Submission #46625

#	Time	Username	Problem	Language	Result	Execution time	Memory
46625		dqhungdl	Split the sequence (APIO14_sequence)	C++17	100 / 100	616 ms	83200 KiB

sequence

#include <bits/stdc++.h>
using namespace std;

struct Data
{
    int64_t a,b;
    int id;
};

typedef pair<int64_t,int> ii;
int n,k,top,pointer,Trace[205][100005];
int64_t a[100005],f[100005];
Data S[100005];

bool Check(Data x1,Data x2,Data x3)
{
    ///Intersection(x1,x2)=(x1.b-x2.b)/(x2.a-x1.a)
    ///Intersection(x1,x3)=(x1.b-x3.b)/(x3.a-x1.a)
    return (x1.b-x3.b)*(x2.a-x1.a)<=(x1.b-x2.b)*(x3.a-x1.a);
}

void Update(int64_t x,int64_t y,int id)
{
    while(top>=2&&Check(S[top-1],S[top],{x,y,id})==true)
        top--;
    S[++top]={x,y,id};
}

ii Query(int64_t x)
{
    pointer=min(pointer,top);
    while(pointer<top&&S[pointer+1].a*x+S[pointer+1].b<=S[pointer].a*x+S[pointer].b)
        pointer++;
    return ii(S[pointer].a*x+S[pointer].b,S[pointer].id);
}

void Process(int kk)
{
    top=0;
    pointer=1;
    Update(0,0,0);
    for(int i=1;i<=n;i++)
    {
        ii tmp=Query(a[i]);
        Update(-a[i],a[i]*a[i]-f[i],i);
        f[i]=-tmp.first;
        Trace[kk][i]=tmp.second;
    }
}

int main()
{
    ios_base::sync_with_stdio(false);
    //freopen("TEST.INP","r",stdin);
    cin>>n>>k;
    for(int i=1;i<=n;i++)
    {
        cin>>a[i];
        a[i]+=a[i-1];
    }
    for(int i=1;i<=k;i++)
        Process(i);
    cout<<f[n]<<"\n";
    while(k>0)
    {
        n=Trace[k][n];
        k--;
        cout<<n<<' ';
    }
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29