test/segment_tree.test.cpp

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• Last update: 2022-01-07 21:48:21+09:00
• Problem: https://judge.yosupo.jp/problem/point_set_range_composite

Depends on

• container/segment_tree.cpp
• internal/enable_avx2.cpp
• math/rem_euclid.cpp
• math/static_modint.cpp
• math/totient.cpp
• traits/affine_composite_monoid.cpp
• utility/bit_width.cpp
• utility/ceil_log2.cpp
• utility/countl_zero.cpp
• utility/int_alias.cpp
• utility/rep.cpp
• utility/revrep.cpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
#include "../math/static_modint.cpp"
#include "../container/segment_tree.cpp"
#include "../utility/int_alias.cpp"
#include "../utility/rep.cpp"
#include "../traits/affine_composite_monoid.cpp"
#include <iostream>

using Fp = StaticModint<998244353>;

int main() {
    int N, Q;
    std::cin >> N >> Q;
    std::vector<Affine<Fp>> initial(N);
    for (const int i: rep(0, N)) {
        u32 a, b;
        std::cin >> a >> b;
        initial[i] = {a, b};
    }
    SegmentTree<AffineCompositeMonoid<Fp>> seg(initial);
    while (Q--) {
        int t;
        std::cin >> t;
        if (t == 0) {
            int p;
            std::cin >> p;
            u32 c, d;
            std::cin >> c >> d;
            seg.assign(p, {Fp(c), Fp(d)});
        }
        else {
            int l, r;
            std::cin >> l >> r;
            u32 x;
            std::cin >> x;
            std::cout << seg.fold(l, r).eval(Fp(x)) << '\n';
        }
    }
    return 0;
}

#line 1 "test/segment_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
#line 2 "math/static_modint.cpp"
#include <ostream>
#include <type_traits>
#line 2 "utility/int_alias.cpp"
#include <cstdint>

using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
#line 2 "math/rem_euclid.cpp"
#include <cassert>

template <class T> constexpr T rem_euclid(T value, const T& mod) {
    assert(mod > 0);
    return (value %= mod) >= 0 ? value : value + mod;
}
#line 2 "math/totient.cpp"

template <class T> constexpr T totient(T x) {
    T ret = x;
    for (T i = 2; i * i <= x; ++i) {
        if (x % i == 0) {
            ret /= i;
            ret *= i - 1;
            while (x % i == 0) x /= i;
        }
    }
    if (x > 1) {
        ret /= x;
        ret *= x - 1;
    }
    return ret;
}
#line 7 "math/static_modint.cpp"

template <u32 MOD, std::enable_if_t<((u32)1 <= MOD and MOD <= ((u32)1 << 31))>* = nullptr> class StaticModint {
    using Self = StaticModint;

    static inline constexpr u32 PHI = totient(MOD);
    u32 v;

  public:
    static constexpr u32 mod() noexcept { return MOD; }

    template <class T, std::enable_if_t<std::is_integral_v<T>>* = nullptr>
    static constexpr T normalize(const T& x) noexcept {
        return rem_euclid<std::common_type_t<T, i64>>(x, MOD);
    }

    constexpr StaticModint() noexcept : v(0) {}
    template <class T> constexpr StaticModint(const T& x) noexcept : v(normalize(x)) {}
    template <class T> static constexpr Self raw(const T& x) noexcept {
        Self ret;
        ret.v = x;
        return ret;
    }

    constexpr u32 val() const noexcept { return v; }
    constexpr Self neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
    constexpr Self inv() const noexcept { return pow(PHI - 1); }
    constexpr Self pow(u64 exp) const noexcept {
        Self ret(1), mult(*this);
        for (; exp > 0; exp >>= 1) {
            if (exp & 1) ret *= mult;
            mult *= mult;
        }
        return ret;
    }

    constexpr Self operator-() const noexcept { return neg(); }
    constexpr Self operator~() const noexcept { return inv(); }

