Submission #1011802

#	Time	Username	Problem	Language	Result	Execution time	Memory
1011802		baodeptrai	Split the sequence (APIO14_sequence)	C++14	0 / 100	58 ms	131072 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
#define endl "\n"
#define ll long long
template <bool kGetMin = false>
struct LineDeque
{
    using T = long long;

    struct Line
    {
        mutable T a, b, p;
        bool operator<(const Line &other) const { return a < other.a; }
        bool operator<(T x) const { return p < x; }
        T eval(T x) const { return a * x + b; }
    };

    using Set = std::deque<pair<Line, int>>;
    using Iterator = typename Set::iterator;
    Set s;

    static const T inf = std::numeric_limits<T>::max();

    // doubles: inf = 1/.0, div(a, b) = a / b
    T div(T a, T b)
    { // floored division
        return a / b - ((a ^ b) < 0 && a % b);
    }

    bool intersect(Line &x, Line &y)
    {
        if (x.a == y.a)
        {
            x.p = x.b > y.b ? inf : -inf;
        }
        else
        {
            x.p = div(y.b - x.b, x.a - y.a);
        }
        return x.p >= y.p;
    }

    void _add_line1(T a, T b, int id)
    { // increasing slope
        Line to_add = {a, b, inf};
        if (s.size())
        {
            intersect(s.back().first, to_add);
        }
        while (s.size() >= 2 && intersect(s.at(s.size() - 2).first, s.at(s.size() - 1).first))
        {
            s.pop_back();
            intersect(s.back().first, to_add);
        }
        s.push_back({to_add, id});
    }

    void _add_line2(T a, T b, int id)
    { // decreasing slope
        Line to_add = {a, b, 0};
        while (s.size() && intersect(to_add, s.front()))
        {
            s.pop_front();
        }
        s.push_front({to_add, id});
    }

    void add_line_increasing_slope(T a, T b, int id)
    {
        if constexpr (kGetMin)
        {
            _add_line2(-a, -b, id);
        }
        else
        {
            _add_line1(a, b, id);
        }
    }

    void add_line_decreasing_slope(T a, T b, int id)
    {
        if constexpr (kGetMin)
        {
            _add_line1(-a, -b, id);
        }
        else
        {
            _add_line2(a, b, id);
        }
    }

    T query(T x)
    { // arbitrary
        assert(!s.empty());
        auto l = *std::lower_bound(s.begin(), s.end());
        // To get min
        if constexpr (kGetMin)
        {
            return -l.eval(x);
        }
        else
        {
            return l.eval(x);
        }
    }

    pair<T, int> query_increasing(T x)
    {
        while (s.size() >= 2 && s[0].first.eval(x) <= s[1].first.eval(x))
        {
            s.pop_front();
        }
        if constexpr (kGetMin)
        {
            return {-s[0].first.eval(x), s[0].second};
        }
        else
        {
            return {s[0].first.eval(x), s[0].second};
        }
    }

    pair<T, int> query_decreasing(T x)
    {
        while (s.size() >= 2 && s.at(s.size() - 1).first.eval(x) <= s.at(s.size() - 2).first.eval(x))
        {
            s.pop_back();
        }
        if constexpr (kGetMin)
        {
            return {-s[0].first.eval(x), s[0].second};
        }
        else
        {
            return {s[0].first.eval(x), s[0].second};
        }
    }
};
int n, k, a[100005];
int s[100005];
pair<ll, int> dp[100005][250];
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin >> n >> k;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i];
        s[i] = s[i - 1] + a[i];
    }
    LineDeque<false> d[205];
    for (int i = 1; i <= k; i++)
    {
        d[i - 1].add_line_increasing_slope(s[0], dp[0][i - 1].first - s[0] * s[0], 0);
        for (int j = 1; j <= n; j++)
        {
            dp[j][i] = max(dp[j][i], d[i - 1].query_increasing(s[j]));
            d[i - 1].add_line_increasing_slope(s[j - 1], dp[j - 1][i - 1].first - s[j - 1] * s[j - 1], j - 1);
            // cout << i << " " << j << " " << dp[j][i].first << " " << dp[j][i].second << endl;
            // d[i].add_line_increasing_slope(s[j], dp[j][i] - s[j] * s[j]);
        }
    }
    vector<int> res;
    int x = n;
    int the = k;
    // cout << dp[x][the].second << endl;
    // cout << dp[6][the - 1].second << endl;
    // cout << dp[4][the - 2].second << endl;
    // cout << d
    while (x != 0 && the != 0)
    {
        x = dp[x][the].second;
        res.push_back(x);
        the--;
    }
    cout << dp[n][k].first << endl;
    reverse(res.begin(), res.end());
    for (int i : res)
    {
        cout << i << " ";
    }
}

Compilation message (stderr)

sequence.cpp: In member function 'void LineDeque<kGetMin>::add_line_increasing_slope(LineDeque<kGetMin>::T, LineDeque<kGetMin>::T, int)':
sequence.cpp:70:12: warning: 'if constexpr' only available with '-std=c++17' or '-std=gnu++17'
   70 |         if constexpr (kGetMin)
      |            ^~~~~~~~~
sequence.cpp: In member function 'void LineDeque<kGetMin>::add_line_decreasing_slope(LineDeque<kGetMin>::T, LineDeque<kGetMin>::T, int)':
sequence.cpp:82:12: warning: 'if constexpr' only available with '-std=c++17' or '-std=gnu++17'
   82 |         if constexpr (kGetMin)
      |            ^~~~~~~~~
sequence.cpp: In member function 'LineDeque<kGetMin>::T LineDeque<kGetMin>::query(LineDeque<kGetMin>::T)':
sequence.cpp:97:12: warning: 'if constexpr' only available with '-std=c++17' or '-std=gnu++17'
   97 |         if constexpr (kGetMin)
      |            ^~~~~~~~~
sequence.cpp: In member function 'std::pair<long long int, int> LineDeque<kGetMin>::query_increasing(LineDeque<kGetMin>::T)':
sequence.cpp:113:12: warning: 'if constexpr' only available with '-std=c++17' or '-std=gnu++17'
  113 |         if constexpr (kGetMin)
      |            ^~~~~~~~~
sequence.cpp: In member function 'std::pair<long long int, int> LineDeque<kGetMin>::query_decreasing(LineDeque<kGetMin>::T)':
sequence.cpp:129:12: warning: 'if constexpr' only available with '-std=c++17' or '-std=gnu++17'
  129 |         if constexpr (kGetMin)
      |            ^~~~~~~~~

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