結果

問題 No.1710 Minimum OR is X
ユーザー keijak
提出日時 2021-10-16 01:56:46
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 41 ms / 2,000 ms
コード長 4,626 bytes
コンパイル時間 3,891 ms
コンパイル使用メモリ 383,912 KB
最終ジャッジ日時 2025-01-25 01:29:17
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
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ファイルパターン 結果
sample AC * 3
other AC * 30
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

diff # 

#include <bits/stdc++.h>
#define REP_(i, a_, b_, a, b, ...) \
  for (int i = (a), END_##i = (b); i < END_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using i64 = long long;
#include <atcoder/modint>
using Mint = atcoder::modint998244353;
std::ostream &operator<<(std::ostream &os, const Mint &m) {
  return os << m.val();
}

#include <boost/multiprecision/cpp_int.hpp>
using Int = boost::multiprecision::checked_cpp_int;
namespace multip = boost::multiprecision;

template<typename T, typename U>
inline bool chmax(T &a, U b) {
  return a < b and ((a = std::move(b)), true);
}
template<typename T, typename U>
inline bool chmin(T &a, U b) {
  return a > b and ((a = std::move(b)), true);
}
template<typename T>
inline int ssize(const T &a) {
  return (int) a.size();
}

template<class T>
inline std::ostream &print_one(const T &x, char endc) {
  if constexpr (std::is_same_v<T, bool>) {
    return std::cout << (x ? "Yes" : "No") << endc;
  } else {
    return std::cout << x << endc;
  }
}
template<class T>
inline std::ostream &print(const T &x) { return print_one(x, '\n'); }
template<typename T, typename... Ts>
std::ostream &print(const T &head, Ts... tail) {
  return print_one(head, ' '), print(tail...);
}
inline std::ostream &print() { return std::cout << '\n'; }

template<typename Container>
std::ostream &print_seq(const Container &a, std::string_view sep = " ",
                        std::string_view ends = "\n",
                        std::ostream &os = std::cout) {
  auto b = std::begin(a), e = std::end(a);
  for (auto it = std::begin(a); it != e; ++it) {
    if (it != b) os << sep;
    os << *it;
  }
  return os << ends;
}

template<typename T, typename = void>
struct is_iterable : std::false_type {};
template<typename T>
struct is_iterable<T, std::void_t<decltype(std::begin(std::declval<T>())),
                                  decltype(std::end(std::declval<T>()))>>
    : std::true_type {
};

template<typename T, typename = std::enable_if_t<
    is_iterable<T>::value && !std::is_same<T, std::string>::value>>
std::ostream &operator<<(std::ostream &os, const T &a) {
  return print_seq(a, ", ", "", (os << "{")) << "}";
}

struct VersatileInput {
  template<typename T>
  operator T() const {
    T x;
    std::cin >> x;
    return x;
  }
  struct Sized {
    std::size_t n;
    template<typename T>
    operator T() const {
      T x(n);
      for (auto &e: x) std::cin >> e;
      return x;
    }
  };
  Sized operator()(std::size_t n) const { return {n}; }
} const in;

inline void check(bool cond, const char *message = "!ERROR!") {
  if (not cond) throw std::runtime_error(message);
}

#ifdef MY_DEBUG
#include "debug_dump.hpp"
#else
#define DUMP(...)
#define cerr if(false)std::cerr
#endif

using namespace std;

template<class T = Mint>
struct Factorials {
  // factorials and inverse factorials.
  std::vector<T> fact, ifact;

  // n: max cached value.
  Factorials(int n) : fact(n + 1), ifact(n + 1) {
    assert(n >= 0);
    assert(n < T::mod());
    fact[0] = 1;
    for (int i = 1; i <= n; ++i) {
      fact[i] = fact[i - 1] * i;
    }
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i) {
      ifact[i - 1] = ifact[i] * i;
    }
  }

  // Combination (nCk)
  T C(int n, int k) const {
    if (k < 0 || k > n) return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};

template<typename T>
std::vector<T> pow_seq(int n, int base = 2) {
  assert(n >= 0 and base > 0);
  std::vector<T> p(n + 1);
  p[0] = 1;
  for (int i = 0; i < n; ++i) {
    p[i + 1] = p[i] * base;
  }
  return p;
}

auto solve() {
  const int n = in, m = in, K = in;
  string X = in;
  Factorials fs(n);
  auto dp = vector(2, vector(n + 1, Mint(0)));
  dp[0][n] = 1;
  auto pow2 = pow_seq<Mint>(n);
  REP(i, m) {
    if (X[i] == '1') {
      REP(j, K, n + 1) {
        if (dp[0][j].val() == 0) continue;
        Mint q = 0;
        REP(t, K) q += fs.C(j, t);
        if (q.val() == 0) continue;
        dp[1][j] += dp[0][j] * pow2[n - j] * q;
      }
    } else {
      REP(j, K, n + 1) {
        if (dp[0][j].val() == 0) continue;
        auto q = dp[0][j] * pow2[n - j];
        for (int j2 = j; j2 >= K; --j2) {
          dp[1][j2] += q * fs.C(j, j2);
        }
      }
    }
    dp[0].swap(dp[1]);
    dp[1].assign(n + 1, 0);
  }
  Mint ans;
  for (int i = K; i <= n; ++i) {
    ans += dp[0][i];
  }
  return ans;
}

int main() {
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  cout << std::fixed << std::setprecision(18);
  const int T = 1;//in;
  REP(t, T) {
    auto ans = solve();
    print(ans);
  }
}
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