Submission #569884

#	Time	Username	Problem	Language	Result	Execution time	Memory
569884		shiomusubi496	Split the sequence (APIO14_sequence)	C++17	100 / 100	1102 ms	85192 KiB

sequence

#line 2 "library/other/template.hpp"

#include<bits/stdc++.h>

#ifndef __COUNTER__
#define __COUNTER__ __LINE__
#endif

#define REP_SELECTER(a, b, c, d, e, ...) e
#define REP1_0(b, c) REP1_1(b, c)
#define REP1_1(b, c) for (ll REP_COUNTER_ ## c = 0; REP_COUNTER_ ## c < (ll)(b); ++ REP_COUNTER_ ## c)
#define REP1(b) REP1_0(b, __COUNTER__)
#define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i)
#define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define rep(...) REP_SELECTER(__VA_ARGS__, REP4, REP3, REP2, REP1) (__VA_ARGS__)
#define RREP2(i, a) for (ll i = (ll)(a) - 1; i >= 0; --i)
#define RREP3(i, a, b) for (ll i = (ll)(a) - 1; i >= (ll)(b); --i)
#define RREP4(i, a, b, c) for (ll i = (ll)(a) - 1; i >= (ll)(b); i -= (ll)(c))
#define rrep(...) REP_SELECTER(__VA_ARGS__, RREP4, RREP3, RREP2) (__VA_ARGS__)
#define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i)
#define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i)
#define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c))
#define reps(...) REP_SELECTER(__VA_ARGS__, REPS4, REPS3, REPS2) (__VA_ARGS__)
#define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i)
#define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i)
#define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c))
#define rreps(...) REP_SELECTER(__VA_ARGS__, RREPS4, RREPS3, RREPS2) (__VA_ARGS__)

#define each_for(...) for (auto&& __VA_ARGS__)
#define each_const(...) for (const auto& __VA_ARGS__)

#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)

#if __cplusplus >= 201402L
#define CONSTEXPR constexpr
#else
#define CONSTEXPR
#endif

#ifdef __cpp_if_constexpr
#define IF_CONSTEXPR constexpr
#else
#define IF_CONSTEXPR
#endif

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PLL = std::pair<ll, ll>;
template<class T> using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>;

template<class T> class infinity {
  public:
    static constexpr T value = std::numeric_limits<T>::max() / 2;
    static constexpr T mvalue = std::numeric_limits<T>::min() / 2;
    static constexpr T max = std::numeric_limits<T>::max();
    static constexpr T min = std::numeric_limits<T>::min();
};

#if __cplusplus <= 201402L
template<class T> constexpr T infinity<T>::value;
template<class T> constexpr T infinity<T>::mvalue;
template<class T> constexpr T infinity<T>::max;
template<class T> constexpr T infinity<T>::min;
#endif

#if __cplusplus >= 201402L
template<class T> constexpr T INF = infinity<T>::value;
#endif

constexpr ll inf = infinity<ll>::value;
constexpr ld EPS = 1e-8;
constexpr ld PI = 3.1415926535897932384626;

template<class T, class U> std::ostream& operator<<(std::ostream& ost, const std::pair<T, U>& p) {
    return ost << p.first << ' ' << p.second;
}
template<class T, class U> std::istream& operator>>(std::istream& ist, std::pair<T, U>& p) {
    return ist >> p.first >> p.second;
}

template<class Container,
        typename std::enable_if<!std::is_same<Container, std::string>::value>::type* = nullptr>
auto operator<<(std::ostream& ost, const Container& cont)
        -> decltype(cont.begin(), cont.end(), ost)
{
    for (auto itr = cont.begin(); itr != cont.end(); ++itr) {
        if (itr != cont.begin()) ost << ' ';
        ost << *itr;
    }
    return ost;
}
template<class Container,
        typename std::enable_if<!std::is_same<Container, std::string>::value>::type* = nullptr>
auto operator>>(std::istream& ist, Container& cont)
        -> decltype(cont.begin(), cont.end(), ist)
{
    for (auto itr = cont.begin(); itr != cont.end(); ++itr) ist >> *itr;
    return ist;
}