    constexpr Self operator+(const Self& rhs) const noexcept { return Self(*this) += rhs; }
    constexpr Self& operator+=(const Self& rhs) noexcept {
        if ((v += rhs.v) >= MOD) v -= MOD;
        return *this;
    }

    constexpr Self operator-(const Self& rhs) const noexcept { return Self(*this) -= rhs; }
    constexpr Self& operator-=(const Self& rhs) noexcept {
        if (v < rhs.v) v += MOD;
        v -= rhs.v;
        return *this;
    }

    constexpr Self operator*(const Self& rhs) const noexcept { return Self(*this) *= rhs; }
    constexpr Self& operator*=(const Self& rhs) noexcept {
        v = (u64)v * rhs.v % MOD;
        return *this;
    }

    constexpr Self operator/(const Self& rhs) const noexcept { return Self(*this) /= rhs; }
    constexpr Self& operator/=(const Self& rhs) noexcept { return *this *= rhs.inv(); }

    constexpr bool operator==(const Self& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const Self& rhs) const noexcept { return v != rhs.v; }
    friend std::ostream& operator<<(std::ostream& stream, const Self& rhs) { return stream << rhs.v; }
};

using Modint1000000007 = StaticModint<1000000007>;
using Modint998244353 = StaticModint<998244353>;
#line 3 "container/segment_tree.cpp"
#include <vector>
#line 2 "internal/enable_avx2.cpp"

#ifdef ENABLE_AVX2
#define TARGET_AVX2 __attribute__((target("avx2")))
#else
#define TARGET_AVX2
#endif
#line 4 "utility/countl_zero.cpp"

TARGET_AVX2 constexpr int countl_zero(u64 x) {
#ifdef __GNUC__
    return x == 0 ? 64 : __builtin_clzll(x);
#else
    x |= x >> 1;
    x |= x >> 2;
    x |= x >> 4;
    x |= x >> 8;
    x |= x >> 16;
    x |= x >> 32;
    return 64 - countr_zero(~x);
#endif
}
#line 4 "utility/bit_width.cpp"

TARGET_AVX2 constexpr int bit_width(const u64 x) { return 64 - countl_zero(x); }
#line 5 "utility/ceil_log2.cpp"

TARGET_AVX2 constexpr int ceil_log2(const u64 x) {
#ifdef __GNUC__
    return x == 0 ? 0 : bit_width(x - 1);
#else
    int e = 0;
    while (((u64)1 << e) < x) ++e;
    return e;
#endif
}
#line 2 "utility/rep.cpp"
#include <algorithm>

class Range {
    struct Iter {
        int itr;
        constexpr Iter(const int pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { ++itr; }
        constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
        constexpr int operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr Range(const int first, const int last) noexcept : first(first), last(std::max(first, last)) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

constexpr Range rep(const int l, const int r) noexcept { return Range(l, r); }
constexpr Range rep(const int n) noexcept { return Range(0, n); }
#line 3 "utility/revrep.cpp"

class ReversedRange {
    struct Iter {
        int itr;
        constexpr Iter(const int pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { --itr; }
        constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
        constexpr int operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr ReversedRange(const int first, const int last) noexcept
        : first(last - 1), last(std::min(first, last) - 1) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

constexpr ReversedRange revrep(const int l, const int r) noexcept { return ReversedRange(l, r); }
constexpr ReversedRange revrep(const int n) noexcept { return ReversedRange(0, n); }
#line 7 "container/segment_tree.cpp"

template <class M> class SegmentTree {
    using T = typename M::Type;
    int internal_size, seg_size;
    std::vector<T> data;

    void fetch(const int k) { data[k] = M::operation(data[2 * k], data[2 * k + 1]); }

  public:
    explicit SegmentTree(const int size = 0, const T& value = M::identity())
        : SegmentTree(std::vector<T>(size, value)) {}
    explicit SegmentTree(const std::vector<T>& vec) : internal_size(vec.size()) {
        seg_size = 1 << ceil_log2(internal_size);
        data = std::vector<T>(2 * seg_size, M::identity());
        for (const int i : rep(internal_size)) data[seg_size + i] = vec[i];
        for (const int i : revrep(1, seg_size)) fetch(i);
    }

    int size() const { return internal_size; }

    void assign(int i, const T& value) {
        assert(0 <= i and i < internal_size);
        i += seg_size;
        data[i] = value;
        while (i > 1) {
            i >>= 1;
            fetch(i);
        }
    }

