Submission #814126

#	Time	Username	Problem	Language	Result	Execution time	Memory
814126		TCLMinh	Split the sequence (APIO14_sequence)	C++17	89 / 100	1772 ms	87844 KiB

sequence

#include <iostream>
#include <deque>
#include <algorithm>
#include <utility>
#include <vector>
#define int long long
using namespace std;

struct Line
{
    int a = 0, b = 0;
    Line(int a, int b) :a(a), b(b) {}
    Line() {}

    const inline int operator()(int x) const
    {
        return a * x + b - x * x;
    }

    const bool operator<(const Line& other) const
    {
        return a == other.a ? b < other.b : a < other.a;
    }

    const inline int intersect(const Line& other) const
    {
        return (other.b - b) / (a - other.a) + ((other.b - b) % (a - other.a) != 0);
    }
};

struct Node
{
    int idx = 0;
    int itsPos = 0;
    Line line = Line();
    Node(int itsPos, const Line& line, int idx) :itsPos(itsPos), line(line), idx(idx) {}
    Node(int itsPos) {}
    Node() {}
    const bool operator<(const Node& other) const
    {
        return itsPos < other.itsPos;
    }
};

std::deque<Node> dq;

void addLine(const Line& line, int idx)
{
    while (!dq.empty())
    {
        if (dq.back().line.a == line.a)
        {
            if (dq.back().line.b < line.b) dq.pop_back();
            return;
        }
        if (dq.back().line.intersect(line) <= dq.back().itsPos) dq.pop_back();
        else break;
    }
    if (dq.empty()) dq.push_back({ -99999999999999999LL,line,idx });
    else dq.push_back({ dq.back().line.intersect(line),line, idx });
}

void clearDeque()
{
    while (!dq.empty()) dq.pop_back();
}

pair<int, int> query(int x)
{
    int l = 0, r = dq.size() - 1;
    int result = 0;
    int idx = 0;
    while (l <= r)
    {
        int mid = (l + r) / 2;
        if (result < dq[mid].line(x))
        {
            result = dq[mid].line(x);
            idx = dq[mid].idx;
        }
        if (dq[mid].itsPos < x)
        {
            l = mid + 1;
        }
        else
        {
            r = mid - 1;
        }
    }
    return{ result,idx };
}

int n, k;
signed trace[201][100001];
int dp[2][100001];
Line pre[2][100001];
int a[100001];
int prx[100001];


void debug()
{
    for (int i = 0; i <= k; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            cerr << trace[i][j] << " ";
        }
        cerr << "\n";
    }
    cerr << "\n";

}

int sum(int l, int r)
{
    return prx[r] - prx[l - 1];
}


signed main()
{
    cin >> n >> k;
    //k++;
    k--;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i];
        prx[i] = prx[i - 1] + a[i];
    }

    //maximize this dp: dp[t][i] = max(dp[t][i],dp[t - 1][j - 1] + sum(j,i) * sum(i + 1,n));

    for (int i = 2; i <= n; i++)
    {
        dp[0][i] = prx[i - 1] * (prx[n] + prx[0]) - prx[i - 1] * prx[i - 1] - prx[0] * prx[n];
        pre[0][i] = Line((prx[n] + prx[i - 1]), dp[0][i] - prx[i - 1] * prx[n]);
    }


    for (signed t = 1; t <= k; t++)
    {
        //cerr << t << "\n";
        clearDeque();
        for (signed i = t + 1; i <= n; i++)
        {
            //add previous one
            addLine(pre[(t-1)&1][i - 1], i - 1);
            //get
            pair<int,int> x = query(prx[i - 1]);
            int val = x.first;
            int idx = x.second;
            dp[t&1][i] = val;
            trace[t][i] = idx;
            //apply
            if (i < n)
            {
                pre[t&1][i] = Line(prx[n] + prx[i - 1], val - prx[i - 1] * prx[n]);
            }
        }
        /*
        for (auto x : dq)
        {
            cerr << x.itsPos << " " << x.line.a << "x " << x.line.b << " -x^2 \n";
        }
        */
    }
    vector<int> res;
    int result = 0, idx = 0;
    for (int i = n; i >= 1; i--)
    {
        if (result < dp[k&1][i])
        {
            result = dp[k&1][i];
            idx = i;
        }
    }
    res.push_back(idx-1);
    for (int i = k; i >= 1; i--)
    {
        res.push_back(trace[i][idx] - 1);
        idx = trace[i][idx];
    }

    //debug();
    cout << result << '\n';
    sort(res.begin(), res.end());

    int id = 1;
    for (auto x : res)
    {
        if (x < 0 || x < id)
        {
            cout << id++ << " ";
        }else
        cout << x << " ";
    }
    return 0;
}

Compilation message (stderr)

sequence.cpp: In constructor 'Node::Node(long long int, const Line&, long long int)':
sequence.cpp:35:10: warning: 'Node::line' will be initialized after [-Wreorder]
   35 |     Line line = Line();
      |          ^~~~
sequence.cpp:33:9: warning:   'long long int Node::idx' [-Wreorder]
   33 |     int idx = 0;
      |         ^~~
sequence.cpp:36:5: warning:   when initialized here [-Wreorder]
   36 |     Node(int itsPos, const Line& line, int idx) :itsPos(itsPos), line(line), idx(idx) {}
      |     ^~~~

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