#751789 (C++17) No.1891 Static Xor Range Composite Query

• 問題: No.1891 Static Xor Range Composite Query
• ユーザー: Forested
• 提出日時: 2022-04-04 20:34:22
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 504 ms / 5,000 ms
• コード長: 8,891 bytes
• コンパイル時間: 1,225 ms
• コンパイル使用メモリ: 121,448 KB
• 最終ジャッジ日時: 2025-01-28 15:02:43
• ジャッジサーバーID （参考情報）: judge4 / judge2

ファイルパターン	結果
sample	AC * 1
other	AC * 30

ソースコード

// ===== template.hpp =====
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;

struct FastIO {
    FastIO() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout << fixed << setprecision(10);
    }
} fast_io;
// ===== template.hpp =====

#ifdef DEBUGF
#include "new_library/other/debug.hpp"
#else
#define DBG(x) (void) 0
#endif

// ===== mod_int.hpp =====
#ifndef MOD_INT_HPP
#define MOD_INT_HPP

#include <cassert>
#include <iostream>
#include <type_traits>

// ===== utils.hpp =====
#ifndef UTILS_HPP
#define UTILS_HPP

#include <cstddef>

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1)
        return false;
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0)
            return false;
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1)
            ret = (unsigned long long)ret * self % mod;
        self = (unsigned long long)self * self % mod;
        y >>= 1;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2)
        return 1;

    unsigned primes[32] = {};
    std::size_t it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0)
                    m /= i;
            }
        }
        if (m != 1)
            primes[it++] = m;
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (std::size_t j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

#endif
// ===== utils.hpp =====

template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
constexpr unsigned safe_mod(T x, unsigned mod) {
    if (x < 0) {
        return (unsigned)(x % (T)mod + mod);
    } else {
        return (unsigned)(x % (T)mod);
    }
}

template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
constexpr unsigned safe_mod(T x, unsigned mod) {
    return (unsigned)(x % mod);
}

template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

public:
    constexpr ModInt() : val(0) {}
    template <typename T>
    constexpr ModInt(T x) : val(safe_mod(x, mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const {
        return val;
    }

    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if (val < rhs.val)
            val += mod;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        is >> x.val;
        // x.val %= mod;
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;

#endif
// ===== mod_int.hpp =====

using Mint = ModInt<mod998244353>;

// ===== linear_function.hpp =====
#ifndef LINEAR_FUNCTION_HPP
#define LINEAR_FUNCTION_HPP

template <typename T>
struct LinearFunction {
    T slope;
    T intercept;

    LinearFunction() : slope(), intercept() {}
    LinearFunction(const T &s, const T &i) : slope(s), intercept(i) {}

    T operator()(const T &x) const {
        return intercept + slope * x;
    }

    // (this)(other(x))
    LinearFunction<T> composite(const LinearFunction<T> &other) const {
        return LinearFunction<T>(
            slope * other.slope,
            slope * other.intercept + intercept);
    }
};

#endif
// ===== linear_function.hpp =====

using F = LinearFunction<Mint>;

i32 floor_log2(i32 n) {
    return 31 - __builtin_clz(n);
}

int main() {
    i32 n, q;
    cin >> n >> q;
    Vec<F> f(n);
    REP(i, n) {
        cin >> f[i].slope >> f[i].intercept;
    }
    
    i32 m = floor_log2(n);
    
    Vec<Vec<F>> segtree(2 * n);
    REP(i, n) {
        segtree[n + i] = {f[i]};
    }
    for (i32 i = n - 1; i > 0; --i) {
        i32 k = segtree[2 * i].size();
        segtree[i].resize(2 * k);
        REP(j, k) {
            segtree[i][j] = segtree[2 * i + 1][j].composite(segtree[2 * i][j]);
            segtree[i][k + j] = segtree[2 * i][j].composite(segtree[2 * i + 1][j]);
        }
    }
    
    REP(qi, q) {
        i32 l, r, p;
        Mint x;
        cin >> l >> r >> p >> x;
        
        F lf(Mint(1), Mint(0)), rf(Mint(1), Mint(0));
        l += n;
        r += n;
        i32 upper_l = l - n, upper_r = r - n;
        i32 depth = m;
        while (l < r) {
            if (l % 2 == 1) {
                i32 p_lower = p & ((1 << (m - depth)) - 1);
                i32 p_upper = p >> (m - depth);
                i32 node = (p_upper ^ upper_l) + (1 << depth);
                lf = segtree[node][p_lower].composite(lf);
                ++l;
                ++upper_l;
            }
            if (r % 2 == 1) {
                --r;
                --upper_r;
                i32 p_lower = p & ((1 << (m - depth)) - 1);
                i32 p_upper = p >> (m - depth);
                i32 node = (p_upper ^ upper_r) + (1 << depth);
                rf = rf.composite(segtree[node][p_lower]);
            }
            l /= 2;
            r /= 2;
            --depth;
            upper_l /= 2;
            upper_r /= 2;
        }
        F prod = rf.composite(lf);
        cout << prod(x) << '\n';
    }
}