#677589 (C++17) No.1460 Max of Min

提出ソース

結果

問題	No.1460 Max of Min
ユーザー	NyaanNyaan
提出日時	2021-07-11 22:28:23
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	412 ms / 2,000 ms
コード長	14,018 bytes
コンパイル時間	2,817 ms
コンパイル使用メモリ	256,192 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-07-02 03:17:43
合計ジャッジ時間	15,825 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
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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 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	412 ms 5,376 KB
testcase_04	AC	405 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	406 ms 5,376 KB
testcase_07	AC	404 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	404 ms 5,376 KB
testcase_11	AC	404 ms 5,376 KB
testcase_12	AC	40 ms 5,376 KB
testcase_13	AC	168 ms 5,376 KB
testcase_14	AC	61 ms 5,376 KB
testcase_15	AC	30 ms 5,376 KB
testcase_16	AC	152 ms 5,376 KB
testcase_17	AC	74 ms 5,376 KB
testcase_18	AC	5 ms 5,376 KB
testcase_19	AC	79 ms 5,376 KB
testcase_20	AC	7 ms 5,376 KB
testcase_21	AC	14 ms 5,376 KB
testcase_22	AC	87 ms 5,376 KB
testcase_23	AC	4 ms 5,376 KB
testcase_24	AC	100 ms 5,376 KB
testcase_25	AC	3 ms 5,376 KB
testcase_26	AC	177 ms 5,376 KB
testcase_27	AC	31 ms 5,376 KB
testcase_28	AC	11 ms 5,376 KB
testcase_29	AC	97 ms 5,376 KB
testcase_30	AC	139 ms 5,376 KB
testcase_31	AC	81 ms 5,376 KB
testcase_32	AC	51 ms 5,376 KB
testcase_33	AC	13 ms 5,376 KB
testcase_34	AC	26 ms 5,376 KB
testcase_35	AC	10 ms 5,376 KB
testcase_36	AC	2 ms 5,376 KB
testcase_37	AC	30 ms 5,376 KB
testcase_38	AC	36 ms 5,376 KB
testcase_39	AC	22 ms 5,376 KB
testcase_40	AC	16 ms 5,376 KB
testcase_41	AC	12 ms 5,376 KB
testcase_42	AC	7 ms 5,376 KB
testcase_43	AC	48 ms 5,376 KB
testcase_44	AC	80 ms 5,376 KB
testcase_45	AC	4 ms 5,376 KB
testcase_46	AC	33 ms 5,376 KB
testcase_47	AC	42 ms 5,376 KB
testcase_48	AC	92 ms 5,376 KB
testcase_49	AC	66 ms 5,376 KB
testcase_50	AC	5 ms 5,376 KB
testcase_51	AC	54 ms 5,376 KB
testcase_52	AC	14 ms 5,376 KB
testcase_53	AC	29 ms 5,376 KB
testcase_54	AC	49 ms 5,376 KB
testcase_55	AC	108 ms 5,376 KB
testcase_56	AC	44 ms 5,376 KB
testcase_57	AC	80 ms 5,376 KB
testcase_58	AC	404 ms 5,376 KB
testcase_59	AC	78 ms 5,376 KB
testcase_60	AC	86 ms 5,376 KB
testcase_61	AC	49 ms 5,376 KB
testcase_62	AC	50 ms 5,376 KB
testcase_63	AC	3 ms 5,376 KB
testcase_64	AC	2 ms 5,376 KB
testcase_65	AC	110 ms 5,376 KB
testcase_66	AC	50 ms 5,376 KB
testcase_67	AC	42 ms 5,376 KB
testcase_68	AC	87 ms 5,376 KB
testcase_69	AC	72 ms 5,376 KB
testcase_70	AC	60 ms 5,376 KB
testcase_71	AC	102 ms 5,376 KB
testcase_72	AC	49 ms 5,376 KB
testcase_73	AC	48 ms 5,376 KB
testcase_74	AC	44 ms 5,376 KB
testcase_75	AC	44 ms 5,376 KB
testcase_76	AC	42 ms 5,376 KB
testcase_77	AC	43 ms 5,376 KB
testcase_78	AC	41 ms 5,376 KB
testcase_79	AC	43 ms 5,376 KB
testcase_80	AC	42 ms 5,376 KB
testcase_81	AC	41 ms 5,376 KB
testcase_82	AC	42 ms 5,376 KB
testcase_83	AC	42 ms 5,376 KB
testcase_84	AC	394 ms 5,376 KB
testcase_85	AC	393 ms 5,376 KB
testcase_86	AC	384 ms 5,376 KB
testcase_87	AC	398 ms 5,376 KB
testcase_88	AC	382 ms 5,376 KB
testcase_89	AC	402 ms 5,376 KB
testcase_90	AC	393 ms 5,376 KB
testcase_91	AC	402 ms 5,376 KB
testcase_92	AC	399 ms 5,376 KB
testcase_93	AC	385 ms 5,376 KB

