Submission #415218

#	Time	Username	Problem	Language	Result	Execution time	Memory
415218		blue	Split the sequence (APIO14_sequence)	C++17	0 / 100	2082 ms	2636 KiB

sequence

#include <iostream>
#include <vector>
#include <deque>
using namespace std;

/*
Add a[i]*a[j] to the score if i and j are in different parts.

dp[i][p] = maximum score if 1..i is split into p parts

dp[i][p] = max{dp[j][p-1] + (a_sum[i] - a_sum[j])*(a_sum[j]) | j=1..i-1}

dp[i][p] = max{(-a_sum[j])*a_sum[i] + (dp[j][p-1] + a_sum[j]*a_sum[j]) | j=1..i-1}
*/

long long INF = 1'000'000'000'000'000'000;

int main()
{
    int n, k;
    cin >> n >> k;

    long long a[n+1];
    a[0] = 0;
    for(int i = 1; i <= n; i++)
    {
        cin >> a[i];
        a[i] += a[i-1];
    }

    long long lo = 0, hi = 1000'000'000'00'00, ct;
    long long dp[n+1];
    int prev[n+1], cuts[n+1];

    while(1)
    {
        ct = (lo+hi)/2;
        dp[1] = 0;
        prev[1] = 0;
        cuts[1] = 0;

        // cerr << "ct = " << ct << '\n';

        for(int i = 2; i <= n; i++)
        {
            dp[i] = -INF;
            for(int j = 1; j < i; j++)
            {
                long long newdp = dp[j] - ct + (a[i]-a[j])*a[j];
                if(newdp > dp[i])
                {
                    dp[i] = newdp;
                    prev[i] = j;
                    cuts[i] = cuts[j] + 1;
                }
                else if(newdp == dp[i] && cuts[j] + 1 < cuts[i])
                {
                    cuts[i] = cuts[j] + 1;
                    prev[i] = j;
                }
                // cerr << i << ' ' << j << " newdp = " << newdp << '\n';
            }
        }

        // for(int i = 1; i <= n; i++) cerr << i << ' ' << dp[i] << ' ' << prev[i] << ' ' << cuts[i] << '\n';

        if(cuts[n] == k)
            break;
        else if(cuts[n] < k)
            hi = ct-1;
        else
            lo = ct+1;

        // cerr << "\n\n\n\n\n\n\n";
    }

    // for(int i = 1; i <= n; i++) cerr << i << ' ' << dp[i] << ' ' << prev[i] << ' ' << cuts[i] << '\n';

    cout << dp[n] + ct*cuts[n] << '\n';
    for(int j = prev[n]; j != 0; j = prev[j]) cout << j << ' ';
    cout << '\n';
}

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