Submission #374252

#	Time	Username	Problem	Language	Result	Execution time	Memory
374252		KoD	Split the sequence (APIO14_sequence)	C++17	100 / 100	942 ms	82276 KiB

sequence

#include <bits/stdc++.h>

template <class T>
using Vec = std::vector<T>;
using ll = long long;

constexpr ll INF = 1000000000000000000 + 5;

ll square(const ll x) {
    return x * x;
}

struct Line {
    ll a, b;
    Line() = default;
    ll eval(const ll x) const {
        return a * x + b;
    }
};

bool is_fixed(const Line &l, const Line &m, const Line &n) {
    return __int128_t(m.b - l.b) * (m.a - n.a) < __int128_t(n.b - m.b) * (l.a - m.a);
}

int main() {
    int N, K;
    std::cin >> N >> K;
    Vec<int> A(N);
    for (auto &x: A) {
        std::cin >> x;
    }
    Vec<int> cum(N + 1);
    for (int i = 0; i < N; ++i) {
        cum[i + 1] = cum[i] + A[i];
    }
    Vec<ll> dp(N + 1);
    for (int i = 0; i <= N; ++i) {
        dp[i] = square(cum[i]);
    }
    Vec<Vec<int>> index(K, Vec<int>(N + 1, -1));
    for (int k = 0; k < K; ++k) {
        Vec<Line> line(N + 1);
        for (int i = 0; i <= N; ++i) {
            line[i].a = -2 * cum[i];
            line[i].b = dp[i] + square(cum[i]);
        }
        std::fill(dp.begin(), dp.end(), INF);
        std::deque<int> active;
        for (int i = 0; i <= N; ++i) {
            if (!active.empty()) {
                const ll x = cum[i];
                while (active.size() >= 2) {
                    const auto &l = line[active[0]];
                    const auto &m = line[active[1]];
                    if (l.eval(x) >= m.eval(x)) {
                        active.pop_front();
                    }
                    else {
                        break;
                    }
                }
                index[k][i] = active[0];
                dp[i] = line[active[0]].eval(x) + square(x);
            }
            while (active.size() >= 2) {
                const auto &l = line[active[active.size() - 2]];
                const auto &m = line[active[active.size() - 1]];
                const auto &n = line[i];
                if (is_fixed(l, m, n)) {
                    break;
                }
                else {
                    active.pop_back();
                }
            }
            active.push_back(i);
        }
    }
    std::cout << (square(cum[N]) - dp[N]) / 2 << '\n';
    int i = N;
    Vec<int> split(K);
    for (int k = K - 1; k >= 0; --k) {
        i = index[k][i];
        split[k] = i;
    }
    for (int k = 0; k < K; ++k) {
        std::cout << split[k] << " \n"[k + 1 == K];
    }
    return 0;
}

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