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ソースコード

raw source code

/**
 *  date : 2021-07-11 22:28:19
 */

#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; }
};

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 T, T (*add)(T, T), T (*mul)(T, T), T (*I0)(), T (*I1)()>
struct semiring {
  T x;
  semiring() : x(I0()) {}
  semiring(T y) : x(y) {}
  static T id0() { return I0(); }
  static T id1() { return I1(); }

  semiring &operator+=(const semiring &p) {
    if (x == I0()) return *this = p;
    if (p.x == I0()) return *this;
    return *this = add(x, p.x);
  }

  semiring &operator*=(const semiring &p) {
    if (x == I0() || p.x == I0()) return *this = I0();
    if (x == I1()) return *this = p;
    if (p.x == I1()) return *this;
    return *this = mul(x, p.x);
  }

  semiring operator+(const semiring &p) const { return semiring(*this) += p; }
  semiring operator*(const semiring &p) const { return semiring(*this) *= p; }
  bool operator==(const semiring &p) const { return x == p.x; }
  bool operator!=(const semiring &p) const { return x != p.x; }
  friend ostream &operator<<(ostream &os, const semiring &p) {
    return os << p.x;
  }
};

template <typename rig, int N>
struct Mat {
  using Array = array<array<rig, N>, N>;
  Array A;

  Mat() {
    for (int i = 0; i < N; i++) A[i].fill(rig::id0());
  }
  int height() const { return N; }
  int width() const { return N; }
  inline const array<rig, N> &operator[](int k) const { return A[k]; }
  inline array<rig, N> &operator[](int k) { return A[k]; }

  static Mat I() {
    Mat m;
    for (int i = 0; i < N; i++) m[i][i] = rig::id1();
    return m;
  }

  Mat &operator+=(const Mat &B) {
    for (int i = 0; i < N; i++)
      for (int j = 0; j < N; j++) A[i][j] += B[i][j];
    return (*this);
  }

  Mat &operator*=(const Mat &B) {
    Mat C;
    for (int i = 0; i < N; i++)
      for (int k = 0; k < N; k++)
        for (int j = 0; j < N; j++) C[i][j] += A[i][k] * B[k][j];
    A.swap(C.A);
    return (*this);
  }

  Mat &operator^=(long long k) {
    Mat B = Mat::I();
    for (; k; *this *= *this, k >>= 1)
      if (k & 1) B *= *this;
    A.swap(B.A);
    return (*this);
  }

  Mat operator+(const Mat &B) const { return (Mat(*this) += B); }
  Mat operator*(const Mat &B) const { return (Mat(*this) *= B); }
  Mat operator^(long long k) const { return (Mat(*this) ^= k); }

  friend ostream &operator<<(ostream &os, Mat &p) {
    for (int i = 0; i < N; i++) {
      os << "[";
      for (int j = 0; j < N; j++) {
        os << p[i][j].x << (j == N - 1 ? "]\n" : ",");
      }
    }
    return (os);
  }
};

/**
 * @brief 半環ライブラリ
 * @docs docs/math/semiring.md
 */


template <typename rig>
struct LinearRecursive {
  vector<rig> C;
  int N;
  LinearRecursive(const vector<rig>& c) : C(c), N(c.size()) {}

  rig calc(vector<rig> a, long long k) {
    assert(a.size() == C.size());
    if (k < (int)a.size()) return a[k];
    auto coeff = get_coeff(k);
    rig res = rig::id0();
    for (int i = 0; i < N; i++) res += a[i] * coeff[N - 1 - i];
    return res;
  }

  vector<rig> get_coeff(long long k) {
    if (k == 0) {
      vector<rig> b(N, rig::id0());
      b.back() = rig::id1();
      return b;
    }
    auto half = get_coeff(k / 2);
    doubling(half);
    if (k & 1) increment(half);
    return half;
  }

  void increment(vector<rig>& b) {
    vector<rig> v{begin(b) + 1, end(b)};
    v.push_back(rig::id0());
    for (int i = 0; i < N; i++) v[i] += b[0] * C[i];
    b.swap(v);
  }

  void doubling(vector<rig>& b) {
    vector<rig> v(N, rig::id0()), bb{b};
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        v[j] += bb[j] * b[N - 1 - i];
      }
      increment(bb);
    }
    swap(b, v);
  }
};

using namespace Nyaan;

using U = long long;
U add(U a, U b) { return max(a, b); }
U mul(U a, U b) { return min(a, b); }
U i0() { return -infLL; }
U i1() { return infLL; }
using rig = semiring<U, add, mul, i0, i1>;

void Nyaan::solve() {
  inl(K, N);
  V<rig> a(K), b(K);
  for (auto& x : a) cin >> x.x;
  for (auto& x : b) cin >> x.x;
  reverse(all(b));
  LinearRecursive<rig> lr(b);
  out(lr.calc(a, N));
}

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結果

テストケース

ソースコード