#869017 (C++17) No.2304 Distinct Elements

提出ソース

結果

問題	No.2304 Distinct Elements
ユーザー	haruki_K
提出日時	2023-05-12 23:17:04
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	60 ms / 3,000 ms
コード長	13,649 bytes
コンパイル時間	3,064 ms
コンパイル使用メモリ	218,644 KB
実行使用メモリ	9,216 KB
最終ジャッジ日時	2024-05-06 13:17:36
合計ジャッジ時間	6,499 ms
ジャッジサーバーID （参考情報）	judge2 / judge3

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	54 ms 9,088 KB
testcase_05	AC	54 ms 9,028 KB
testcase_06	AC	54 ms 9,088 KB
testcase_07	AC	54 ms 9,088 KB
testcase_08	AC	55 ms 9,088 KB
testcase_09	AC	59 ms 9,216 KB
testcase_10	AC	58 ms 9,092 KB
testcase_11	AC	59 ms 9,092 KB
testcase_12	AC	59 ms 9,088 KB
testcase_13	AC	58 ms 8,960 KB
testcase_14	AC	2 ms 5,376 KB
testcase_15	AC	2 ms 5,376 KB
testcase_16	AC	2 ms 5,376 KB
testcase_17	AC	2 ms 5,376 KB
testcase_18	AC	2 ms 5,376 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	AC	2 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	2 ms 5,376 KB
testcase_24	AC	2 ms 5,376 KB
testcase_25	AC	2 ms 5,376 KB
testcase_26	AC	2 ms 5,376 KB
testcase_27	AC	2 ms 5,376 KB
testcase_28	AC	2 ms 5,376 KB
testcase_29	AC	44 ms 8,568 KB
testcase_30	AC	5 ms 5,376 KB
testcase_31	AC	36 ms 6,448 KB
testcase_32	AC	46 ms 8,624 KB
testcase_33	AC	5 ms 5,376 KB
testcase_34	AC	47 ms 8,752 KB
testcase_35	AC	52 ms 9,064 KB
testcase_36	AC	5 ms 5,376 KB
testcase_37	AC	19 ms 5,376 KB
testcase_38	AC	57 ms 8,936 KB
testcase_39	AC	58 ms 9,092 KB
testcase_40	AC	35 ms 8,568 KB
testcase_41	AC	19 ms 5,892 KB
testcase_42	AC	46 ms 9,092 KB
testcase_43	AC	60 ms 8,960 KB
testcase_44	AC	43 ms 8,644 KB
testcase_45	AC	33 ms 6,396 KB
testcase_46	AC	27 ms 6,184 KB
testcase_47	AC	2 ms 5,376 KB
testcase_48	AC	2 ms 5,376 KB
testcase_49	AC	54 ms 9,092 KB
testcase_50	AC	58 ms 9,088 KB
testcase_51	AC	57 ms 9,088 KB
testcase_52	AC	52 ms 9,092 KB
testcase_53	AC	40 ms 9,088 KB
testcase_54	AC	50 ms 9,068 KB
testcase_55	AC	48 ms 8,964 KB
testcase_56	AC	47 ms 9,088 KB
testcase_57	AC	57 ms 9,092 KB
testcase_58	AC	54 ms 8,964 KB
testcase_59	AC	50 ms 9,092 KB
testcase_60	AC	2 ms 5,376 KB
testcase_61	AC	2 ms 5,376 KB

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ソースコード

raw source code

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
using pii = pair<int, int>;
#define rep(i, n) if (const int _rep_n = n; true) for (int i = 0; i < _rep_n; i++)
#define rep1(i, n) if (const int _rep_n = n; true) for (int i = 1; i <= _rep_n; i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#define oj_local(x, y) (y)
#else
#define dump(...) (void)(0)
#define debug if (0)
#define oj_local(x, y) (x)
#endif

template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> {
    vector<T> &data() { return this->c; }
    void clear() { this->c.clear(); }
};
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;

template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) {
    bool f = true;
    for (auto const& x : a) os << (f ? "" : " ") << x, f = false;
    return os;
}
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) {
    bool f = true;
    for (auto const& x : a) os << (f ? "" : " ") << x, f = false;
    return os;
}
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) {
    return os << p.first << " " << p.second;
}
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) {
    return is >> p.first >> p.second;
}
template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t) {
    bool f = true;
    apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t);
    return os;
}
template <class... T> istream& operator>>(istream& is, tuple<T...>& t) {
    apply([&](auto&&... x) { ((is >> x), ...); }, t);
    return is;
}
struct IOSetup {
    IOSetup() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
    }
} iosetup;