template<class T, class U> inline constexpr bool chmin(T &a, const U &b) noexcept {
    return a > b ? a = b, true : false;
}
template<class T, class U> inline constexpr bool chmax(T &a, const U &b) noexcept {
    return a < b ? a = b, true : false;
}

inline CONSTEXPR ll gcd(ll a, ll b) noexcept {
    while (b) {
        const ll c = a;
        a = b;
        b = c % b;
    }
    return a;
}
inline CONSTEXPR ll lcm(ll a, ll b) noexcept {
    return a / gcd(a, b) * b;
}

inline CONSTEXPR bool is_prime(ll N) noexcept {
    if (N <= 1) return false;
    for (ll i = 2; i * i <= N; ++i) {
        if (N % i == 0) return false;
    }
    return true;
}
inline std::vector<ll> prime_factor(ll N) noexcept {
    std::vector<ll> res;
    for (ll i = 2; i * i <= N; ++i) {
        while (N % i == 0) {
            res.push_back(i);
            N /= i;
        }
    }
    if (N != 1) res.push_back(N);
    return res;
}

inline CONSTEXPR ll my_pow(ll a, ll b) noexcept {
    ll res = 1;
    while (b) {
        if (b & 1) res *= a;
        b >>= 1;
        a *= a;
    }
    return res;
}
inline CONSTEXPR ll mod_pow(ll a, ll b, ll mod) noexcept {
    a %= mod;
    ll res = 1;
    while (b) {
        if (b & 1) (res *= a) %= mod;
        b >>= 1;
        (a *= a) %= mod;
    }
    return res;
}

inline PLL extGCD(ll a, ll b) noexcept {
    const ll n = a, m = b;
    ll x = 1, y = 0, u = 0, v = 1;
    ll t;
    while (b) {
        t = a / b;
        std::swap(a -= t * b, b);
        std::swap(x -= t * u, u);
        std::swap(y -= t * v, v);
    }
    if (x < 0) {
        x += m;
        y -= n;
    }
    return {x, y};
}
inline ll mod_inv(ll a, ll mod) noexcept {
    ll b = mod;
    ll x = 1, u = 0;
    ll t;
    while (b) {
        t = a / b;
        std::swap(a -= t * b, b);
        std::swap(x -= t * u, u);
    }
    if (x < 0) x += mod;
    assert(a == 1);
    return x;
}
inline PLL ChineseRemainder(ll b1, ll m1, ll b2, ll m2) noexcept {
    const PLL p = extGCD(m1, m2);
    const ll g = p.first * m1 + p.second * m2;
    const ll l = m1 / g * m2;
    if ((b2 - b1) % g != 0) return PLL{-1, -1};
    const ll x = (b2 - b1) / g * p.first % (m2 / g);
    return {(x * m1 + b1 + l) % l, l};
}
PLL ChineseRemainders(const std::vector<ll>& b, const std::vector<ll>& m) noexcept {
    PLL res{0, 1};
    rep (i, b.size()) {
        res = ChineseRemainder(res.first, res.second, b[i], m[i]);
        if (res.first == -1) return res;
    }
    return res;
}

template<class F> class RecLambda {
  private:
    F f;
  public:
    explicit constexpr RecLambda(F&& f_) : f(std::forward<F>(f_)) {}
    template<class... Args> constexpr auto operator()(Args&&... args) const
            -> decltype(f(*this, std::forward<Args>(args)...)) {
        return f(*this, std::forward<Args>(args)...);
    }
};

template<class F> inline constexpr RecLambda<F> rec_lambda(F&& f) {
    return RecLambda<F>(std::forward<F>(f));
}

template<class Head, class... Tail> struct multi_dim_vector {
    using type = std::vector<typename multi_dim_vector<Tail...>::type>;
};
template<class T> struct multi_dim_vector<T> {
    using type = T;
};

