#868449 (C++17) No.2304 Distinct Elements

提出ソース

結果

問題	No.2304 Distinct Elements
ユーザー	NyaanNyaan
提出日時	2023-05-12 21:32:21
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	62 ms / 3,000 ms
コード長	12,891 bytes
コンパイル時間	2,934 ms
コンパイル使用メモリ	262,532 KB
実行使用メモリ	9,216 KB
最終ジャッジ日時	2024-05-06 11:10:43
合計ジャッジ時間	6,356 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

このコードへのチャレンジ
（要ログイン）

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 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	1 ms 5,376 KB
testcase_04	AC	62 ms 9,216 KB
testcase_05	AC	61 ms 9,088 KB
testcase_06	AC	48 ms 9,088 KB
testcase_07	AC	48 ms 9,092 KB
testcase_08	AC	50 ms 9,092 KB
testcase_09	AC	54 ms 9,092 KB
testcase_10	AC	52 ms 9,092 KB
testcase_11	AC	52 ms 9,084 KB
testcase_12	AC	53 ms 9,092 KB
testcase_13	AC	53 ms 9,088 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	1 ms 5,376 KB
testcase_20	AC	1 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	1 ms 5,376 KB
testcase_24	AC	2 ms 5,376 KB
testcase_25	AC	1 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	41 ms 8,688 KB
testcase_30	AC	5 ms 5,376 KB
testcase_31	AC	33 ms 6,452 KB
testcase_32	AC	43 ms 8,624 KB
testcase_33	AC	4 ms 5,376 KB
testcase_34	AC	43 ms 8,784 KB
testcase_35	AC	48 ms 8,936 KB
testcase_36	AC	4 ms 5,376 KB
testcase_37	AC	17 ms 5,376 KB
testcase_38	AC	53 ms 9,064 KB
testcase_39	AC	52 ms 8,960 KB
testcase_40	AC	31 ms 8,564 KB
testcase_41	AC	17 ms 6,148 KB
testcase_42	AC	41 ms 9,092 KB
testcase_43	AC	55 ms 9,084 KB
testcase_44	AC	39 ms 8,644 KB
testcase_45	AC	30 ms 6,272 KB
testcase_46	AC	25 ms 6,056 KB
testcase_47	AC	2 ms 5,376 KB
testcase_48	AC	2 ms 5,376 KB
testcase_49	AC	49 ms 9,088 KB
testcase_50	AC	52 ms 9,088 KB
testcase_51	AC	50 ms 9,092 KB
testcase_52	AC	48 ms 9,092 KB
testcase_53	AC	37 ms 9,092 KB
testcase_54	AC	44 ms 9,088 KB
testcase_55	AC	46 ms 9,088 KB
testcase_56	AC	47 ms 9,092 KB
testcase_57	AC	53 ms 8,956 KB
testcase_58	AC	49 ms 9,092 KB
testcase_59	AC	45 ms 9,092 KB
testcase_60	AC	1 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

/**
 *  date : 2023-05-12 21:32:17
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N,F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}

template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug

#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//

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;
  }
};

/**
 * @brief Slope Trick
 */

using namespace Nyaan;

void q() {
  inl(N);
  vl A(N);
  in(A);
  sort(all(A));

  // dp[x] : 最後の要素が x に置かれている, とする
  //
  // ndp[x]
  // = min_{y < x} dp[y] + |x - A_i|
  SlopeTrick st;

  rep(i, N) {
    st.chmin_right();
    st.shift_L(1);
    st.add_abs_xma(A[i]);
  }
  out(st.get_min().se);
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}

yukicoder

結果

テストケース

ソースコード