Submission #1222010

#	Time	Username	Problem	Language	Result	Execution time	Memory
1222010		Szymon_Pilipczuk	Split the sequence (APIO14_sequence)	C++20	71 / 100	909 ms	196608 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define int long long
#define st first
#define nd second
#define pb push_back
#define all(a) a.begin(),a.end()
#define rep(a,b) for(int a = 0;a<b;a++)
const int inf = 1e9;
const ll infl = 1e18;
vector<vector<ll>> l[201];
int n,k;
ll sq(ll a)
{
    return a*a;
}
/*void add(ll a,ll b,ll p,ll i,int c)
{
    ll d = l[c][p][0],e = l[c][p][1],lp = l[c][p][2],rp = l[c][p][3],ci = l[c][p][6];
    if(a * (lp+rp)/2 + b < d * (lp+rp)/2 + e) 
    {
        l[c][p][0] = a;
        l[c][p][1] = b;
        l[c][p][6] = i;
        i = ci;
        a = d;
        b = e;
    }
    //cerr<<a<<" "<<b<<" "<<p<<" "<<i<<" "<<c<<" "<<l[c][p][4]<<" "<<l[c][p][5]<<"\n";
    if(a * lp + b < l[c][p][0] * lp + l[c][p][1])
    {
        if(lp <= (lp+rp)/2 -1)
        {
            if(l[c][p][4] != -1)
            {
                add(a,b,l[c][p][4],i,c);
            }
            else
            {
                l[c][p][4] = l[c].size();
                l[c].pb({a,b,lp,(lp+rp)/2,-1,-1,i});
            }
        }
    }
    else
    {
        if(rp >= (lp+rp)/2 + 1)
        {
            if(l[c][p][5] != -1)
            {
                add(a,b,l[c][p][5],i,c);
            }
            else
            {
                l[c][p][5] = l[c].size();
                l[c].pb({a,b,(lp+rp)/2+1,rp,-1,-1,i});
            }
        }
    }
}
vector<ll> check(ll v,int p,int c)
{
    vector<ll> ans;
    ans = {l[c][p][0] * v + l[c][p][1],l[c][p][6]};
    if((l[c][p][2]+l[c][p][3])/2 < v && l[c][p][5] != -1)
    {
        vector<ll> cans = check(v,l[c][p][5],c);
        if(cans[0] < ans[0])
        {
            ans = cans;
        }
    }
    else if((l[c][p][2]+l[c][p][3])/2 > v && l[c][p][4] != -1)
    {
        vector<ll> cans = check(v,l[c][p][4],c);
        if(cans[0] < ans[0])
        {
            ans = cans;
        }
    }   
    return ans;
}*/
deque<vector<ll>> dq;
void add(ll a,ll b,int i)
{
    if(dq.size() == 0)
    {
        dq.push_back({0,infl,a,b,i});
        return;
    }
    vector<ll> c = dq.back();
    if(c[2] == a)
    {
        if(c[3] > b)
        {
            dq.pop_back();
            add(a,b,i);
        }
    }
    else
    {
        ll cu = (b-c[3])/(c[2]-a) + 1;
        if(cu <= c[0])
        {
            dq.pop_back();
            add(a,b,i);
        }
        else
        {
            dq.back()[1] = cu-1;
            dq.pb({cu,infl,a,b,i});
        }
    }
}
pair<ll,ll> check(ll c)
{
    if(dq.front()[1] >=c)
    {
        return {c * dq.front()[2] + dq.front()[3],dq.front()[4]};
    }
    else
    {
        dq.pop_front();
        return check(c);
    }
}
ll pref[100000];
vector<int> ord;
ll solve()
{
    vector<vector<ll>> nx;
    vector<vector<ll>> nxnx;
    vector<vector<pair<ll,ll>>> ans(k);
    rep(q,k)
    {
        ans[q].resize(n-1);
        nx = nxnx;
        nxnx.clear();
        dq.clear();
        add(0,inf,-1);
        if(q == 0)
        {
            add(0,0,-1);
        }
        rep(i,n-1)
        {

            //cout<<i<<"\n";
            ans[q][i] = {check(pref[i]).st + pref[i]*pref[i],check(pref[i]).nd};
            //cerr<<q<<" "<<i<<" "<<ans[q][i].st<<" "<<ans[q][i].nd<<"\n";
            nxnx.pb({-2 * pref[i],ans[q][i].st + pref[i]*pref[i],i});
            if(q != 0) add(nx[i][0],nx[i][1],nx[i][2]);
            //cout<<ans[i][j][0]<<" "<<ans[i][j][1]<<" "<<i<<" "<<j<<"\n";
            //cout<<-2*pref[i]<<" "<<ans[i][j][0] +pref[i]*pref[i]<<"\n";
        }
    }
    //cout<<'a'<<"\n";
    dq.clear();
    rep(i,n-1)
    {
        add(nxnx[i][0],nxnx[i][1],nxnx[i][2]);
    }
    int ci = check(pref[n-1]).nd;
    int cu = k-1;
    while(ci != -1)
    {
       // cout<<ci<<"\n";
        ord.pb(ci);
        ci = ans[cu][ci].nd;
        cu--;
    }
    reverse(all(ord));
    return check(pref[n-1]).st + pref[n-1]*pref[n-1];
}
int32_t main()
{
    cin>>n>>k;
    int cu;
    cin>>cu;
    pref[0] = cu;  
    rep(i,n-1)
    {
        int c;
        cin>>c;
        pref[i+1] = pref[i]+c;
    }
    ll ans = solve();
    //cerr<<ans<<"\n";
    cout<<(sq(pref[n-1])-ans)/2<<"\n";
    rep(i,k)
    {
        cout<<ord[i]+1<<" ";
    }
    cout<<"\n";
}  

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29