#725296 (C++17) No.1786 Maximum Suffix Median (Online)

• 問題: No.1786 Maximum Suffix Median (Online)
• ユーザー: NyaanNyaan
• 提出日時: 2021-12-20 14:31:45
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 861 ms / 2,000 ms
• コード長: 19,355 bytes
• コンパイル時間: 2,586 ms
• コンパイル使用メモリ: 254,364 KB
• 実行使用メモリ: 12,928 KB
• 最終ジャッジ日時: 2024-09-15 15:18:52
• 合計ジャッジ時間: 17,434 ms
• ジャッジサーバーID （参考情報）: judge2 / judge1

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	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	815 ms; 11,648 KB
testcase_09	AC	475 ms; 9,216 KB
testcase_10	AC	543 ms; 9,728 KB
testcase_11	AC	410 ms; 8,576 KB
testcase_12	AC	793 ms; 12,288 KB
testcase_13	AC	608 ms; 11,648 KB
testcase_14	AC	417 ms; 9,600 KB
testcase_15	AC	520 ms; 10,496 KB
testcase_16	AC	501 ms; 10,752 KB
testcase_17	AC	422 ms; 9,472 KB
testcase_18	AC	847 ms; 12,800 KB
testcase_19	AC	856 ms; 12,800 KB
testcase_20	AC	836 ms; 12,800 KB
testcase_21	AC	850 ms; 12,800 KB
testcase_22	AC	861 ms; 12,928 KB
testcase_23	AC	148 ms; 10,624 KB
testcase_24	AC	101 ms; 8,576 KB
testcase_25	AC	169 ms; 12,032 KB
testcase_26	AC	193 ms; 11,008 KB
testcase_27	AC	172 ms; 10,240 KB
testcase_28	AC	205 ms; 11,392 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	2 ms; 5,376 KB
testcase_31	AC	241 ms; 12,800 KB
testcase_32	AC	180 ms; 12,800 KB

ソースコード

/**
 *  date : 2021-12-20 14:31:32
 */

#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;

  T &x() { return first; }
  const T &x() const { return first; }
  U &y() { return second; }
  const U &y() const { return 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;
  }
  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; }

  P operator*(int r) const { return {first * r, second * 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;
}

}  // 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;
}

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...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
  cout << t;
  outr(u...);
}

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

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (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(); }

//

template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
          E (*h)(E, E), T (*ti)(), E (*ei)()>
struct RBSTSegmentTree {
  struct Node {
    Node *l, *r;
    I index;
    T key, sum;
    E lazy;
    int cnt;
    Node(const I &i, const T &t = ti())
        : l(), r(), index(i), key(t), sum(t), lazy(ei()), cnt(1) {}
  };

 protected:
  using Ptr = Node *;
  // 呼んだあと必ず update すること！
  template <typename... Args>
  inline Ptr my_new(Args... args) {
    return new Node(args...);
  }
  inline void my_del(Ptr t) { delete t; }

  inline int count(const Ptr t) const { return t ? t->cnt : 0; }

  static uint64_t rng() {
    static uint64_t x_ = 88172645463325252ULL;
    return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull;
  }

  Ptr merge(Ptr l, Ptr r) {
    if (!l || !r) return l ? l : r;
    if (int((rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) {
      push(l);
      l->r = merge(l->r, r);
      return update(l);
    } else {
      push(r);
      r->l = merge(l, r->l);
      return update(r);
    }
  }

  Ptr build(int l, int r, const vector<pair<I, T>> &dat) {
    if (l == r) return nullptr;
    if (l + 1 == r) return my_new(dat[l].first, dat[l].second);
    int m = (l + r) / 2;
    return merge(build(l, m, dat), build(m, r, dat));
  };

  void push(Ptr t) {
    if (!t) return;
    if (t->lazy != ei()) {
      if (t->l) propagate(t->l, t->lazy);
      if (t->r) propagate(t->r, t->lazy);
      t->lazy = ei();
    }
  }

  Ptr update(Ptr t) {
    if (!t) return t;
    push(t);
    t->cnt = 1;
    t->sum = t->key;
    if (t->l) t->cnt += t->l->cnt, t->sum = f(t->l->sum, t->sum);
    if (t->r) t->cnt += t->r->cnt, t->sum = f(t->sum, t->r->sum);
    return t;
  }

  void propagate(Ptr t, const E &x) {
    if (!t) return;
    t->lazy = h(t->lazy, x);
    t->key = g(t->key, x);
    t->sum = g(t->sum, x);
  }

