Submission #1027072

#	Time	Username	Problem	Language	Result	Execution time	Memory
1027072		borisAngelov	Split the sequence (APIO14_sequence)	C++17	50 / 100	22 ms	131072 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

const int maxn = 10005;
const int maxk = 205;
const long long inf = 1e18;

int n, k;
long long a[maxn];
long long pref[maxn];

long long dp[maxn][maxk];
int prvState[maxn][maxn];

long long sum(int from, int to)
{
    return pref[to] - pref[from - 1];
}

struct Line
{
    long long a;
    long long b;
    int idx;

    long long calc(long long x)
    {
        return a * x + b;
    }
};

struct ConvexHullTrickMAX
{
    vector<pair<Line, double>> upperEnvelope;

    double cross(const Line& l1, const Line& l2)
    {
        return (1.0 * (l1.b - l2.b)) / (1.0 * (l2.a - l1.a));
    }

    bool toRemove(const Line& newLine, pair<Line, double> last)
    {
        if (newLine.a == last.first.a)
        {
            return newLine.b >= last.first.b;
        }

        return cross(newLine, last.first) <= last.second;
    }

    void addLine(Line newLine)
    {
        while (upperEnvelope.size() >= 1 && toRemove(newLine, upperEnvelope.back()) == true)
        {
            upperEnvelope.pop_back();
        }

        if (upperEnvelope.empty())
        {
            upperEnvelope.push_back({newLine, -inf});
        }
        else
        {
            upperEnvelope.push_back({newLine, cross(newLine, upperEnvelope.back().first)});
        }
    }

    Line query(long long x)
    {
        /*cout << "now query " << x << endl;

        for (auto [line, point] : upperEnvelope)
        {
            cout << line.idx << " " << point << endl;
        }*/

        int l = 0;
        int r = upperEnvelope.size() - 1;

        while (l <= r)
        {
            int mid = (l + r) / 2;

            if (upperEnvelope[mid].second <= 1.0 * x)
            {
                l = mid + 1;
            }
            else
            {
                r = mid - 1;
            }
        }

        return upperEnvelope[r].first;
    }
};

ConvexHullTrickMAX cht[maxk];

void fastIO()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
}

int main()
{
    fastIO();

    cin >> n >> k;

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

    for (int i = 1; i <= n; ++i)
    {
        for (int j = 0; j <= min(i - 1, k); ++j)
        {
            if (j != 0)
            {
                Line curr = cht[j - 1].query(pref[i]);
                dp[i][j] = curr.calc(pref[i]);
                prvState[i][j] = curr.idx;
            }
            else
            {
                dp[i][j] = 0;
            }

            //cout << i << " " << j << " :: " << dp[i][j] << endl;
        }

        for (int j = 0; j <= min(i - 1, k); ++j)
        {
            //cout << "add " << j << " " << pref[i] << " :: " << dp[i][j] - pref[i] * pref[i] << endl;;
            cht[j].addLine({pref[i], dp[i][j] - pref[i] * pref[i], i});
        }

        //cout << "end of " << i << endl;
        //cout << "------------------------------" << endl;
    }

    long long ans = dp[n][k];
    int pos = n;
    stack<int> splits;

    while (k > 0)
    {
        splits.push(prvState[pos][k]);
        pos = splits.top();
        --k;
    }

    cout << ans << endl;

    while (!splits.empty())
    {
        cout << splits.top() << " ";
        splits.pop();
    }

    cout << endl;

    return 0;
}

/*
6 1
0 0 0 0 1 1

7 3
4 1 3 4 0 2 3

2 1 4
3 1 16
3 2 19
4 1 35
4 2 48
4 3 51
5 1 35
5 2 48
5 3 51
6 1 48
6 2 64
6 3 72
7 1 72
7 2 95
7 3 108
*/

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