data_structure/test/1891.test.cpp

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Last update: 2023-05-04 19:50:45+09:00
Problem: https://yukicoder.me/problems/no/1891

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Code

#define PROBLEM "https://yukicoder.me/problems/no/1891"

#define FAST_IO

#include "../../template/template.hpp"
#include "../../number_theory/mod_int.hpp"
#include "../../data_structure/segment_tree_xor_range.hpp"

using Mint = ModInt<mod998244353>;

struct Linear {
    Mint a, b;
    Linear() : a(Mint(1)), b(Mint(0)) {}
    Linear(Mint _a, Mint _b) : a(_a), b(_b) {}
    Mint operator()(Mint x) {
        return a * x + b;
    }
};

// f \circ g
Linear composite(const Linear &f, const Linear &g) {
    return Linear(f.a * g.a, f.a * g.b + f.b);
}

struct Ops {
    using Value = Linear;
    static Value id() {
        return Linear();
    }
    static Value op(const Value &x, const Value &y) {
        return composite(y, x);
    }
};

int main() {
    i32 n, q;
    cin >> n >> q;
    Vec<Linear> fs(n);
    REP(i, n) {
        cin >> fs[i].a >> fs[i].b;
    }
    SegmentTreeXorRange<Ops> seg(fs);
    REP(qi, q) {
        i32 l, r, p;
        Mint x;
        cin >> l >> r >> p >> x;
        cout << seg.prod(l, r, p)(x) << '\n';
    }
}

#line 1 "data_structure/test/1891.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1891"

#define FAST_IO

#line 1 "template/template.hpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#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;
using f64 = double;
using f80 = long double;

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;
}

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64) x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64) x;
    return os;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
#line 2 "number_theory/mod_int.hpp"

#line 5 "number_theory/mod_int.hpp"
#include <type_traits>

#line 2 "number_theory/utils.hpp"

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) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    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] = {};
    int 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 (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
#line 8 "number_theory/mod_int.hpp"

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:
    static constexpr unsigned get_mod() {
        return mod;
    }
    
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (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) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        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;

#line 2 "data_structure/segment_tree_xor_range.hpp"

#line 5 "data_structure/segment_tree_xor_range.hpp"

template <typename Monoid>
class SegmentTreeXorRange {
public:
    using Value = typename Monoid::Value;
    
private:
    static int floor_log2(int n) {
        return 31 - __builtin_clz(n);
    }
    
    int depth;
    std::vector<std::vector<Value>> node;
    
public:
    SegmentTreeXorRange(const std::vector<Value> &a) :
        depth(floor_log2((int) a.size())),
        node(2 * (int) a.size()) {
        assert(!a.empty());
        assert((int) a.size() == (1 << depth));
        for (int i = 0; i < (int) a.size(); ++i) {
            node[a.size() + i] = {a[i]};
        }
        for (int i = (int) a.size() - 1; i > 0; --i) {
            int k = (int) node[2 * i].size();
            node[i].resize(2 * k);
            for (int j = 0; j < k; ++j) {
                node[i][j] = Monoid::op(node[2 * i][j], node[2 * i + 1][j]);
                node[i][j + k] = Monoid::op(node[2 * i + 1][j], node[2 * i][j]);
            }
        }
    }
    
    Value prod(int l, int r, int x) const {
        assert(l >= 0 && l <= r && r <= (1 << depth));
        int d = depth;
        int nodel_prefix = l;
        int noder_prefix = r;
        l += 1 << depth;
        r += 1 << depth;
        Value lp = Monoid::id();
        Value rp = Monoid::id();
        while (l < r) {
            int x_upper = x >> (depth - d);
            int x_lower = x ^ (x_upper << (depth - d));
            if (l % 2 == 1) {
                int nodei = (x_upper ^ nodel_prefix) + (1 << d);
                lp = Monoid::op(lp, node[nodei][x_lower]);
                ++l;
                ++nodel_prefix;
            }
            if (r % 2 == 1) {
                --r;
                --noder_prefix;
                int nodei = (x_upper ^ noder_prefix) + (1 << d);
                rp = Monoid::op(node[nodei][x_lower], rp);
            }
            --d;
            l /= 2;
            nodel_prefix /= 2;
            r /= 2;
            noder_prefix /= 2;
        }
        return Monoid::op(lp, rp);
    }
};

#line 8 "data_structure/test/1891.test.cpp"

using Mint = ModInt<mod998244353>;

struct Linear {
    Mint a, b;
    Linear() : a(Mint(1)), b(Mint(0)) {}
    Linear(Mint _a, Mint _b) : a(_a), b(_b) {}
    Mint operator()(Mint x) {
        return a * x + b;
    }
};

// f \circ g
Linear composite(const Linear &f, const Linear &g) {
    return Linear(f.a * g.a, f.a * g.b + f.b);
}

struct Ops {
    using Value = Linear;
    static Value id() {
        return Linear();
    }
    static Value op(const Value &x, const Value &y) {
        return composite(y, x);
    }
};

int main() {
    i32 n, q;
    cin >> n >> q;
    Vec<Linear> fs(n);
    REP(i, n) {
        cin >> fs[i].a >> fs[i].b;
    }
    SegmentTreeXorRange<Ops> seg(fs);
    REP(qi, q) {
        i32 l, r, p;
        Mint x;
        cin >> l >> r >> p >> x;
        cout << seg.prod(l, r, p)(x) << '\n';
    }
}