  // [k 未満, k 以上]
  pair<Ptr, Ptr> split_left(Ptr t, I k) {
    if (!t) return {nullptr, nullptr};
    push(t);
    if (k == t->index) {
      Ptr tl = t->l;
      t->l = nullptr;
      return {tl, update(t)};
    } else if (k < t->index) {
      auto s = split_left(t->l, k);
      t->l = s.second;
      return {s.first, update(t)};
    } else {
      auto s = split_left(t->r, k);
      t->r = s.first;
      return {update(t), s.second};
    }
  }

  // [k 未満, k, k 超過]
  array<Ptr, 3> split_by_index(Ptr t, I k) {
    if (!t) return {{nullptr, nullptr, nullptr}};
    push(t);
    if (k == t->index) {
      Ptr tl = t->l, tr = t->r;
      t->l = t->r = nullptr;
      return {{tl, update(t), tr}};
    } else if (k < t->index) {
      auto s = split_by_index(t->l, k);
      t->l = s[2];
      return {{s[0], s[1], update(t)}};
    } else {
      auto s = split_by_index(t->r, k);
      t->r = s[0];
      return {{update(t), s[1], s[2]}};
    }
  }

  // t を根とする木の上で最小の index は？ (t が空の場合は failed)
  I _min_index(Ptr t, const I &failed) {
    if (t == nullptr) return failed;
    while (t->l) t = t->l;
    return t->index;
  }

  // t を根とする木の上で最大の index は？ (t が空の場合は failed)
  I _max_index(Ptr t, const I &failed) {
    if (t == nullptr) return failed;
    while (t->r) t = t->r;
    return t->index;
  }

  // t を根とする木のうち、[0, i の区間 fold が true になる最大の i は何か？
  // exclusive かつ (空 または[0,右]が真の場合) の場合は failed(inf)
  // inclusive かつ (空 または[0,0] が偽の場合) の場合は failed
  template <typename C>
  I _max_right(Ptr t, C check, const I &failed, bool exclusive) {
    if (t == nullptr) return failed;
    push(t);
    Ptr now = t;
    T prod_now = ti();
    while (true) {
      if (now->l != nullptr) {
        push(now->l);
        auto pl = f(prod_now, now->l->sum);
        if (check(pl)) {
          prod_now = pl;
        } else {
          now = now->l;
          continue;
        }
      }
      auto pl = f(prod_now, now->key);
      if (!check(pl)) {
        return exclusive ? now->index : _max_index(t->l, failed);
      }
      prod_now = pl;
      if (now->r == nullptr) {
        return exclusive ? failed : now->index;
      }
      push(now->r);
      now = now->r;
    }
  }

  // t を根とする木のうち、i, inf) の区間 fold が true になる最小の i は何か？
  // inclusive かつ (空 または 存在しない) 場合は failed
  // exlucisve かつ (空 または [左, inf) が真) の場合は failed
  template <typename C>
  I _min_left(Ptr t, C check, const I &failed, bool inclusive) {
    if (t == nullptr) return failed;
    push(t);
    Ptr now = t;
    T prod_now = ti();
    while (true) {
      if (now->r != nullptr) {
        push(now->r);
        auto pr = f(now->r->sum, prod_now);
        if (check(pr)) {
          prod_now = pr;
        } else {
          now = now->r;
          continue;
        }
      }
      auto pr = f(now->key, prod_now);
      if (!check(pr)) {
        return inclusive ? _min_index(now->r, failed) : now->index;
      }
      prod_now = pr;
      if (now->l == nullptr) {
        return inclusive ? now->index : failed;
      }
      push(now->l);
      now = now->l;
    }
  }

  void inner_dump(Ptr t) {
    push(t);
    if (t->l) inner_dump(t->l);
    cerr << "## i = " << t->index << ", ";
    cerr << "\tkey = " << t->key << ", ";
    cerr << "\tsum = " << t->sum << ", ";
    cerr << "\tchild = ";
    cerr << "( " << (t->l ? to_string(t->l->index) : "nil");
    cerr << ", ";
    cerr << (t->r ? to_string(t->r->index) : "nil");
    cerr << " )" << endl;
    if (t->r) inner_dump(t->r);
  }

 public:
  Ptr root;

