#708804 (C++14) No.1712 Read and Pile

提出ソース

結果

問題	No.1712 Read and Pile
ユーザー	👑 hos.lyric
提出日時	2021-10-22 21:08:21
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	TLE (最新) AC (最初)
実行時間	-
コード長	15,724 bytes
コンパイル時間	3,074 ms
コンパイル使用メモリ	148,040 KB
実行使用メモリ	59,020 KB
最終ジャッジ日時	2024-09-23 04:04:08
合計ジャッジ時間	41,109 ms
ジャッジサーバーID （参考情報）	judge1 / 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 6,820 KB
testcase_01	AC	2 ms 6,812 KB
testcase_02	AC	2 ms 6,816 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,944 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	1,538 ms 28,728 KB
testcase_09	TLE	-
testcase_10	AC	1,472 ms 28,812 KB
testcase_11	AC	1,911 ms 48,356 KB
testcase_12	AC	1,314 ms 28,852 KB
testcase_13	AC	1,645 ms 28,348 KB
testcase_14	AC	1,520 ms 28,772 KB
testcase_15	AC	1,891 ms 28,744 KB
testcase_16	AC	1,965 ms 29,296 KB
testcase_17	AC	1,706 ms 29,012 KB
testcase_18	AC	1,779 ms 28,368 KB
testcase_19	AC	1,628 ms 27,928 KB
testcase_20	AC	1,716 ms 28,704 KB
testcase_21	TLE	-
testcase_22	AC	1,750 ms 47,812 KB
testcase_23	TLE	-
testcase_24	TLE	-
testcase_25	TLE	-
testcase_26	TLE	-
testcase_27	TLE	-
testcase_28	AC	1,449 ms 28,512 KB
testcase_29	TLE	-
testcase_30	AC	1,823 ms 48,932 KB
testcase_31	AC	1,132 ms 51,656 KB
testcase_32	AC	1,008 ms 49,376 KB
testcase_33	TLE	-
testcase_34	TLE	-
testcase_35	TLE	-
testcase_36	TLE	-
testcase_37	TLE	-
testcase_38	AC	2 ms 6,940 KB
testcase_39	AC	13 ms 6,944 KB
testcase_40	AC	16 ms 6,944 KB
testcase_41	AC	19 ms 6,944 KB
testcase_42	AC	24 ms 6,940 KB

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ソースコード

raw source code

#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#pragma GCC target ("avx")

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;


// T: monoid representing information of an interval.
//   T()  should return the identity.
//   T(S s)  should represent a single element of the array.
//   T::push(T &l, T &r)  should push the lazy update.
//   T::merge(const T &l, const T &r)  should merge two intervals.
template <class T> struct SegmentTreeRange {
  int logN, n;
  vector<T> ts;
  SegmentTreeRange() {}
  explicit SegmentTreeRange(int n_) {
    for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
    ts.resize(n << 1);
  }
  template <class S> explicit SegmentTreeRange(const vector<S> &ss) {
    const int n_ = ss.size();
    for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
    ts.resize(n << 1);
    for (int i = 0; i < n_; ++i) at(i) = T(ss[i]);
    build();
  }
  T &at(int i) {
    return ts[n + i];
  }
  void build() {
    for (int u = n; --u; ) merge(u);
  }

  inline void push(int u) {
    ts[u].push(ts[u << 1], ts[u << 1 | 1]);
  }
  inline void merge(int u) {
    ts[u].merge(ts[u << 1], ts[u << 1 | 1]);
  }

  // Applies T::f(args...) to [a, b).
  template <class F, class... Args>
  void ch(int a, int b, F f, Args &&... args) {
    assert(0 <= a); assert(a <= b); assert(b <= n);
    if (a == b) return;
    a += n; b += n;
    for (int h = logN; h; --h) {
      const int aa = a >> h, bb = b >> h;
      if (aa == bb) {
        if ((aa << h) != a || (bb << h) != b) push(aa);
      } else {
        if ((aa << h) != a) push(aa);
        if ((bb << h) != b) push(bb);
      }
    }
    for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
      if (aa & 1) (ts[aa++].*f)(args...);
      if (bb & 1) (ts[--bb].*f)(args...);
    }
    for (int h = 1; h <= logN; ++h) {
      const int aa = a >> h, bb = b >> h;
      if (aa == bb) {
        if ((aa << h) != a || (bb << h) != b) merge(aa);
      } else {
        if ((aa << h) != a) merge(aa);
        if ((bb << h) != b) merge(bb);
      }
    }
  }

