#918442 (C++14) No.2498 OX Operations

提出ソース

結果

問題	No.2498 OX Operations
ユーザー	👑 hos.lyric
提出日時	2023-10-06 21:57:23
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2,113 ms / 4,000 ms
コード長	11,061 bytes
コンパイル時間	1,550 ms
コンパイル使用メモリ	118,660 KB
実行使用メモリ	9,896 KB
最終ジャッジ日時	2024-07-26 16:05:22
合計ジャッジ時間	22,659 ms
ジャッジサーバーID （参考情報）	judge1 / 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 6,812 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,944 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 6,944 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,940 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	5 ms 6,940 KB
testcase_12	AC	10 ms 6,944 KB
testcase_13	AC	8 ms 6,944 KB
testcase_14	AC	11 ms 6,940 KB
testcase_15	AC	1,230 ms 9,084 KB
testcase_16	AC	1,945 ms 9,780 KB
testcase_17	AC	809 ms 8,504 KB
testcase_18	AC	1,483 ms 9,280 KB
testcase_19	AC	1,025 ms 8,796 KB
testcase_20	AC	1,655 ms 9,512 KB
testcase_21	AC	2,064 ms 9,828 KB
testcase_22	AC	1,328 ms 6,940 KB
testcase_23	AC	1,249 ms 6,940 KB
testcase_24	AC	2,098 ms 9,880 KB
testcase_25	AC	2,107 ms 9,896 KB
testcase_26	AC	2,113 ms 9,896 KB

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ソースコード

raw source code

#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 <limits>
#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> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
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; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
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::pull(const T &l, const T &r)  should pull two intervals.
template <class T> struct SegmentTreeRange {
  int logN, n;
  vector<T> ts;
  SegmentTreeRange() : logN(0), n(0) {}
  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; ) pull(u);
  }

  inline void push(int u) {
    ts[u].push(ts[u << 1], ts[u << 1 | 1]);
  }
  inline void pull(int u) {
    ts[u].pull(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) pull(aa);
      } else {
        if ((aa << h) != a) pull(aa);
        if ((bb << h) != b) pull(bb);
      }
    }
  }

  // Calculates the product for [a, b).
  T get(int a, int b) {
    assert(0 <= a); assert(a <= b); assert(b <= n);
    if (a == b) return T();
    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);
      }
    }
    T prodL, prodR, t;
    for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) {
      if (aa & 1) { t.pull(prodL, ts[aa++]); prodL = t; }
      if (bb & 1) { t.pull(ts[--bb], prodR); prodR = t; }
    }
    t.pull(prodL, prodR);
    return t;
  }

  // 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);
          if (!(ts[a <<= 1].*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);
          if (!(ts[(b <<= 1) - 1].*f)(args...)) --b;
        }
        return b - n - 1;
      }
      --b;
      if (!(b & (b - 1))) return -1;
    }
  }
};

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

constexpr int E = 30;

struct Func {
  int ps[2];
  Func() : ps{0, (1 << E) - 1} {}
  void mul(const Func &g) {
    for (int s = 0; s < 2; ++s) {
      int q = 0;
      for (int e = 0; e < E; ++e) {
        q |= g.ps[ps[s] >> e & 1] & 1 << e;
      }
      ps[s] = q;
    }
  }
};
struct Node {
  Func f, lz;
  Node() : f(), lz() {}
  void push(Node &l, Node &r) {
    l.apply(lz);
    r.apply(lz);
    lz = Func();
  }
  void pull(const Node &l, const Node &r) {
    //
  }
  void apply(const Func &g) {
    f.mul(g);
    lz.mul(g);
  }
};


int N, Q;
vector<int> M;
vector<char> C;
vector<int> L, R, X;

int main() {
  for (; ~scanf("%d%d", &N, &Q); ) {
    M.resize(N);
    for (int i = 0; i < N; ++i) {
      scanf("%d", &M[i]);
    }
    C.resize(Q);
    L.resize(Q);
    R.resize(Q);
    X.resize(Q);
    for (int q = 0; q < Q; ++q) {
      scanf(" %c%d%d%d", &C[q], &L[q], &R[q], &X[q]);
      --L[q];
    }
    
    SegmentTreeRange<Node> seg(N);
    for (int q = 0; q < Q; ++q) {
      Func g;
      if (C[q] == 'o') {
        g.ps[0] |= X[q];
        g.ps[1] |= X[q];
      } else if (C[q] == 'x') {
        g.ps[0] ^= X[q];
        g.ps[1] ^= X[q];
      } else {
        assert(false);
      }
      seg.ch(L[q], R[q], &Node::apply, g);
    }
    
    vector<Func> fs(N);
    for (int i = 0; i < N; ++i) {
      seg.get(i, i + 1);
      fs[i] = seg.at(i).f;
// cerr<<i<<": "<<fs[i].ps[0]<<" "<<fs[i].ps[1]<<endl;
    }
    
    vector<Mint> hs(E + 1, 1);
    for (int i = 0; i < N; ++i) {
      Mint dp[E + 1][2][E + 1] = {};
      dp[E][0][0] = 1;
      for (int e = E; --e >= 0; ) {
        const int m = M[i] >> e & 1;
        for (int s = 0; s < 2; ++s) for (int a = 0; a < 2; ++a) if (s || a <= m) {
          const int b = fs[i].ps[a] >> e & 1;
          const int ss = (s || a < m) ? 1 : 0;
          for (int k = 0; k < E - e; ++k) {
            dp[e][ss][k + b] += dp[e + 1][s][k];
          }
        }
      }
      Mint sum = 0;
      for (int k = 0; k <= E; ++k) {
        for (int s = 0; s < 2; ++s) {
          sum += dp[0][s][k];
        }
// if(N<=3)cerr<<i<<" "<<k<<": "<<sum<<endl;
        hs[k] *= sum;
      }
    }
    for (int k = E; k > 0; --k) {
      hs[k] -= hs[k - 1];
    }
    Mint ans = 0;
    for (int k = 0; k <= E; ++k) {
      ans += hs[k] * k;
    }
    printf("%u\n", ans.x);
  }
  return 0;
}

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結果

テストケース

ソースコード