template<class T, class Arg> constexpr std::vector<T> make_vec(int n, Arg&& arg) {
    return std::vector<T>(n, std::forward<Arg>(arg));
}
template<class T, class... Args>
constexpr typename multi_dim_vector<Args..., T>::type make_vec(int n, Args&&... args) {
    return typename multi_dim_vector<Args..., T>::type (n, make_vec<T>(std::forward<Args>(args)...));
}

inline CONSTEXPR int popcnt(ull x) {
#if __cplusplus >= 202002L
    return std::popcount(x);
#endif
    x = (x & 0x5555555555555555) + ((x >> 1 ) & 0x5555555555555555);
    x = (x & 0x3333333333333333) + ((x >> 2 ) & 0x3333333333333333);
    x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4 ) & 0x0f0f0f0f0f0f0f0f);
    x = (x & 0x00ff00ff00ff00ff) + ((x >> 8 ) & 0x00ff00ff00ff00ff);
    x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff);
    return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff);
}

template<class T, class Comp = std::less<T>> class presser {
  protected:
    std::vector<T> dat;
    Comp cmp;
    bool sorted = false;
  public:
    presser() : presser(Comp()) {}
    presser(const Comp& cmp) : cmp(cmp) {}
    presser(const std::vector<T>& vec, const Comp& cmp = Comp()) : dat(vec), cmp(cmp) {}
    presser(std::vector<T>&& vec, const Comp& cmp = Comp()) : dat(std::move(vec)), cmp(cmp) {}
    presser(std::initializer_list<T> il, const Comp& cmp = Comp()) : dat(il.begin(), il.end()), cmp(cmp) {}
    void reserve(int n) {
        assert(!sorted);
        dat.reserve(n);
    }
    void push_back(const T& v) {
        assert(!sorted);
        dat.push_back(v);
    }
    void push_back(T&& v) {
        assert(!sorted);
        dat.push_back(std::move(v));
    }
    void push(const std::vector<T>& vec) {
        assert(!sorted);
        const int n = dat.size();
        dat.resize(n + vec.size());
        rep (i, vec.size()) dat[n + i] = vec[i];
    }
    int build() {
        assert(!sorted); sorted = true;
        std::sort(all(dat), cmp);
        dat.erase(std::unique(all(dat), [&](const T& a, const T& b) -> bool {
            return !cmp(a, b) && !cmp(b, a);
        }), dat.end());
        return dat.size();
    }
    const T& operator[](int k) const& {
        assert(sorted);
        assert(0 <= k && k < (int)dat.size());
        return dat[k];
    }
    T operator[](int k) && {
        assert(sorted);
        assert(0 <= k && k < (int)dat.size());
        return std::move(dat[k]);
    }
    int get_index(const T& val) const {
        assert(sorted);
        return static_cast<int>(std::lower_bound(all(dat), val, cmp) - dat.begin());
    }
    std::vector<int> pressed(const std::vector<T>& vec) const {
        assert(sorted);
        std::vector<int> res(vec.size());
        rep (i, vec.size()) res[i] = get_index(vec[i]);
        return res;
    }
    void press(std::vector<T>& vec) const {
        static_assert(std::is_integral<T>::value, "template argument must be convertible from int type");
        assert(sorted);
        each_for (i : vec) i = get_index(i);
    }
    int size() const {
        assert(sorted);
        return dat.size();
    }
    const std::vector<T>& data() const& { return dat; }
    std::vector<T> data() && { return std::move(dat); }
};
#line 2 "library/data-struct/cht/ConvexHullTrickAddMonotone.hpp"