  RBSTSegmentTree() : root(nullptr) {}
  RBSTSegmentTree(const vector<T> xs, const vector<I> &is = {}) {
    if (!is.empty()) assert(xs.size() == is.size());
    int n = xs.size();
    vector<pair<I, T>> dat(n);
    for (int i = 0; i < n; i++) dat[i] = {is.empty() ? i : is[i], xs[i]};
    root = build(0, n, dat);
  }

  // 1 点 値の書き換え
  void set_val(I i, T x) {
    auto s = split_by_index(root, i);
    if (s[1] == nullptr) {
      s[1] = my_new(i, x);
    } else {
      s[1]->key = x;
    }
    root = merge(merge(s[0], update(s[1])), s[2]);
  }

  // 1 点取得
  T get_val(I i) {
    auto s = split_by_index(root, i);
    T res = s[1] ? s[1]->key : ti();
    root = merge(merge(s[0], s[1]), s[2]);
    return res;
  }

  // 頂点の削除
  void erase(I i) {
    auto s = split_by_index(root, i);
    if (s[1]) my_del(s[1]);
    root = merge(s[0], s[2]);
  }

  // 範囲作用
  void apply(I l, I r, const E &e) {
    auto [x, aux] = split_left(root, l);
    auto [y, z] = split_left(aux, r);
    propagate(y, e);
    root = merge(merge(x, y), z);
  }

  // 範囲取得
  T fold(I l, I r) {
    auto [x, aux] = split_left(root, l);
    auto [y, z] = split_left(aux, r);
    T res = y ? y->sum : ti();
    root = merge(merge(x, y), z);
    return res;
  }

  // n 未満の i のうち、[i, n) の区間 fold が true になる最小の i は何か？
  // (存在しない場合は failed を返す)
  template <typename C>
  I min_left(I n, C check, I failed) {
    assert(check(ti()) == true);
    auto [x, y] = split_left(root, n);
    I res = _min_left(x, check, failed, true);
    root = merge(x, y);
    return res;
  }

  // n 未満の i のうち、(i, n) の区間 fold が true になる最小の i は何か？
  // (空だったり (左端, n) が 真の場合は minus_infty を返す)
  template <typename C>
  I min_left_exclusive(I n, C check, I minus_infty) {
    assert(check(ti()) == true);
    auto [x, y] = split_left(root, n);
    I res = _min_left(x, check, minus_infty, false);
    root = merge(x, y);
    return res;
  }

  // n 以上の i のうち、[n, i) の区間 fold が true になる最大の i は何か？
  // (空だったり [n, 右端] が true の場合は infty を返す)
  template <typename C>
  I max_right(I n, C check, I infty) {
    assert(check(ti()) == true);
    auto [x, y] = split_left(root, n);
    I res = _max_right(y, check, infty, true);
    root = merge(x, y);
    return res;
  }

  // n 以上の i のうち、[n, i] の区間 fold が true になる最大の i は何か？
  // (存在しない場合は failed を返す)
  template <typename C>
  I max_right_inclusive(I n, C check, I failed) {
    assert(check(ti()) == true);
    auto [x, y] = split_left(root, n);
    I res = _max_right(y, check, failed, false);
    root = merge(x, y);
    return res;
  }

  void dump() { inner_dump(root); }
};

//
using namespace Nyaan;

int f(int a, int b) { return max(a, b); }
int g(int a, int b) { return a + b; }
int ti() { return -inf; }
int ei() { return 0; }
using Seg = RBSTSegmentTree<ll, int, int, f, g, g, ti, ei>;

void Nyaan::solve() {
  inl(N);
  int pre = 0;
  Seg seg;
  rep(i, N) {
    inl(A);
    A ^= pre;
    int mx = seg.fold(A, infLL);
    int sc = max(0, mx + 1);
    seg.apply(0, A, 1);
    seg.apply(A, infLL, -1);
    seg.set_val(A, sc);
    ll ans = seg.min_left_exclusive(
        infLL, [](int x) { return x < 0; }, -infLL);
    out(ans);
    pre = ans;
  }
}