  // Calculates T::f(args...) of a monoid type for [a, b).
  //   op(-, -)  should calculate the product.
  //   e()  should return the identity.
  template <class Op, class E, class F, class... Args>
#if __cplusplus >= 201402L
  auto
#else
  decltype((std::declval<T>().*F())())
#endif
  get(int a, int b, Op op, E e, F f, Args &&... args) {
    assert(0 <= a); assert(a <= b); assert(b <= n);
    if (a == b) return e();
    a += n; b += n;
    for (int h = logN; h; --h) {
      const int aa = a >> h, bb = b >> h;
      if (aa == bb) {
        if ((aa << h) != a || (bb << h) != b) push(aa);
      } else {
        if ((aa << h) != a) push(aa);
        if ((bb << h) != b) push(bb);
      }
    }
    auto prodL = e(), prodR = e();
    for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
      if (aa & 1) prodL = op(prodL, (ts[aa++].*f)(args...));
      if (bb & 1) prodR = op((ts[--bb].*f)(args...), prodR);
    }
    return op(prodL, prodR);
  }

  // Find min b s.t. T::f(args...) returns true,
  // when called for the partition of [a, b) from left to right.
  //   Returns n + 1 if there is no such b.
  template <class F, class... Args>
  int findRight(int a, F f, Args &&... args) {
    assert(0 <= a); assert(a <= n);
    if ((T().*f)(args...)) return a;
    if (a == n) return n + 1;
    a += n;
    for (int h = logN; h; --h) push(a >> h);
    for (; ; a >>= 1) {
      if (a & 1) {
        if ((ts[a].*f)(args...)) {
          for (; a < n; ) {
            push(a);
            a <<= 1;
            if (!(ts[a].*f)(args...)) ++a;
          }
          return a - n + 1;
        }
        ++a;
        if (!(a & (a - 1))) return n + 1;
      }
    }
  }

  // Find max a s.t. T::f(args...) returns true,
  // when called for the partition of [a, b) from right to left.
  //   Returns -1 if there is no such a.
  template <class F, class... Args>
  int findLeft(int b, F f, Args &&... args) {
    assert(0 <= b); assert(b <= n);
    if ((T().*f)(args...)) return b;
    if (b == 0) return -1;
    b += n;
    for (int h = logN; h; --h) push((b - 1) >> h);
    for (; ; b >>= 1) {
      if ((b & 1) || b == 2) {
        if ((ts[b - 1].*f)(args...)) {
          for (; b <= n; ) {
            push(b - 1);
            b <<= 1;
            if (!(ts[b - 1].*f)(args...)) --b;
          }
          return b - n - 1;
        }
        --b;
        if (!(b & (b - 1))) return -1;
      }
    }
  }
};

////////////////////////////////////////////////////////////////////////////////

struct Node0 {
  int sz, sum;
  int lz;
  Node0() : sz(0), sum(0), lz(0) {}
  void push(Node0 &l, Node0 &r) {
    l.add(lz);
    r.add(lz);
    lz = 0;
  }
  void merge(const Node0 &l, const Node0 &r) {
    sz = l.sz + r.sz;
    sum = l.sum + r.sum;
  }
  void add(int val) {
    sum += sz * val;
    lz += val;
  }
  int getSum() const {
    return sum;
  }
};

int getSum(SegmentTreeRange<Node0> &seg, int a, int b) {
  return seg.get(a, b,
                 [&](int l, int r) -> int { return l + r; },
                 [&]() -> int { return 0; },
                 &Node0::getSum);
}


struct Node {
  Mint x[2], y[3];
  int lz;
  Node() : x{}, y{}, lz(0) {}
  void push(Node &l, Node &r) {
    l.add(lz);
    r.add(lz);
    lz = 0;
  }
  void merge(const Node &l, const Node &r) {
    x[0] = l.x[0] + r.x[0];
    x[1] = l.x[1] + r.x[1];
    y[0] = l.y[0] + r.y[0];
    y[1] = l.y[1] + r.y[1];
    y[2] = l.y[2] + r.y[2];
  }
  void add(int val) {
    x[1] += val * x[0];
    y[2] += val * (2 * y[1] + val * y[0]);
    y[1] += val * y[0];
    lz += val;
  }
  Node getSum() const {
    return *this;
  }
};

