Submission #908584

#	Time	Username	Problem	Language	Result	Execution time	Memory
908584		sofija6	Split the sequence (APIO14_sequence)	C++14	100 / 100	1165 ms	84824 KiB

sequence

#include <bits/stdc++.h>
#define ll long long
#define MAXN 100002
#define MAXK 202
using namespace std;
ll dp[MAXN][2],pref[MAXN];
int prevv[MAXN][MAXK];
struct line
{
    long double k,m;
    long double Calc(ll x)
    {
        return k*x+m;
    }
    long double Intersect(line l)
    {
        return (m-l.m)/(l.k-k);
    }
};
int main()
{
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    ll n,k,a;
    cin >> n >> k;
    for (int i=1;i<=n;i++)
    {
        cin >> a;
        pref[i]=pref[i-1]+a;
    }
    deque<pair<line,ll> > d;
    for (int i=1;i<n;i++)
        dp[i][0]=pref[i]*(pref[n]-pref[i]);
    for (int j=2;j<=k;j++)
    {
        d.clear();
        d.push_front({{-pref[j-1],dp[j-1][0]},j-1});
        for (int i=j;i<n;i++)
        {
            while (d.size()>1)
            {
                ll sz=d.size();
                if (d[sz-1].first.Calc(pref[n]-pref[i])<=d[sz-2].first.Calc(pref[n]-pref[i]))
                    d.pop_back();
                else
                    break;
            }
            dp[i][1]=d.back().first.Calc(pref[n]-pref[i])+pref[i]*(pref[n]-pref[i]);
            prevv[i][j]=d.back().second;
            if (pref[i]!=pref[i-1])
            {
                line cur={-pref[i],dp[i][0]};
                while (d.size()>1 && cur.Intersect(d[1].first)>=d[0].first.Intersect(d[1].first))
                    d.pop_front();
                d.push_front({cur,i});
            }
        }
        d.clear();
        for (int i=1;i<n;i++)
            dp[i][0]=dp[i][1];
    }
    ll maxx=LLONG_MIN,pos=0;
    for (int i=k;i<n;i++)
    {
        if (dp[i][0]>=maxx)
        {
            maxx=dp[i][0];
            pos=i;
        }
    }
    cout << maxx << "\n";
    for (int i=k;i>0;i--)
    {
        cout << pos << " ";
        pos=prevv[pos][i];
    }
    return 0;
}
/**
7 3
4 1 3 4 0 2 3
**/

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:36:24: warning: narrowing conversion of '- pref[(j - 1)]' from 'long long int' to 'long double' [-Wnarrowing]
   36 |         d.push_front({{-pref[j-1],dp[j-1][0]},j-1});
      |                        ^~~~~~~~~~
sequence.cpp:36:44: warning: narrowing conversion of 'dp[(j - 1)][0]' from 'long long int' to 'long double' [-Wnarrowing]
   36 |         d.push_front({{-pref[j-1],dp[j-1][0]},j-1});
      |                                   ~~~~~~~~~^
sequence.cpp:51:27: warning: narrowing conversion of '- pref[i]' from 'long long int' to 'long double' [-Wnarrowing]
   51 |                 line cur={-pref[i],dp[i][0]};
      |                           ^~~~~~~~
sequence.cpp:51:43: warning: narrowing conversion of 'dp[i][0]' from 'long long int' to 'long double' [-Wnarrowing]
   51 |                 line cur={-pref[i],dp[i][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