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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#681342#9489. 0100 Insertionnhuang685WA 99ms4808kbC++238.2kb2024-10-27 05:38:202024-10-27 05:38:21

Judging History

你现在查看的是最新测评结果

  • [2024-10-27 05:38:21]
  • 评测
  • 测评结果:WA
  • 用时:99ms
  • 内存:4808kb
  • [2024-10-27 05:38:20]
  • 提交

answer

/**
 * @author n685
 * @brief
 * @date 2024-10-26 16:22:15
 *
 *
 */
#include <algorithm>

#include "bits/stdc++.h"

#ifdef LOCAL
#include "dd/debug.h"
#else
#define dbg(...) 42
#define dbg_proj(...) 420
#define dbg_rproj(...) 420420
void nline() {}
void bar() {}
void start_clock() {}
void end_clock() {}
#endif

namespace rs = std::ranges;
namespace rv = std::views;

template <class T> constexpr std::pair<T, T> ex_eucl(T a, T b) {
  if (a < b) {
    auto [x, y] = ex_eucl(b, a);
    return {y, x};
  }
  if (b == 0) {
    assert(a == 1);
    return {1, 0};
  }
  auto [x, y] = ex_eucl(b, a % b);
  return {y, x - (a / b) * y};
}

template <class Md, class V = int64_t>
  requires std::signed_integral<std::decay_t<decltype(Md::value)>>
struct Mod {
  using T = std::decay_t<decltype(Md::value)>;
  T val = 0;

  static constexpr T normalize(std::integral auto val) {
    using U = decltype(Md::value + val);
    U uval = static_cast<U>(val);
    U umd = static_cast<U>(Md::value);
    if (uval <= -umd || umd <= uval) {
      uval %= umd;
    }
    if (val < 0) {
      uval += umd;
    }
    return static_cast<T>(uval);
  }
  constexpr Mod() : val(0) {}
  constexpr explicit Mod(std::integral auto _val) : val(normalize(_val)) {}

  static inline const Mod ZERO = Mod(0);
  static inline const Mod ONE = Mod(1);
  static inline const Mod TWO = Mod(2);

  // addition
  constexpr Mod& operator+=(Mod b) {
    val += b.val;
    if (val >= Md::value) {
      val -= Md::value;
    }
    return *this;
  }
  friend constexpr Mod operator+(Mod a, Mod b) { return a += b; }
  constexpr Mod& operator++() { return *this += Mod(1); }
  constexpr Mod operator++(int) {
    Mod res = *this;
    ++(*this);
    return res;
  }

  // subtraction
  constexpr Mod& operator-=(Mod b) {
    val -= b.val;
    if (val < 0) {
      val += Md::value;
    }
    return *this;
  }
  friend constexpr Mod operator-(Mod a, Mod b) { return a -= b; }
  constexpr Mod& operator--() { return *this -= Mod(1); }
  constexpr Mod operator--(int) {
    Mod res = *this;
    --(*this);
    return res;
  }
  // negation
  constexpr Mod operator-() const { return Mod(-val); }

  // multiplication
  constexpr Mod& operator*=(Mod b) {
    val = static_cast<T>(static_cast<V>(val) * b.val % Md::value);
    return *this;
  }
  friend constexpr Mod operator*(Mod a, Mod b) { return a *= b; }
  constexpr Mod binpow(std::integral auto b) const {
    Mod res = Mod(1), a = *this;
    while (b > 0) {
      if (b % 2 == 1) {
        res *= a;
      }
      a *= a;
      b /= 2;
    }
    return res;
  }

  // factorial
  // align with fft, if code fails to compile make this smaller (if using array)
  static constexpr int MXINV = 1 << 22;
  static inline bool init = false;
  static inline std::vector<Mod> ff, iff;
  static void reset_fac() { init = false; }
  static void init_fac() {
    if (init) {
      return;
    }
    ff.resize(MXINV + 1);
    ff[0] = Mod(1);
    for (int i = 1; i <= MXINV; ++i) {
      ff[i] = ff[i - 1] * Mod(i);
    }
    iff.resize(MXINV + 1);
    iff[MXINV] = ff[MXINV].large_inv();
    for (int i = MXINV - 1; i >= 0; --i) {
      iff[i] = iff[i + 1] * Mod(i + 1);
    }
    init = true;
  }
  static Mod fac(int v) {
    if (!init) {
      init_fac();
    }
    return ff[v];
  }
  static Mod ifac(int v) {
    if (!init) {
      init_fac();
    }
    return iff[v];
  }
  static Mod comb(int n, int k) {
    if (n < 0 || k < 0 || n < k) {
      return Mod(0);
    }
    return fac(n) * ifac(n - k) * ifac(k);
  }
  static Mod perm(int n, int k) {
    if (n < 0 || k < 0 || n < k) {
      return Mod(0);
    }
    return fac(n) * ifac(n - k);
  }

  // inverse
  Mod small_inv() const { return ifac(static_cast<int>(val)) * fac(static_cast<int>(val) - 1); }
  constexpr Mod large_inv() const {
    return Mod(ex_eucl(static_cast<V>(val), static_cast<V>(Md::value)).first);
    // return binpow(Md::value - 2);
  }
  Mod inv() const {
    if (val <= MXINV) {
      return small_inv();
    }
    return large_inv();
  }

