Submission #1258804

#	Time	Username	Problem	Language	Result	Execution time	Memory
1258804		proofy	Intergalactic ship (IZhO19_xorsum)	C++20	100 / 100	638 ms	14456 KiB

xorsum

#include <bits/stdc++.h>
using namespace std;
#define ll long long

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { value += other.value; value -= (value >= mod()) * mod(); return *this; }
  Modular& operator-=(const Modular& other) { value -= other.value; value += (value < 0) * mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) { Modular result(*this); *this += 1; return result; }
  Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
    int64_t q = int64_t(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  friend const Type& abs(const Modular& x) { return x.value; }

  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);

 private:
  Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}

template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}

// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}

// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

constexpr int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

const int N = 1012;
const int M = 100123;
int a[N], n, q;
tuple<int, int, int> Q[M];

void take_input() {
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];

    cin >> q;
    for (int i = 1; i <= q; i++) {
        auto& [l, r, x] = Q[i];
        cin >> l >> r >> x;
    }
}

void step1_1() {
    take_input();
}


Mint pow2[M + M];

void calculate_pow2() {
    pow2[0] = 1;
    for (int i = 1; i < M + M; i++) pow2[i] = pow2[i - 1] + pow2[i - 1];
}

void step1_2() {
    calculate_pow2();
}

int G[7][N];

void calculate_G() {
    for (int s = 0; s < 7; s++) {
        for (int i = 1; i <= q; i++) {
            auto& [l, r, x] = Q[i];
            if ((x >> s) & 1) G[s][l] += 1, G[s][r + 1] -= 1;
        }
        for (int i = 1; i <= n + 1; i++) G[s][i] += G[s][i - 1];
    }
}

void step1_3() {
    calculate_G();
}


Mint A[1 << 4][4];
int basis[2];

void calculate_A() {
    for (int m = 0; m < (1 << 4); m++) {
        basis[0] = basis[1] = 0;
        int b = 0; // basis size
        for (int j = 0; j < 4; j++) if ((1 << j) & m) {
            // insert j into the basis
            int x = j;
            for (int k = 0; k < 2; k++) if ((1 << k) & x) {
                if (!basis[k]) {
                    basis[k] = x;
                    b += 1;
                    break;
                }

                x ^= basis[k];
            }
        }


        if (basis[0] == 0) basis[0] = basis[1];

        for (int w = 0; w < (1 << b); w++) {
            int x = 0;
            for (int k = 0; k < b; k++) if ((1 << k) & w) x ^= basis[k];
            A[m][x] = pow2[q - b];
        }
    }
}

void step1_4() {
    calculate_A();
}


int F[N][N];

void calculate_F(int s, int t) {
    for (int i = 1; i <= q; i++) {
        auto [l, r, x] = Q[i];
        int bit_s = (x >> s) & 1;
        int bit_t = (x >> t) & 1;
        if (bit_s && bit_t) 
            F[l][r] += 1;
    }

    for (int x = 1; x <= n; x++)
        for (int y = n; y >= 1; --y) 
            F[x][y] += F[x - 1][y] + F[x][y + 1] - F[x - 1][y + 1];
}

void step2(int s, int t) {
    calculate_F(s, t);
}

Mint H[N][N];

int convert(int x, int y) {
    return (x << 1) | y;
}

int convert2(int x, int y, int z, int l) {
    l -= (x + y + z);
    x = !!x; y = !!y; z = !!z; l = !!l;
    return (x << 3) | (y << 2) | (z << 1) | l;
}

void calculate_H(int s, int t) {
    for (int x = 1; x <= n; x++)
        for (int y = 1; y <= n; y++) {
            int F_val = F[min(x, y)][max(x, y)];

            if (s == t && x == y) {
                if ((a[x] >> s) & 1) {
                    if (F_val) H[x][y] = pow2[q - 1];
                    else H[x][y] = pow2[q];
                } else {
                    H[x][y] = 0;
                    if (F_val) H[x][y] = pow2[q - 1];
                }
                continue;
            }

            int m = convert2(F_val, (G[s][x] - F_val), (G[t][y] - F_val), q);
            
            int bx = (a[x] >> s) & 1;
            int by = (a[y] >> t) & 1;
            H[x][y] = A[m][convert(1 - bx, 1 - by)];
        }
}


void step3(int s, int t) {
    calculate_H(s, t);
}

Mint J[N][N];

void calculate_J(int s, int t) {
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++) {
            J[i][j] = pow2[s + t] * H[i][j];
            J[i][j] += J[i - 1][j] + J[i][j - 1] - J[i - 1][j - 1];
        }
}

void step4(int s, int t) {
    calculate_J(s, t);
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

    for (auto func : {step1_1, step1_2, step1_3, step1_4}) {
        func();
    }
    
    Mint X = 0;
    Mint Y = 0;

    for (int s = 0; s < 7; s++)
        for (int t = 0; t < 7; t++) {
            memset(F, 0, sizeof(F));
            memset(H, 0, sizeof(H));
            memset(J, 0, sizeof(J));
            for (auto func : {step2, step3, step4}) {
                func(s, t);
            }
            for (int i = 1; i <= n; i++) {
                X += J[i][i];
                for (int j = 1; j <= n; j++) Y += J[i][j];
            }
        }

    cout << Mint(n + 1) * X - Y << "\n";
}

• Subtask 1: 4 / 4
• Subtask 2: 5 / 5
• Subtask 3: 6 / 6
• Subtask 4: 9 / 9
• Subtask 5: 8 / 8
• Subtask 6: 11 / 11
• Subtask 7: 19 / 19
• Subtask 8: 30 / 30
• Subtask 9: 8 / 8