CodeForces 674C Levels and Regions

Posted 2021-01-23 maoruimas

#include<bits/stdc++.h>
using namespace std;
const int maxn=2e5+5;
int N,K,head,tair;
int q[maxn];
double S[maxn],A[maxn],B[maxn],dp[maxn][55];
double calc(int i,int j,int k){return dp[k][j-1]+A[i]-A[k]-S[k]*(B[i]-B[k]);}
double x(int k){return S[k];}
double y(int k,int j){return dp[k][j-1]-A[k]+S[k]*B[k];}
bool judge(int a,int b,int c,int j){return (x(a)-x(c))*(y(a,j)-y(b,j))>=(y(a,j)-y(c,j))*(x(a)-x(b));}
int main()
{
    while(~scanf("%d%d",&N,&K))
    {
        S[0]=A[0]=B[0]=0;
        for(int i=1;i<=N;++i)
        {
            double t;scanf("%lf",&t);
            S[i]=S[i-1]+t;
            B[i]=B[i-1]+1/t;
            A[i]=A[i-1]+S[i]/t;
        }
        //printf("start
");
        for(int i=1;i<=N;++i)dp[i][1]=A[i];
        for(int j=2;j<=K;++j)
        {
            q[head=tair=1]=j-1;
            for(int i=j;i<=N;++i)
            {
                while(head<tair&&calc(i,j,q[head])>=calc(i,j,q[head+1]))head++;
                dp[i][j]=calc(i,j,q[head]);
                while(head<tair&&judge(q[tair-1],q[tair],i,j))tair--;
                q[++tair]=i;
            }
        }
        printf("%.6f
",dp[N][K]);
    }
}