template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const {
        return F::operator()(*this, forward<T>(x)...);
    }
};
struct MakeFixPoint {
    template <class F> constexpr auto operator|(F&& f) const {
        return FixPoint<F>(forward<F>(f));
    }
};
#define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__)

template <class F> struct FixPoint_d : private F {
    const char* const name;
    constexpr FixPoint_d(F&& f, const char* name) : F(forward<F>(f)), name(name) {}
    template <class... T> constexpr auto operator()(T&&... x) const {
        auto ret = F::operator()(*this, forward<T>(x)...);
#ifdef LOCAL
        cerr << name << to_s(tuple(x...)) << " -> " << to_s(ret) << '\n';
#endif
        return ret;
    }
};
struct MakeFixPoint_d {
    const char* const name;
    MakeFixPoint_d(const char* name) : name(name) {}
    template <class F> constexpr auto operator|(F&& f) const {
        return FixPoint_d<F>(forward<F>(f), name);
    }
};
#ifdef LOCAL
#define def_d(name, ...) auto name = MakeFixPoint_d(#name) | [&](auto &&name, __VA_ARGS__)
#else
#define def_d def
#endif

template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) {
        return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...));
    }
};
template <class T> struct vec_impl<T, 0> {
    using type = T;
    static type make_v(T const& x = {}) { return x; }
};
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) {
    return vec_impl<T, d>::make_v(forward<Args>(args)...);
}
template <class T> void quit(T const& x) { cout << x << '\n'; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) {
    return x > (T)y ? x = (T)y, true : false;
}
template <class T, class U> constexpr bool chmax(T& x, U const& y) {
    return x < (T)y ? x = (T)y, true : false;
}
template <class It> constexpr auto sumof(It b, It e) {
    return accumulate(b, e, typename iterator_traits<It>::value_type{});
}
template <class T, class = decltype(begin(declval<T&>()))>
constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); }
template <class T, class = decltype(begin(declval<T&>()))>
constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); }
template <class T> constexpr T min(set<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(set<T> const& st) { assert(st.size()); return *prev(st.end()); }
template <class T> constexpr T min(multiset<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(multiset<T> const& st) { assert(st.size()); return *prev(st.end()); }
constexpr ll max(signed x, ll y) { return max<ll>(x, y); }
constexpr ll max(ll x, signed y) { return max<ll>(x, y); }
constexpr ll min(signed x, ll y) { return min<ll>(x, y); }
constexpr ll min(ll x, signed y) { return min<ll>(x, y); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T>
int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x) - begin(v); }
template <class C, class T>
int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x) - begin(v); }
constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
template <class Comp> vector<int> iota(int n, Comp comp) {
    vector<int> idx(n);
    iota(begin(idx), end(idx), 0);
    stable_sort(begin(idx), end(idx), comp);
    return idx;
}
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }
template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }
bool next_product(vector<int> &v, int m) {
    repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;
    return false;
}
bool next_product(vector<int> &v, vector<int> const& s) {
    repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;
    return false;
}
template <class Vec> int sort_unique(Vec &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class Vec, class Comp> int sort_unique(Vec &v, Comp comp) {
    sort(begin(v), end(v), comp);
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class It> auto prefix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(s.back() + *l++);
    return s;
}
template <class It> auto suffix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(*--r + s.back());
    reverse(s.begin(), s.end());
    return s;
}
template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_back(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }
template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }
template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }
template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }
template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }
template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class A, class B>
pair<vector<A>, vector<B>> unzip(vector<pair<A, B>> const& c) {
    vector<A> a;
    vector<B> b;
    for (auto const& [x, y] : c) {
        a.push_back(x);
        b.push_back(y);
    }
    return { a, b };
}
template <class A, class B>
pair<vector<A>, vector<B>> unzip(map<A, B> const& c) {
    vector<A> a;
    vector<B> b;
    for (auto const& [x, y] : c) {
        a.push_back(x);
        b.push_back(y);
    }
    return { a, b };
}
// <<<

