Submission #553535

#	Time	Username	Problem	Language	Result	Execution time	Memory
553535		andrei_boaca	Split the sequence (APIO14_sequence)	C++17	100 / 100	872 ms	106988 KiB

sequence

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
ll n,k,v[100005],s[100005];
int from[100005][205];
struct date
{
    ll a,b,l,r,poz;
};
deque<date> coada[205];
ll dp[205];
ll f(date F, ll x)
{
    return F.a*x+F.b;
}
void out(ll i,ll val)
{
    while(!coada[i].empty()&&coada[i].front().r<val)
        coada[i].pop_front();
}
void add(ll i,date line)
{
    while(!coada[i].empty())
    {
        date prv=coada[i].back();
        if(prv.a==line.a)
        {
            if(line.b>=prv.b)
                break;
            coada[i].pop_back();
            continue;
        }
        ll x=(line.b-prv.b)/(prv.a-line.a);
        while(f(line,x)>=f(prv,x))
            x++;
        if(x<=prv.l)
        {
            coada[i].pop_back();
            continue;
        }
        coada[i].pop_back();
        prv.r=x-1;
        line.l=x;
        line.r=1e18;
        coada[i].push_back(prv);
        coada[i].push_back(line);
        break;
    }
    if(coada[i].empty())
    {
        line.l=0;
        line.r=1e18;
        coada[i].push_back(line);
        return;
    }
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin>>n>>k;
    k++;
    for(int i=1;i<=n;i++)
    {
        cin>>v[i];
        s[i]=s[i-1]+v[i];
    }
    ll ans=0;
    for(int i=1;i<=n;i++)
    {
        dp[1]=s[i]*s[i];
        date q;
        q.a=-2*s[i];
        q.b=s[i]*s[i]+dp[1];
        q.poz=i;
        add(1,q);
        for(int j=2;j<=min(k,i*1LL);j++)
        {
            out(j-1,s[i]);
            date x=coada[j-1].front();
            from[i][j]=x.poz;
            ll val=x.a*s[i]+x.b;
            dp[j]=s[i]*s[i]+val;
            q.a=-2*s[i];
            q.b=s[i]*s[i]+dp[j];
            q.poz=i;
            add(j,q);
        }
        if(i==n)
            ans=dp[k];
    }
    ans=s[n]*s[n]-ans;
    ans/=2;
    cout<<ans<<'\n';
    ll i=n;
    ll j=k;
    vector<ll> sol;
    while(i>0)
    {
        ll x=from[i][j];
        if(x>0)
            sol.push_back(x);
        i=x;
        j--;
    }
    reverse(sol.begin(),sol.end());
    for(int i:sol)
        cout<<i<<' ';
    return 0;
}

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