#998880 (C++17) No.1867 Partitions and Inversions

提出ソース

結果

問題	No.1867 Partitions and Inversions
ユーザー	NyaanNyaan
提出日時	2024-08-02 01:46:21
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,727 ms / 5,000 ms
コード長	16,247 bytes
コンパイル時間	3,081 ms
コンパイル使用メモリ	267,644 KB
実行使用メモリ	50,048 KB
最終ジャッジ日時	2024-08-02 01:47:46
合計ジャッジ時間	69,157 ms
ジャッジサーバーID （参考情報）	judge1 / judge2

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 6,812 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	1,671 ms 49,916 KB
testcase_03	AC	1,702 ms 50,048 KB
testcase_04	AC	1,725 ms 49,920 KB
testcase_05	AC	1,657 ms 49,920 KB
testcase_06	AC	1,653 ms 49,920 KB
testcase_07	AC	1,717 ms 49,920 KB
testcase_08	AC	1,624 ms 50,048 KB
testcase_09	AC	1,600 ms 50,048 KB
testcase_10	AC	1,641 ms 50,044 KB
testcase_11	AC	1,659 ms 50,048 KB
testcase_12	AC	1,656 ms 49,920 KB
testcase_13	AC	1,671 ms 49,920 KB
testcase_14	AC	1,637 ms 50,048 KB
testcase_15	AC	1,658 ms 49,920 KB
testcase_16	AC	1,694 ms 49,920 KB
testcase_17	AC	1,674 ms 50,048 KB
testcase_18	AC	1,681 ms 49,920 KB
testcase_19	AC	1,674 ms 49,920 KB
testcase_20	AC	1,652 ms 49,920 KB
testcase_21	AC	1,663 ms 50,048 KB
testcase_22	AC	1,620 ms 50,048 KB
testcase_23	AC	1,727 ms 49,920 KB
testcase_24	AC	1,681 ms 49,920 KB
testcase_25	AC	1,682 ms 50,048 KB
testcase_26	AC	1,668 ms 50,048 KB
testcase_27	AC	1,676 ms 49,920 KB
testcase_28	AC	1,644 ms 50,044 KB
testcase_29	AC	1,695 ms 49,920 KB
testcase_30	AC	1,727 ms 50,048 KB
testcase_31	AC	1,683 ms 50,048 KB
testcase_32	AC	2 ms 6,944 KB
testcase_33	AC	1 ms 6,944 KB
testcase_34	AC	2 ms 6,944 KB
testcase_35	AC	2 ms 6,940 KB
testcase_36	AC	2 ms 6,940 KB
testcase_37	AC	1 ms 6,940 KB
testcase_38	AC	28 ms 6,940 KB
testcase_39	AC	29 ms 6,944 KB
testcase_40	AC	28 ms 6,944 KB
testcase_41	AC	29 ms 6,944 KB
testcase_42	AC	28 ms 6,940 KB
testcase_43	AC	582 ms 27,136 KB
testcase_44	AC	622 ms 27,136 KB
testcase_45	AC	598 ms 27,264 KB
testcase_46	AC	598 ms 27,136 KB
testcase_47	AC	606 ms 27,264 KB
testcase_48	AC	586 ms 27,136 KB
testcase_49	AC	582 ms 27,264 KB
testcase_50	AC	614 ms 27,264 KB
testcase_51	AC	592 ms 27,136 KB
testcase_52	AC	626 ms 27,264 KB
testcase_53	AC	629 ms 27,264 KB
testcase_54	AC	585 ms 27,264 KB
testcase_55	AC	585 ms 27,136 KB
testcase_56	AC	609 ms 27,136 KB
testcase_57	AC	580 ms 27,136 KB
testcase_58	AC	613 ms 27,136 KB
testcase_59	AC	573 ms 27,136 KB
testcase_60	AC	602 ms 27,136 KB
testcase_61	AC	583 ms 27,264 KB
testcase_62	AC	594 ms 27,264 KB
testcase_63	AC	1,528 ms 50,048 KB
testcase_64	AC	2 ms 6,940 KB
testcase_65	AC	2 ms 6,944 KB
testcase_66	AC	2 ms 6,940 KB
testcase_67	AC	950 ms 50,048 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

/**
 * date   : 2024-08-02 01:46:13
 * author : Nyaan
 */

#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 <tr2/dynamic_bitset>
#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>
using minpq = priority_queue<T, vector<T>, greater<T>>;

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(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan


// bit operation

namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(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(); }


//



using namespace std;

// Line : T operator(ll) を定義する
template <typename Line, bool MINIMIZE = true, bool RANGE_GET = false>
struct LiChaoTree {
  using T = decltype(Line{}(0));

  vector<long long> xs;
  vector<Line> dat;
  vector<pair<int, T>> val;  // (評価点(座圧後), 評価した値)
  int n, size;
  T inf;

  LiChaoTree(const vector<long long>& _xs, Line I) { init(_xs, I); }
  LiChaoTree(int _n, Line I) {
    vector<long long> _xs(_n);
    for (int i = 0; i < _n; i++) _xs[i] = i;
    init(_xs, I);
  }

  int get_idx(long long x) {
    return lower_bound(begin(xs), end(xs), x) - begin(xs);
  }

  void add_line(Line f) { return apply(1, f); }

  // [xl, xr) 半開
  void add_segment(long long xl, long long xr, Line f) {
    xl = get_idx(xl), xr = get_idx(xr);
    if (xl == xr) return;
    xl += size, xr += size;
    int l = xl, r = xr;
    for (; xl < xr; xl >>= 1, xr >>= 1) {
      if (xl & 1) apply(xl++, f);
      if (xr & 1) apply(--xr, f);
    }
    if (RANGE_GET) {
      for (int i = 1; i <= __builtin_ctz(size); i++) {
        if (((l >> i) << i) != l) update(l >> i);
        if (((r >> i) << i) != r) update((r - 1) >> i);
      }
    }
  }