  // sqrt
  std::optional<Mod> sqrt() {
    static std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
    Mod c = Mod::ZERO;
    while ((c * c - *this).binpow((Md::value - 1) / 2) == Mod::ONE) {
      c = Mod(rng());
    }
    if (c == Mod::ZERO) {
      return std::nullopt;
    }
    std::pair<Mod, Mod> res(Mod::ONE, Mod::ZERO), a(c, Mod::ONE);
    T b = (Md::value + 1) / 2;
    auto mul
      = [&c,
         this](const std::pair<Mod, Mod>& u, const std::pair<Mod, Mod>& v) -> std::pair<Mod, Mod> {
      return {
        u.first * v.first + u.second * v.second * (c * c - *this),
        u.second * v.first + u.first * v.second
      };
    };
    while (b > 0) {
      if (b % 2 == 1) {
        res = mul(res, a);
      }
      a = mul(a, a);
      b /= 2;
    }
    return res.first;
    // return std::min(res.first, -res.first);
  }

  // comparison
  constexpr bool operator==(const Mod& b) const = default;
  constexpr std::strong_ordering operator<=>(const Mod& b) const = default;

  // io
  friend std::istream& operator>>(std::istream& in, Mod& a) {
    int64_t v;
    in >> v;
    a = Mod(v);
    return in;
  }
  friend std::ostream& operator<<(std::ostream& out, const Mod& a) {
    out << a.val;
    return out;
  }

  // conversion
  constexpr T value() const { return val; }
};

#if defined(LOCAL) && __cplusplus >= 202302L
template <class Md, class V>
  requires std::formattable<typename Mod<Md, V>::T, char>
struct std::formatter<Mod<Md, V>, char> {
  using T = typename Mod<Md, V>::T;
  std::formatter<T, char> underlying;
  constexpr formatter() {
    if constexpr (requires { underlying.set_debug_format(); }) {
      underlying.set_debug_format();
    }
  }
  template <class ParseContext> constexpr auto parse(ParseContext& ctx) {
    return underlying.parse(ctx);
  }
  template <class FormatContext> auto format(const Mod<Md, V>& val, FormatContext& ctx) const {
    return underlying.format(val.value(), ctx);
  }
};
#endif

constexpr int MOD = 1'000'000'007;
using Mint = Mod<std::integral_constant<std::decay_t<decltype(MOD)>, MOD>>;

template <class T> struct NArr {
  using iterator = std::vector<T>::iterator;
  using const_iterator = std::vector<T>::const_iterator;
  int sz{0}, off{0};
  std::vector<T> data;
  NArr() = default;
  NArr(int l, int r) : sz(r - l + 1), off(l), data(sz) {}
  NArr(int l, int r, const T& v) : sz(r - l + 1), off(l), data(sz, v) {}
  T& operator[](int ind) { return data[ind - off]; }
  const T& operator[](int ind) const { return data[ind - off]; }
  iterator begin() { return data.begin(); }
  const_iterator begin() const { return data.begin(); }
  iterator end() { return data.end(); }
  const_iterator end() const { return data.end(); }
  void swap(NArr& other) noexcept {
    std::swap(sz, other.sz);
    std::swap(off, other.off);
    data.swap(other.data);
  }
};

int main() {
#ifndef LOCAL
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
#endif

  int n;
  std::cin >> n;
  n /= 4;
  std::vector<char> s(4 * n);
  for (int i = 4 * n - 1; i >= 0; --i) {
    char c;
    std::cin >> c;
    s[i] = c;
  }
  NArr id(-n, 3 * n, NArr<std::array<Mint, 2>>(-n, 0));
  std::array<NArr<NArr<std::array<Mint, 2>>>, 2> dp;
  dp.fill(id);
  dp[0][0][0][0] = Mint::ONE;
  for (int i = 0; i < 4 * n; ++i) {
    for (int pre = -n; pre <= 3 * n; ++pre) {
      for (int mi = -n; mi <= std::min(0, pre); ++mi) {
        for (int last : {0, 1}) {
          if (dp[0][pre][mi][last] == Mint::ZERO) {
            continue;
          }
          // add 1 (0)
          if (s[i] != '1' && pre + 1 <= 3 * n) {
            dp[1][pre + 1][mi][0] += dp[0][pre][mi][last];
          }
          // subtract 3 (1)
          if (s[i] != '0' && last != 1 && pre - 3 >= std::max(-n, mi - 1)) {
            dp[1][pre - 3][std::min(pre - 3, mi)][1] += dp[0][pre][mi][last];
          }
        }
      }
    }
    dp[0].swap(dp[1]);
    dp[1] = id;
  }
  Mint ans{0};
  for (int mi = -n; mi <= 0; ++mi) {
    ans += dp[0][0][mi][0];
  }
  std::cout << ans << '\n';
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3524kb

input:

8
0??0?100

output:

2

result:

ok "2"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3540kb

input:

4
?10?

output:

1

result:

ok "1"

Test #3:

score: 0
Accepted
time: 0ms
memory: 3656kb

input:

28
???????????0???0??????1???0?

output:

2023

result:

ok "2023"

Test #4:

score: 0
Accepted
time: 0ms
memory: 3592kb

input:

4
????

output:

1

result:

ok "1"

Test #5:

score: 0
Accepted
time: 0ms
memory: 3620kb

input:

8
11111111

output:

0

result:

ok "0"

Test #6:

score: -100
Wrong Answer
time: 99ms
memory: 4808kb

input:

500
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????...

output:

467681810

result:

wrong answer 1st words differ - expected: '870731023', found: '467681810'