Node getSum(SegmentTreeRange<Node> &seg, int a, int b) {
  return seg.get(a, b,
                 [&](const Node &l, const Node &r) -> Node { Node t; t.merge(l, r); return t; },
                 [&]() -> Node { return Node(); },
                 &Node::getSum);
}


int N, M;
vector<int> A;

int main() {
  for (; ~scanf("%d%d", &N, &M); ) {
    A.resize(N + M);
    for (int i = 0; i < N; ++i) {
      A[i] = N - 1 - i;
    }
    for (int i = N; i < N + M; ++i) {
      scanf("%d", &A[i]);
      --A[i];
    }
// cerr<<"A = ";pv(A.begin(),A.end());
    
    if (N == 1) {
      printf("%u\n", Mint(M).x);
      continue;
    }
    if (N == 2) {
      Mint ans2 = M;
      for (int i = N; i < N + M; ++i) {
        for (int a = 0; a < 2; ++a) for (int b = 0; b < 2; ++b) if (a != b) {
          Mint tmp = 1;
          tmp *= ((A[i - 1] == -2) ? Mint(2).inv() : (A[i - 1] == a) ? 1 : 0);
          tmp *= ((A[i] == -2) ? Mint(2).inv() : (A[i] == b) ? 1 : 0);
          ans2 += tmp;
        }
      }
      printf("%u\n", ans2.x);
      continue;
    }
    
    vector<int> ls(N + M + 1, 0);
    for (int i = 0; i < N + M; ++i) {
      ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0);
    }
// cerr<<"ls = ";pv(ls.begin(),ls.end());
    
    Mint ans[2][2] = {};
    
    vector<Mint> pw0(N + M + 1), pw1(N + M + 1), pw2(N + M + 1), invPw1(N + M + 1), invPw2(N + M + 1);
    pw0[0] = pw1[0] = pw2[0] = invPw1[0] = invPw2[0] = 1;
    pw0[1] = Mint(N);
    pw1[1] = Mint(N - 1);
    pw2[1] = Mint(N - 2);
    invPw1[1] = Mint(N - 1).inv();
    invPw2[1] = Mint(N - 2).inv();
    for (int i = 2; i <= N + M; ++i) {
      pw0[i] = pw0[i - 1] * pw0[1];
      pw1[i] = pw1[i - 1] * pw1[1];
      pw2[i] = pw2[i - 1] * pw2[1];
      invPw1[i] = invPw1[i - 1] * invPw1[1];
      invPw2[i] = invPw2[i - 1] * invPw2[1];
    }
    {
      vector<int> app(N, 0);
      SegmentTreeRange<Node0> seg0(N + M);
      SegmentTreeRange<Node> seg(N + M);
      for (int i = 0; i < N + M; ++i) {
        seg0.at(i).sz = 1;
        if (A[i] == -2) {
          seg.at(i).x[0] = pw0[ls[i]] * invPw1[ls[i + 1]];
          seg.at(i).y[0] = pw0[ls[i]] * invPw2[ls[i + 1]];
        }
      }
      seg0.build();
      seg.build();
      for (int i = 0; i < N + M; ++i) {
        // get
        if (i >= N) {
          if (A[i] != -2) {
            {
              const int m = getSum(seg0, app[A[i]], app[A[i]] + 1);
              Mint tmp = 0;
              tmp += pw1[ls[i] - ls[app[A[i]] + 1]] * Mint(1 + m);
              tmp += Mint(N - 1 - m) * (pw1[ls[i] - ls[app[A[i]] + 1]] - pw2[ls[i] - ls[app[A[i]] + 1]]);
              tmp *= pw0[ls[app[A[i]]] + (ls[N + M] - ls[i + 1])];
              ans[0][0] += tmp;
            }
            {
              const Node res = getSum(seg, app[A[i]], i);
              Mint tmp = 0;
              tmp += pw1[ls[i]] * (res.x[0] + res.x[1]);
              tmp += pw1[ls[i]] * (Mint(N - 1) * res.x[0] - res.x[1])
                   - pw2[ls[i]] * (Mint(N - 1) * res.y[0] - res.y[1]);
              tmp *= pw0[ls[N + M] - ls[i + 1]];
              ans[1][0] += tmp;
            }
          } else {
            {
              const Node res = getSum(seg, 0, i);
              Mint tmp = 0;
              tmp += pw1[ls[i]] * (Mint(N) * res.x[0] + Mint(N - 1) * res.x[1]);
              tmp += pw1[ls[i]] * (Mint(N) * Mint(N - 1) * res.x[0] - Mint(2 * N - 1) * res.x[1])
                   - pw2[ls[i]] * (Mint(N) * Mint(N - 1) * res.y[0] - Mint(2 * N - 1) * res.y[1] + res.y[2]);
              tmp *= pw0[ls[N + M] - ls[i + 1]];
              ans[1][1] += tmp;
            }
          }
        }
        // add
        if (A[i] != -2) {
          seg0.ch(app[A[i]], i, &Node0::add, 1);
          seg.ch(app[A[i]], i, &Node::add, 1);
          app[A[i]] = i;
        }
      }
    }
    
