Submission #110088

#	Time	Username	Problem	Language	Result	Execution time	Memory
110088		TAISA_	Split the sequence (APIO14_sequence)	C++14	100 / 100	1389 ms	87508 KiB

sequence

#include <bits/stdc++.h>
#define all(vec) vec.begin(), vec.end()
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
constexpr ll INF = (1LL << 40) - 1LL;
constexpr ll LINF = (1LL << 60) - 1LL;
constexpr double eps = 1e-9;
constexpr ll MOD = 1000000007LL;
template <typename T>
bool chmin(T& a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
};
template <typename T>
bool chmax(T& a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
};
template <typename T>
ostream& operator<<(ostream& os, vector<T> v) {
    for(int i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "\n" : " ");
    }
    return os;
}
template <typename T>
vector<T> make_v(size_t a) {
    return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T& t, const V& v) {
    t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T& t, const V& v) {
    for(auto& e : t) {
        fill_v(e, v);
    }
};
struct CHT {
    vector<pair<P, int>> lines;
    bool check(pair<P, int> l1, pair<P, int> l2, pair<P, int> l3) {
        return (l2.first.second - l3.first.second) *
                   (l2.first.first - l1.first.first) <=
               (l1.first.second - l2.first.second) *
                   (l3.first.first - l2.first.first);
    }
    void add(ll a, ll b, int idx) {
        pair<P, int> l = make_pair(P(a, b), idx);
        while(lines.size() >= 2 &&
              check(lines[(int)lines.size() - 2], lines.back(), l)) {
            lines.pop_back();
        }
        lines.push_back(l);
    }
    int id = 0;
    ll f(ll i, ll x) {
        return lines[i].first.first * x + lines[i].first.second;
    }
    P query(ll x) {
        int nid = id;
        for(int i = id + 1; i < lines.size(); i++) {
            if(f(i, x) > f(i - 1, x)) {
                nid = i;
            } else {
                break;
            }
        }
        id = nid;
        if(id >= lines.size()) {
            return P(0, 0);
        }
        return P(f(id, x), lines[id].second);
    }
};
int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n, k;
    cin >> n >> k;
    vector<ll> s(n + 10);
    for(int i = 1; i <= n; i++) {
        ll a;
        cin >> a;
        s[i] = s[i - 1] + a;
    }
    vector<ll> res(n + 10);
    vector<vector<int>> id(k + 1, vector<int>(n + 1));
    for(int l = 0; l < k; l++) {
        vector<ll> dp(n + 10);
        CHT cht;
        for(int i = l + 1; i <= n; i++) {
            tie(dp[i], id[l][i]) = cht.query(s[i]);
            cht.add(s[i], -s[i] * s[i] + res[i], i);
        }
        res = dp;
    }
    cout << res[n] << endl;
    vector<int> v;
    int idx = n;
    for(int l = k - 1; l >= 0; l--) {
        v.push_back(id[l][idx]);
        idx = id[l][idx];
    }
    reverse(all(v));
    for(int i = 0; i < k; i++) {
        cout << v[i];
        if(i < k - 1) {
            cout << " ";
        } else {
            cout << endl;
        }
    }
}

Compilation message (stderr)

sequence.cpp: In member function 'P CHT::query(ll)':
sequence.cpp:73:31: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         for(int i = id + 1; i < lines.size(); i++) {
                             ~~^~~~~~~~~~~~~~
sequence.cpp:81:15: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         if(id >= lines.size()) {
            ~~~^~~~~~~~~~~~~~~

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