推出来式子以后斜率优化水过去就完事了
1 #include<cstdio> 2 #include<cstring> 3 #include<algorithm> 4 #include<vector> 5 #include<queue> 6 #include<cmath> 7 #define inf 0x3f3f3f3f 8 #define LL long long int 9 using namespace std; 10 const int maxn=1000010; 11 12 inline LL rd(){ 13 LL x=0;char c=getchar();int neg=1; 14 while(c<'0'||c>'9'){if(c=='-') neg=-1;c=getchar();} 15 while(c>='0'&&c<='9') x=x*10+c-'0',c=getchar(); 16 return x*neg; 17 } 18 19 int N; 20 LL f[maxn],x[maxn],s[maxn],A,B,C; 21 int q[maxn],head,tail; 22 23 inline LL pw2(LL x){return x*x;} 24 25 inline bool judge1(int j1,int j2,int i){ 26 return (f[j1]+A*pw2(s[j1])-f[j2]-A*pw2(s[j2]))>2*A*s[i]*(s[j1]-s[j2]); 27 } 28 inline bool judge2(int j1,int j2,int j3,int i){ 29 return (f[j1]+A*pw2(s[j1])-f[j2]-A*pw2(s[j2]))*(s[j2]-s[j3])< 30 (f[j2]+A*pw2(s[j2])-f[j3]-A*pw2(s[j3]))*(s[j1]-s[j2]); 31 } 32 33 int main(){ 34 //freopen("3628.in","r",stdin); 35 int i,j,k; 36 N=rd();A=rd();B=rd();C=rd(); 37 for(i=1;i<=N;i++) x[i]=rd(),s[i]=s[i-1]+x[i]; 38 LL ans=0; 39 tail=head=1;q[1]=0; 40 for(i=1;i<=N;i++){ 41 while(head<tail&&!judge1(q[head],q[head+1],i)) head++; 42 f[i]=f[q[head]]+A*pw2(s[i]-s[q[head]])+C; 43 while(head<tail&&judge2(q[tail-1],q[tail],i,i)) tail--; 44 q[++tail]=i; 45 }printf("%lld ",f[N]+B*s[N]); 46 return 0; 47 }