#751773 (C++17) No.1891 Static Xor Range Composite Query

提出ソース

結果

問題	No.1891 Static Xor Range Composite Query
ユーザー	Forested
提出日時	2022-04-04 18:54:40
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2,113 ms / 5,000 ms
コード長	8,509 bytes
コンパイル時間	1,340 ms
コンパイル使用メモリ	127,092 KB
実行使用メモリ	7,424 KB
最終ジャッジ日時	2024-11-25 11:12:15
合計ジャッジ時間	24,540 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	2 ms 5,248 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	2 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	2 ms 5,248 KB
testcase_09	AC	2 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	3 ms 5,248 KB
testcase_12	AC	3 ms 5,248 KB
testcase_13	AC	3 ms 5,248 KB
testcase_14	AC	4 ms 5,248 KB
testcase_15	AC	3 ms 5,248 KB
testcase_16	AC	4 ms 5,248 KB
testcase_17	AC	3 ms 5,248 KB
testcase_18	AC	3 ms 5,248 KB
testcase_19	AC	3 ms 5,248 KB
testcase_20	AC	3 ms 5,248 KB
testcase_21	AC	2,112 ms 7,296 KB
testcase_22	AC	2,043 ms 7,424 KB
testcase_23	AC	2,036 ms 7,296 KB
testcase_24	AC	2,038 ms 7,296 KB
testcase_25	AC	2,048 ms 7,424 KB
testcase_26	AC	2,066 ms 7,424 KB
testcase_27	AC	2,044 ms 7,296 KB
testcase_28	AC	2,035 ms 7,296 KB
testcase_29	AC	2,042 ms 7,296 KB
testcase_30	AC	2,113 ms 7,296 KB

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ソースコード

raw source code

// ===== 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);
    i32 bl = m / 2;
    Vec<Vec<F>> precalc(1 << (m - bl), Vec<F>(1 << bl));
    REP(i, 1 << (m - bl)) {
        i32 l = i << bl, r = (i + 1) << bl;
        REP(j, 1 << bl) {
            F g(Mint(1), Mint(0));
            REP(k, l, r) {
                g = f[j ^ k].composite(g);
            }
            precalc[i][j] = g;
        }
    }
    
    REP(qi, q) {
        i32 l, r, p;
        Mint x;
        cin >> l >> r >> p >> x;
        
        if ((l >> bl) == (r >> bl)) {
            F g(Mint(1), Mint(0));
            REP(i, l, r) {
                g = f[i ^ p].composite(g);
            }
            cout << g(x) << '\n';
            continue;
        }
        
        i32 lower = p & ((1 << bl) - 1);
        i32 upper = p >> bl;
        i32 lb = (l >> bl) + 1, rb = r >> bl;
        
        F g(Mint(1), Mint(0));
        REP(i, l, lb << bl) {
            g = f[i ^ p].composite(g);
        }
        REP(i, lb, rb) {
            i32 idx = i ^ upper;
            g = precalc[idx][lower].composite(g);
        }
        REP(i, rb << bl, r) {
            g = f[i ^ p].composite(g);
        }
        cout << g(x) << '\n';
    }
}

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