斜率优化,交叉相乘
#include<cstdio>
#include<algorithm>
using namespace std;
int t[1000005],f[1000005];
long long F[1000005],G[1000005],Sum[1000005],C[1000005];
struct node{
long long k,b;
}stack[1000005];
double check(node a,node b){
return ((double)a.b-b.b)/(b.k-a.k);
}
int main(){
int n,S;
scanf("%d%d",&n,&S);
for (int i=1; i<=n; i++){
scanf("%d%d",&t[i],&f[i]);
Sum[i]=Sum[i-1]+t[i];
C[i]=C[i-1]+f[i];
}
int top=0;
for (int i=0; i<=n; i++){
int L=1,R=top;
while (L<R){
int mid=(L+R)>>1;
double l,r;
if (mid==1) l=-1ll<<60;
else l=check(stack[mid-1],stack[mid]);
if (mid==top) r=1ll<<60;
else r=check(stack[mid+1],stack[mid]);
if (Sum[i]>=l && Sum[i]<=r){
L=mid;
break;
}
else if (Sum[i]<l) R=mid-1;
else L=mid+1;
}
F[i]=stack[L].k*Sum[i]+stack[L].b;
F[i]+=Sum[i]*C[n];
G[i]=F[i]+(-Sum[i]+S)*(C[n]-C[i]);
node line=(node){-C[i],G[i]};
while (top>=2 &&(stack[top].b-stack[top-1].b)*(line.k-stack[top].k)<=
(line.b-stack[top].b)*(stack[top].k-stack[top-1].k))top--;
stack[++top]=line;
}
printf("%lld
",F[n]);
return 0;
}