Submission #944232

#	Time	Username	Problem	Language	Result	Execution time	Memory
944232		wapas	Split the sequence (APIO14_sequence)	C++14	89 / 100	1139 ms	88972 KiB

sequence

// code by wapas
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

struct CHT {
    const ll inf = 1e9;
    vector<pair<ll, ll>> lineStk = {};
    vector<ll> pointStk = {};
    vector<int> idxStk = {};
    ll isMin = 1;
    void toggleMinMax() {
        isMin *= -1;
    }
    void add(ll a, ll b = 0, int idx = -1) {
        a *= isMin; b *= isMin;
        while (lineStk.size()) {
            auto [p, q] = lineStk.back();
            if (a == p) {
                if (b > q) {
                    lineStk.pop_back();
                    pointStk.pop_back();
                    idxStk.pop_back();
                }
                else break;
                continue;
            }
            auto k = pointStk.back();
            ll prev = p * k + q, curr = a * k + b;
            if (curr >= prev) {
                lineStk.pop_back();
                pointStk.pop_back();
                idxStk.pop_back();
            }
            else {
                break;
            }
        }
        if (lineStk.size()) {
            auto [p, q] = lineStk.back();
            if (a != p) {
                ll num = q - b, den = a - p;
                ll t = (num + den - 1) / den;
                lineStk.push_back({ a, b });
                pointStk.push_back(t);
                idxStk.push_back(idx);
            }
        }
        else {
            lineStk.push_back({ a, b });
            pointStk.push_back(-inf);
            idxStk.push_back(idx);
        }
    }
    ll query(ll t) {
        int l = 0, r = pointStk.size();
        while (l + 1 < r) {
            int m = (l + r) / 2;
            if (pointStk[m] <= t) l = m;
            else r = m;
        }
        return l;
    }
    ll value(ll t, ll idx) {
        return (lineStk[idx].first * t + lineStk[idx].second) * isMin;
    }
    void replace(CHT &o) {
        swap(lineStk, o.lineStk);
        swap(pointStk, o.pointStk);
        swap(idxStk, o.idxStk);
        swap(isMin, o.isMin);
    }
};

void solution(int t) {
    ll N, K; cin >> N >> K;
    vector<ll> S(N + 1);
    for (int i = 1; i <= N; i++) {
        ll x; cin >> x;
        S[i] = x;
        S[i] += S[i - 1];
    }
    vector<ll> cache(N + 1, 0);
    vector<vector<int>> prev(K + 1, vector<int>(N + 1, -1));
    CHT cht;
    for (int n = 1; n <= N; n++) cht.add(S[n], - S[n] * S[n], n);
    for (int k = 1; k <= K; k++) {
        CHT ncht;
        vector<ll> ncache(N + 1, 0);
        for (int n = 1; n <= N; n++) {
            int i = cht.query(S[n]);
            ncache[n] = cht.value(S[n], i);
            prev[k][n] = cht.idxStk[i];
            ncht.add(S[n], ncache[n] - S[n] * S[n], n);
        }
        cht.replace(ncht);
        swap(cache, ncache);
    }
    vector<int> history = {};
    int k = K, n = N;
    while (prev[k][n] != -1) {
        history.push_back(prev[k][n]);
        n = prev[k--][n];
    }
    sort(history.begin(), history.end());
    for (int i = 1; i < history.size(); i++) if (history[i] <= history[i - 1]) history[i] = history[i - 1] + 1;
    if (history.back() == N) history[K - 1] -= 1;
    cout << (ll) cache[N] << "\n";
    for (auto e : history) cout << e << " ";
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
    // int T; cin >> T;
    int T = 1;
    for (int t = 0; t < T; t++) {
        solution(t);
    }
}

Compilation message (stderr)

sequence.cpp: In member function 'void CHT::add(ll, ll, int)':
sequence.cpp:20:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   20 |             auto [p, q] = lineStk.back();
      |                  ^
sequence.cpp:42:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   42 |             auto [p, q] = lineStk.back();
      |                  ^
sequence.cpp: In function 'void solution(int)':
sequence.cpp:108:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  108 |     for (int i = 1; i < history.size(); i++) if (history[i] <= history[i - 1]) history[i] = history[i - 1] + 1;
      |                     ~~^~~~~~~~~~~~~~~~

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