Submission #427025

#	Time	Username	Problem	Language	Result	Execution time	Memory
427025		blue	Split the sequence (APIO14_sequence)	C++17	0 / 100	2065 ms	3384 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()
{
    int 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 prev[n+1];
    int cut_count[n+1];
    long long lo = 0, hi = INF/k - 10;


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

        for(int i = 2; i <= n; i++)
        {
            dp[i] = 0;
            prev[i] = 0;
            cut_count[i] = 0;
            for(int j = 1; j < i; j++)
            {
                if(dp[j] + (a_sum[i] - a_sum[j])*a_sum[j] - ct > dp[i])
                {
                    dp[i] = dp[j] + (a_sum[i] - a_sum[j])*a_sum[j] - ct;
                    prev[i] = j;
                    cut_count[i] = cut_count[j] + 1;
                }
                else if(dp[j] + (a_sum[i] - a_sum[j])*a_sum[j] - ct == dp[i])
                {
                    if(cut_count[j] + 1 < cut_count[i])
                    {
                        prev[i] = j;
                        cut_count[i] = cut_count[j] + 1;
                    }
                }
            }
        }

        if(lo == hi)
        {
            break;
        }
        else
        {
            if(cut_count[n] > k) lo = ct+1;
            else hi = ct;
        }
    }

    cout << dp[n] + k*lo << '\n';

    bool res[n + 1];
    int resSize = 0;
    for(int i = 0; i <= n; i++) res[i] = false;
    for(int i = n; prev[i] != 0; i = prev[i]) {
        res[prev[i]] = true;
        resSize++;
    }

    for(int i = 1; i + 2 <= n && resSize < k; i++) {
        if (res[i] && a[i + 1] == 0 && !res[i + 1]) {
            res[i + 1] = true;
            resSize++;
        }
    }
    for(int i = n - 1; i >= 1 && resSize < k; i--) {
        if (res[i] && a[i] == 0 && !res[i-1]) {
            res[i-1] = true;
            resSize++;
        }
    }

}

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