#line 4 "library/data-struct/cht/ConvexHullTrickAddMonotone.hpp"

template<class T = ll, bool is_max = false, class LargeT = __int128_t> class ConvexHullTrickAddMonotone {
  protected:
    struct Line {
        T a, b;
        bool is_query;
        int idx;
        mutable ll nxt_a, nxt_b;
        mutable bool has_nxt;
        T get(T x) const { return a * x + b; }
        T get_nxt(T x) const { return nxt_a * x + nxt_b; }
        Line() = default;
        Line(T a, T b, int id, bool i = false) : a(a), b(b), idx(id), is_query(i), has_nxt(false) {}
        friend bool operator<(const Line& lhs, const Line& rhs) {
            assert(!lhs.is_query || !rhs.is_query);
            if (lhs.is_query) {
                if (!rhs.has_nxt) return true;
                return rhs.get(lhs.a) < rhs.get_nxt(lhs.a);
            }
            if (rhs.is_query) {
                if (!lhs.has_nxt) return false;
                return lhs.get(rhs.a) > lhs.get_nxt(rhs.a);
            }
            return lhs.a == rhs.a ? lhs.b < rhs.b : lhs.a < rhs.a;
        }
    };
    int line_count = 0;
    std::deque<Line> que;
    bool is_necessary(const typename std::deque<Line>::iterator& itr) {
        if (itr != que.begin()     && itr->a == prev(itr)->a) return itr->b < prev(itr)->b;
        if (itr != prev(que.end()) && itr->a == next(itr)->a) return itr->b < next(itr)->b;
        if (itr == que.begin() || itr == prev(que.end())) return true;
        return (LargeT)(itr->b - prev(itr)->b) * (next(itr)->a - itr->a)
            <  (LargeT)(itr->b - next(itr)->b) * (prev(itr)->a - itr->a);
    }
  public:
    ConvexHullTrickAddMonotone() = default;
    int add_line(T a, T b) {
        if IF_CONSTEXPR (is_max) a = - a, b = - b;
        typename std::deque<Line>::iterator itr;
        if (que.empty() || que.back().a <= a) {
            que.emplace_back(a, b, line_count);
            itr = prev(que.end());
        }
        else {
            assert(a <= que.front().a);
            que.emplace_front(a, b, line_count);
            itr = que.begin();
        }
        if (!is_necessary(itr)) {
            que.erase(itr);
            return line_count++;
        }
        while (itr != que.begin() && !is_necessary(prev(itr))) {
            que.pop_back(); que.pop_back();
            que.emplace_back(a, b, line_count);
            itr = prev(que.end());
        }
        while (itr != prev(que.end()) && !is_necessary(next(itr))) {
            que.pop_front(); que.pop_front();
            que.emplace_front(a, b, line_count);
            itr = que.begin();
        }
        if (itr != que.begin()) {
            prev(itr)->nxt_a = itr->a;
            prev(itr)->nxt_b = itr->b;
            prev(itr)->has_nxt = true;
        }
        if (itr != prev(que.end())) {
            itr->nxt_a = next(itr)->a;
            itr->nxt_b = next(itr)->b;
            itr->has_nxt = true;
        }
        else itr->has_nxt = false;
        return line_count++;
    }
    Line get_min_line(T x) const {
        auto itr = lower_bound(all(que), Line{x, 0, -1, true});
        Line res{*itr};
        if IF_CONSTEXPR (is_max) res.a = - res.a, res.b = - res.b;
        return res;
    }
    T get_min(T x) const { return get_min_line(x).get(x); }
    Line dec_get_min_line(T x) {
        while (que.size() > 1 && que.begin()->get(x) > next(que.begin())->get(x)) que.pop_front();
        Line res{que.front()};
        if IF_CONSTEXPR (is_max) res.a = - res.a, res.b = - res.b;
        return res;
    }
    T dec_get_min(T x) { return dec_get_min_line(x).get(x); }
    Line inc_get_min_line(T x) {
        while (que.size() > 1 && prev(que.end())->get(x) > prev(que.end(), 2)->get(x)) que.pop_back();
        Line res{que.back()};
        if IF_CONSTEXPR (is_max) res.a = - res.a, res.b = - res.b;
        return res;
    }
    T inc_get_min(T x) { return inc_get_min_line(x).get(x); }
    bool empty() const { return que.empty(); }
};

