Submission #438462

#	Time	Username	Problem	Language	Result	Execution time	Memory
438462		blue	Split the sequence (APIO14_sequence)	C++17	50 / 100	2078 ms	3532 KiB

sequence

#include <iostream>
#include <vector>
#include <set>
#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()
{
    long long n, k;
    cin >> n >> k;

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

    long long dp[n+1];
    int cut_count_lo[n+1];
    int cut_count_hi[n+1];
    long long lo = 0, hi = INF/k;
    long long ct;


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

        for(int i = 2; i <= n; i++)
        {
            dp[i] = 0;
            cut_count_lo[i] = cut_count_hi[i] = 0;
            for(int j = 1; j < i; j++)
            {
                long long new_dp = dp[j] + (a_sum[i] - a_sum[j])*a_sum[j] - ct;
                // cerr << "i = " << i << ", j = " << j << " => new_dp = " << new_dp << '\n';
                if(new_dp > dp[i])
                {
                    dp[i] = new_dp;
                    cut_count_lo[i] = cut_count_lo[j] + 1;
                    cut_count_hi[i] = cut_count_hi[j] + 1;
                }
                else if(new_dp == dp[i])
                {
                    cut_count_lo[i] = min(cut_count_lo[i], cut_count_lo[j] + 1);
                    cut_count_hi[i] = max(cut_count_hi[i], cut_count_hi[j] + 1);
                }
            }
        }

        // cerr << ct << ": " << cut_count_lo[n] << ' ' << cut_count_hi[n] << '\n';

        if(lo == hi)
        {
            break;
        }
        else
        {
            if(cut_count_lo[n] > k) lo = ct+1;
            else if(cut_count_lo[n] <= k && k <= cut_count_hi[n]) break;
            else if(cut_count_hi[n] < k) hi = ct-1;
        }
    }

    // for(int i = 1; i <= n; i++) cerr << i << ' ' << dp[i] << ' ' << cut_count_lo[i] << ' ' << cut_count_hi[i] << '\n';
    cout << dp[n] + k*ct << '\n';

    vector<int> res;
    int X = n, K = k;
    while(K >= 1)
    {
        for(int i = 1; i < X; i++)
        {
            long long new_dp = dp[i] + (a_sum[X] - a_sum[i])*a_sum[i] - ct;
            if(cut_count_lo[i] <= K-1 && K-1 <= cut_count_hi[i] && new_dp == dp[X])
            {
                X = i;
                K--;
                res.push_back(X);
                break;
            }
        }
    }
    for(int r:res) cout << r << ' ';
    cout << '\n';
}

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