    {
      reverse(A.begin(), A.end());
      for (int i = 0; i < N + M; ++i) {
        ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0);
      }
// cerr<<"A = ";pv(A.begin(),A.end());
// cerr<<"ls = ";pv(ls.begin(),ls.end());
      vector<int> app(N, 0);
      SegmentTreeRange<Node> seg(N + M);
      for (int i = 0; i < N + M; ++i) {
        if (A[i] == -2) {
          seg.at(i).x[0] = pw0[ls[i]] * invPw1[ls[i + 1]];
          seg.at(i).y[0] = pw0[ls[i]] * invPw2[ls[i + 1]];
        }
      }
      seg.build();
      for (int i = 0; i < M + N; ++i) {
        // get
        {
          if (A[i] != -2) {
            {}
            {
              const Node res = getSum(seg, app[A[i]], i);
              Mint tmp = 0;
              tmp += pw1[ls[i]] * (res.x[0] + res.x[1]);
              tmp += pw1[ls[i]] * (Mint(N - 1) * res.x[0] - res.x[1])
                   - pw2[ls[i]] * (Mint(N - 1) * res.y[0] - res.y[1]);
              tmp *= pw0[ls[N + M] - ls[i + 1]];
              ans[0][1] += tmp;
            }
          } else {
            {}
          }
        }
        // add
        if (A[i] != -2) {
          seg.ch(app[A[i]], i, &Node::add, 1);
          app[A[i]] = i;
        }
      }
      reverse(A.begin(), A.end());
      for (int i = 0; i < N + M; ++i) {
        ls[i + 1] = ls[i] + ((A[i] == -2) ? 1 : 0);
      }
    }
    
    printf("%u\n", ((ans[0][0] + ans[0][1] + ans[1][0] + ans[1][1]) / Mint(N).pow(ls[N + M])).x);
    
#ifdef LOCAL
    Mint brt[2][2] = {};
    for (int i = 0; i < N + M; ++i) for (int j = N; j < N + M; ++j) {
      if (i < j) {
        set<int> as(A.begin() + i + 1, A.begin() + j);
        as.erase(-2);
        const int m = as.size();
        Mint tmp = 0;
        tmp += Mint(N - 1).pow(ls[j] - ls[i + 1]) * Mint(1 + m);
        tmp += Mint(N - 1 - m) * (Mint(N - 1).pow(ls[j] - ls[i + 1]) - Mint(N - 2).pow(ls[j] - ls[i + 1]));
        tmp *= Mint(N).pow(ls[i] + (ls[N + M] - ls[j + 1]));
        if (A[i] != -2) {
          if (A[j] != -2) {
            if (A[i] == A[j] && as.find(A[i]) == as.end()) {
              brt[0][0] += tmp;
            }
          } else {
            if (as.find(A[i]) == as.end()) {
              brt[0][1] += tmp;
            }
          }
        } else {
          if (A[j] != -2) {
            if (as.find(A[j]) == as.end()) {
              brt[1][0] += tmp;
            }
          } else {
            brt[1][1] += Mint(N - m) * tmp;
          }
        }
      }
    }
    cerr << "brt = " << ((brt[0][0] + brt[0][1] + brt[1][0] + brt[1][1]) / Mint(N).pow(ls[N + M])) << "; "
         << brt[0][0] << " " << brt[0][1] << " " << brt[1][0] << " " << brt[1][1] << endl;
    cerr << "ans = " << ((ans[0][0] + ans[0][1] + ans[1][0] + ans[1][1]) / Mint(N).pow(ls[N + M])) << "; "
         << ans[0][0] << " " << ans[0][1] << " " << ans[1][0] << " " << ans[1][1] << endl;
#endif
  }
  return 0;
}

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結果

テストケース

ソースコード