/**
 * @brief ConvexHullTrickAddMonotone
 * @docs docs/ConvexHullTrickAddMonotone.md
 */
#line 3 "main.cpp"

using namespace std;

int main() {
    ll n, k; cin >> n >> k;
    vector<ll> a(n); cin >> a;
    vector<ll> r(n + 1);
    rep (i, n) r[i + 1] = r[i] + a[i];
    vector<ll> b(n + 1, -inf);
    vector<vector<int>> c(k + 2, vector<int>(n + 1, -1));
    b[0] = 0;
    rep (j, k + 1) {
        vector<ll> d(n + 1, -inf);
        ConvexHullTrickAddMonotone<ll, true> cht;
        cht.add_line(0, b[0]);
        reps (i, n) {
            auto l = cht.inc_get_min_line(r[i]);
            d[i] = l.get(r[i]);
            c[j + 1][i] = l.idx;
            cht.add_line(r[i], b[i] - r[i] * r[i]);
        }
        b = d;
    }
    cout << b[n] << endl;
    vector<ll> ans(k);
    {
        int x = n;
        rrep (i, k + 2, 2) {
            ans[i - 2] = c[i][x];
            x = c[i][x];
        }
    }
    cout << ans << endl;
}

Compilation message (stderr)

library/data-struct/cht/ConvexHullTrickAddMonotone.hpp: In instantiation of 'ConvexHullTrickAddMonotone<T, is_max, LargeT>::Line::Line(T, T, int, bool) [with T = long long int; bool is_max = true; LargeT = __int128]':
/usr/include/c++/10/ext/new_allocator.h:150:4:   required from 'void __gnu_cxx::new_allocator<_Tp>::construct(_Up*, _Args&& ...) [with _Up = ConvexHullTrickAddMonotone<long long int, true>::Line; _Args = {long long int&, long long int&, int&}; _Tp = ConvexHullTrickAddMonotone<long long int, true>::Line]'
/usr/include/c++/10/bits/alloc_traits.h:512:17:   required from 'static void std::allocator_traits<std::allocator<_CharT> >::construct(std::allocator_traits<std::allocator<_CharT> >::allocator_type&, _Up*, _Args&& ...) [with _Up = ConvexHullTrickAddMonotone<long long int, true>::Line; _Args = {long long int&, long long int&, int&}; _Tp = ConvexHullTrickAddMonotone<long long int, true>::Line; std::allocator_traits<std::allocator<_CharT> >::allocator_type = std::allocator<ConvexHullTrickAddMonotone<long long int, true>::Line>]'
/usr/include/c++/10/bits/deque.tcc:170:30:   required from 'std::deque<_Tp, _Alloc>::reference std::deque<_Tp, _Alloc>::emplace_back(_Args&& ...) [with _Args = {long long int&, long long int&, int&}; _Tp = ConvexHullTrickAddMonotone<long long int, true>::Line; _Alloc = std::allocator<ConvexHullTrickAddMonotone<long long int, true>::Line>; std::deque<_Tp, _Alloc>::reference = ConvexHullTrickAddMonotone<long long int, true>::Line&]'
library/data-struct/cht/ConvexHullTrickAddMonotone.hpp:45:29:   required from 'int ConvexHullTrickAddMonotone<T, is_max, LargeT>::add_line(T, T) [with T = long long int; bool is_max = true; LargeT = __int128]'
main.cpp:17:29:   required from here
library/data-struct/cht/ConvexHullTrickAddMonotone.hpp:10:13: warning: 'ConvexHullTrickAddMonotone<long long int, true>::Line::idx' will be initialized after [-Wreorder]
library/data-struct/cht/ConvexHullTrickAddMonotone.hpp:9:14: warning:   'bool ConvexHullTrickAddMonotone<long long int, true>::Line::is_query' [-Wreorder]
library/data-struct/cht/ConvexHullTrickAddMonotone.hpp:16:9: warning:   when initialized here [-Wreorder]

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