// https://nyaannyaan.github.io/library/data-structure/slope-trick.hpp.html
struct SlopeTrick {
 private:
  using ll = long long;
  // x : 座標, c : 傾きの変化量
  struct P {
    ll x, c;
    P(ll _x, ll _c) : x(_x), c(_c) {}
    friend bool operator<(const P& a, const P& b) { return a.x < b.x; }
    friend bool operator>(const P& a, const P& b) { return a.x > b.x; }
  };
  ll addL, addR, min_y;
  priority_queue<P> L;
  priority_queue<P, vector<P>, greater<>> R;
  void pushL(ll x, ll c = 1) { L.emplace(x - addL, c); }
  void pushR(ll x, ll c = 1) { R.emplace(x - addR, c); }
  P getL() { return P{L.top().x + addL, L.top().c}; }
  P getR() { return P{R.top().x + addR, R.top().c}; }
  void popL() { L.pop(); }
  void popR() { R.pop(); }

 public:
  SlopeTrick() : addL(0), addR(0), min_y(0) {}

  // void debug() {
  //   cerr << "addL, addR, min_y : ";
  //   cerr << addL << ", " << addR << ", " << min_y << endl;

  //   auto LL{L};
  //   cerr << "L : ";
  //   while (!LL.empty()) {
  //     cerr << "( " << LL.top().x + addL << ", " << LL.top().c << " ), ";
  //     LL.pop();
  //   }
  //   cerr << endl;

  //   auto RR{R};
  //   cerr << "R : ";
  //   while (!RR.empty()) {
  //     cerr << "( " << RR.top().x + addR << ", " << RR.top().c << " ), ";
  //     RR.pop();
  //   }
  //   cerr << endl;

  //   cerr << "min : ";
  //   cerr << "( " << get_min().first << ", " << get_min().second << " )" << endl;
  // }

  // return {x, y} s.t. {argmin, min}
  pair<ll, ll> get_min() {
    ll x = L.empty() ? R.empty() ? 0 : getR().x : getL().x;
    return {x, min_y};
  }

  void shift_L(ll a) { addL += a; }
  void shift_R(ll a) { addR += a; }
  // f(x) <- f(x - a)
  void shift_x(ll a) { addL += a, addR += a; }
  // f(x) <- f(x) + a
  void shift_y(ll a) { min_y += a; }

  // add (x-a)_+   _____/
  void add_xma(ll a, ll c = 1) {
    ll used = 0;
    while (used < c && !L.empty()) {
      auto [X, C] = getL();
      if (X <= a) break;
      popL();
      ll tmp = min(c - used, C);
      pushR(X, tmp);
      if (C != tmp) pushL(X, C - tmp);
      min_y += (X - a) * tmp;
      used += tmp;
    }
    if (used) pushL(a, used);
    if (c - used) pushR(a, c - used);
  }

  // add (a-x)_+   \_____
  void add_amx(ll a, ll c = 1) {
    ll used = 0;
    while (used < c && !R.empty()) {
      auto [X, C] = getR();
      if (X >= a) break;
      popR();
      ll tmp = min(c - used, C);
      pushL(X, tmp);
      if (C != tmp) pushR(X, C - tmp);
      min_y += (a - X) * tmp;
      used += tmp;
    }
    if (used) pushR(a, used);
    if (c - used) pushL(a, c - used);
  }

  // add |x-a|     \____/
  void add_abs_xma(ll a, ll c = 1) { add_xma(a, c), add_amx(a, c); }

  //  chmin right side \_/ -> \__
  void chmin_right() { decltype(R){}.swap(R); }
  //  chmin left side  \_/ -> __/
  void chmin_left() { decltype(L){}.swap(L); }

  // destructive merge
  void merge(SlopeTrick& r) {
    if (L.size() + R.size() < r.L.size() + r.R.size()) swap(*this, r);
    while (!r.L.empty()) {
      auto [x, c] = r.getL();
      r.popL();
      add_amx(x, c);
    }
    while (!r.R.empty()) {
      auto [x, c] = r.getR();
      r.popR();
      add_xma(x, c);
    }
    shift_y(r.min_y);
  }

  // eval f(x) O(|L| + |R|) TODO : verify
  ll eval(ll x) {
    ll y = min_y;
    auto LL{L};
    while (!LL.empty()) {
      auto [X, C] = LL.top();
      X += addL;
      if(X < x) break;
      y += (X - x) * C;
      LL.pop();
    }
    auto RR{R};
    while (!RR.empty()) {
      auto [X, C] = RR.top();
      X += addR;
      if(x < X) break;
      y += (x - X) * C;
      RR.pop();
    }
    return y;
  }
};


int32_t main() {
    int n; cin >> n;
    vector<int> a(n); cin >> a;

    sort(all(a));

    SlopeTrick st;
    for (int e : a) {
        st.shift_x(1);
        st.chmin_right();
        st.add_amx(e);
        st.add_xma(e);
    }
    cout << st.get_min().snd << '\n';

}

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結果

テストケース

ソースコード