    T fold() const { return data[1]; }
    T fold(int l, int r) const {
        assert(0 <= l and l <= r and r <= internal_size);
        l += seg_size;
        r += seg_size;
        T ret_l = M::identity(), ret_r = M::identity();
        while (l < r) {
            if (l & 1) ret_l = M::operation(ret_l, data[l++]);
            if (r & 1) ret_r = M::operation(data[--r], ret_r);
            l >>= 1;
            r >>= 1;
        }
        return M::operation(ret_l, ret_r);
    }

    template <class F> int max_right(int l, const F& f) const {
        assert(0 <= l and l <= internal_size);
        assert(f(M::identity()));
        if (l == internal_size) return internal_size;
        l += seg_size;
        T sum = M::identity();
        do {
            while (!(l & 1)) l >>= 1;
            if (!f(M::operation(sum, data[l]))) {
                while (l < seg_size) {
                    l = 2 * l;
                    if (f(M::operation(sum, data[l]))) sum = M::operation(sum, data[l++]);
                }
                return l - seg_size;
            }
            sum = M::operation(sum, data[l++]);
        } while ((l & -l) != l);
        return internal_size;
    }

    template <class F> int min_left(int r, const F& f) const {
        assert(0 <= r and r <= internal_size);
        assert(f(M::identity()));
        if (r == 0) return 0;
        r += seg_size;
        T sum = M::identity();
        do {
            r -= 1;
            while (r > 1 and (r & 1)) r >>= 1;
            if (!f(M::operation(data[r], sum))) {
                while (r < seg_size) {
                    r = 2 * r + 1;
                    if (f(M::operation(data[r], sum))) sum = M::operation(data[r--], sum);
                }
                return r + 1 - seg_size;
            }
            sum = M::operation(data[r], sum);
        } while ((r & -r) != r);
        return 0;
    }
};
#line 2 "traits/affine_composite_monoid.cpp"

template <class T> struct Affine {
    T a, b;
    constexpr Affine(const T& a = 1, const T& b = 0) : a(a), b(b) {}
    constexpr T eval(const T& x) const { return a * x + b; }
    constexpr Affine operator+(const Affine& other) const { return affine(a + other.a, b + other.b); }
    constexpr Affine composite(const Affine& other) const { return Affine(a * other.a, b * other.a + other.b); }
};

template <class T> struct AffineCompositeMonoid {
    using Type = Affine<T>;
    static constexpr Type identity() { return Type(); }
    static constexpr Type operation(const Type& l, const Type& r) noexcept { return l.composite(r); }
};
#line 7 "test/segment_tree.test.cpp"
#include <iostream>

using Fp = StaticModint<998244353>;

int main() {
    int N, Q;
    std::cin >> N >> Q;
    std::vector<Affine<Fp>> initial(N);
    for (const int i: rep(0, N)) {
        u32 a, b;
        std::cin >> a >> b;
        initial[i] = {a, b};
    }
    SegmentTree<AffineCompositeMonoid<Fp>> seg(initial);
    while (Q--) {
        int t;
        std::cin >> t;
        if (t == 0) {
            int p;
            std::cin >> p;
            u32 c, d;
            std::cin >> c >> d;
            seg.assign(p, {Fp(c), Fp(d)});
        }
        else {
            int l, r;
            std::cin >> l >> r;
            u32 x;
            std::cin >> x;
            std::cout << seg.fold(l, r).eval(Fp(x)) << '\n';
        }
    }
    return 0;
}

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