  // (値, Line) の組
  pair<T, Line> get_val(long long x) {
    int i = get_idx(x);
    assert(0 <= i and i < n);
    Line f = dat[0];
    T fx = f(x);
    for (i += size; i; i >>= 1) {
      Line g = dat[i];
      T gx = g(x);
      if ((MINIMIZE && gx < fx) || (!MINIMIZE && gx > fx)) {
        f = g, fx = gx;
      }
    }
    return {fx, f};
  }

  // [xl, xr) 半開
  // 返り値 : (評価点 x, x で評価した値)
  // 追加する直線に単調性がある時のみ使用可能
  // RANGE_GET を true にする必要がある
  pair<long long, T> get(long long xl, long long xr) {
    assert(RANGE_GET == true);
    xl = get_idx(xl), xr = get_idx(xr);
    assert(xl != xr);
    pair<int, T> best = _get(1, 0, size, xl, xr);
    assert(best.first != -1);
    return make_pair(xs[best.first], best.second);
  }

 private:
  void init(const vector<long long>& _xs, Line I) {
    xs = _xs;
    sort(begin(xs), end(xs));
    xs.erase(unique(begin(xs), end(xs)), end(xs));
    n = xs.size();
    int lg = 1;
    while ((1 << lg) < n) lg++;
    size = 1 << lg;
    dat.resize(size * 2, I);
    inf = (MINIMIZE ? numeric_limits<T>::max() : numeric_limits<T>::min()) / 2;
    val.resize(size * 2, make_pair(-1, inf));
    for (int i = size * 2 - 1; i; i--) update(i);
  }

  T eval(int i, Line f) { return f(xs[min(i, n - 1)]); }

  void apply(int i, Line f) {
    int upper_bit = 31 - __builtin_clz(i);
    int l = (size >> upper_bit) * (i - (1 << upper_bit));
    int r = l + (size >> upper_bit);
    Line g = dat[i];
    T fl = eval(l, f), fr = eval(r - 1, f);
    T gl = eval(l, g), gr = eval(r - 1, g);
    bool bl = (MINIMIZE ? fl < gl : fl > gl);
    bool br = (MINIMIZE ? fr < gr : fr > gr);
    if (!bl and !br) return;
    if (bl and br) {
      dat[i] = f;
    } else {
      int m = (l + r) / 2;
      T fm = eval(m, f), gm = eval(m, g);
      bool bm = (MINIMIZE ? fm < gm : fm > gm);
      if (bm) {
        dat[i] = f;
        f = g;
        apply(i * 2 + bl, f);
      } else {
        apply(i * 2 + 1 - bl, f);
      }
    }
    update(i);
  }

  void update(int i) {
    if constexpr (RANGE_GET) {
      if (i == 0) return;
      int upper_bit = 31 - __builtin_clz(i);
      int l = (size >> upper_bit) * (i - (1 << upper_bit));
      int r = l + (size >> upper_bit);
      val[i] = make_pair(-1, inf);
      auto chmin = [&](int x, T y) {
        if (MINIMIZE ? y < val[i].second : val[i].second < y) {
          val[i] = make_pair(x, y);
        }
      };
      if (l < n) {
        chmin(l, eval(l, dat[i]));
        chmin(min(r - 1, n - 1), eval(r - 1, dat[i]));
      }
      if (i < size) {
        chmin(val[i * 2 + 0].first, val[i * 2 + 0].second);
        chmin(val[i * 2 + 1].first, val[i * 2 + 1].second);
      }
    }
  }

  pair<int, T> _get(int idx, int l, int r, int xl, int xr) {
    assert(l < r and xl < xr);
    assert(l <= xl and xr <= r);
    if (xl == l and xr == r) return val[idx];

    pair<int, T> best = make_pair(-1, inf);
    auto chmin = [&](int x, T y) {
      if (MINIMIZE ? y < best.second : y > best.second) {
        best = make_pair(x, y);
      }
    };

    chmin(xl, eval(xl, dat[idx]));
    chmin(xr - 1, eval(xr - 1, dat[idx]));

    int m = (l + r) / 2;
    if (xl < m) {
      auto [x, y] = _get(idx * 2 + 0, l, m, xl, min(xr, m));
      chmin(x, y);
    }
    if (m < xr) {
      auto [x, y] = _get(idx * 2 + 1, m, r, max(xl, m), xr);
      chmin(x, y);
    }
    return best;
  }
};


using namespace Nyaan;

constexpr int nmax = 3030;
ll cost[nmax][nmax];
ll dp[nmax], newdp[nmax];

struct F {
  int i;
  ll operator()(int j) {
    if (i == -1) return inf;
    return dp[i] - cost[i][j];
  }
};

void q() {
  ini(N);
  vi a(N);
  in(a);

  repr(L, N) reg(R, L, N + 1) {
    if (R - L <= 1) continue;
    cost[L][R] = cost[L + 1][R] + cost[L][R - 1] - cost[L + 1][R - 1] +
                 (a[L] > a[R - 1]);
    trc(L, R, cost[L][R]);
  }

  fill(begin(dp), end(dp), inf);
  dp[0] = 0;

  rep1(n, N) {
    LiChaoTree<F, true> lct(N + 1, F{-1});
    rep(i, N + 1) {
      newdp[i] = lct.get_val(i).fi;
      lct.add_line(F{int(i)});
    }
    swap(dp, newdp);
    trc(vi{dp, dp + N + 1}, cost[0][N]);
    out(cost[0][N] + dp[N]);
  }
}

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