-A*pw2(s[j3]))*(s[j1]-s[j2]);
 }

 int main(){
     //freopen("3628.in","r",stdin);
     int i,j,k;
     N=rd();A=rd();B=rd();C=rd();
     for(i=;i<=N;i++) x[i]=rd(),s[i]=s[i-]+x[i];
     LL ans=;
     tail=head=;q[]=;
     for(i=;i<=N;i++){
         while(head<tail&&!judge1(q[head],q[head+],i)) head++;
         f[i]=f[q[head]]+A*pw2(s[i]-s[q[head]])+C;
         while(head<tail&&judge2(q[tail-],q[tail],i,i)) tail--;
         q[++tail]=i;
     }printf("%lld\n",f[N]+B*s[N]);
     return ;
 }