斜率优化n^2的DP
1 #include<cstdio> 2 #include<algorithm> 3 using namespace std; 4 int yp() 5 { 6 int x=0,f=0;char ch=getchar(); 7 while(ch<'0'||ch>'9'){if(ch=='-')f=1;ch=getchar();} 8 while(ch>='0'&&ch<='9')x*=10,x+=ch-'0',ch=getchar(); 9 return !f?x:-x; 10 } 11 int n,l=1,r,q[1000005]; 12 long long a[1000005],b[1000005],tot,ans,h[1000005],sum[1000005]; 13 double js(int a,int b) 14 { 15 return (1.*(h[b]-h[a]))/(1.*(a-b)); 16 } 17 int main() 18 { 19 n=yp(); 20 for(int i=1;i<=n;i++)a[i]=yp(); 21 for(int i=1;i<=n;i++)b[i]=yp(),sum[i]=sum[i-1]+b[i]; 22 for(int i=1;i<n;i++)tot+=b[i]*(n-i); 23 tot+=a[n],q[++r]=n; 24 for(int i=n-1;i;i--) 25 { 26 while(l<r&&js(q[l],q[l+1])>sum[i])l++; 27 int j=q[l]; 28 h[i]=h[j]+sum[i]*(j-i)-a[i]; 29 ans=max(ans,h[i]); 30 while(l<r&&js(q[r],i)>js(q[r-1],q[r]))r--; 31 q[++r]=i; 32 } 33 printf("%lld",tot-ans); 34 return 0; 35 }