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:heavy_check_mark: segment_tree/test/lazy_segment_tree_product_sum_add2.test.cpp

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include <iostream>

#include "../../algebra/acted_monoid/acted_monoid_product_sum_add2.hpp"
#include "../../segment_tree/lazy_segment_tree.hpp"
#include "../../math/static_modint.hpp"
using mint = mint998;

std::vector<int> solve(std::vector<int>& a,
                       std::vector<int>& b,
                       std::vector<std::tuple<int, int, int, int>>& query) {
    const int n = (int)(a.size());
    std::vector<ProductSum<mint>> segi(n);
    for (int i = 0; i < n; i++) {
        segi[i] = {mint(a[i]) * mint(b[i]), mint(a[i]), mint(b[i])};
    }
    LazySegmentTree<ActedMonoidProductSumAdd2<mint>> seg(segi);
    std::vector<int> ans;
    for (auto&& [type, l, r, x] : query) {
        l--;
        if (type == 1) {
            seg.apply(l, r, {x, 0});
        } else if (type == 2) {
            seg.apply(l, r, {0, x});
        } else {
            ans.push_back(seg.prod(l, r).ab.val());
        }
    }
    return ans;
}

void test1_sample1() {
    std::vector<int> a = {1, 3, 5, 6, 8};
    std::vector<int> b = {3, 1, 2, 1, 2};
    std::vector<std::tuple<int, int, int, int>> query = {
        {3, 1, 3, -1}, {1, 2, 5, 3}, {3, 1, 3, -1},
        {1, 1, 3, 1},  {2, 5, 5, 2}, {3, 1, 5, -1}};
    std::vector<int> sol = {16, 25, 84};
    assert(solve(a, b, query) == sol);
}

void test2_sample2() {
    std::vector<int> a = {1000000000, 1000000000};
    std::vector<int> b = {1000000000, 1000000000};
    std::vector<std::tuple<int, int, int, int>> query = {
        {3, 1, 1, -1}, {1, 2, 2, 1000000000}, {3, 1, 2, -1}};
    std::vector<int> sol = {716070898, 151723988};
    assert(solve(a, b, query) == sol);
}

int main() {
    // https://atcoder.jp/contests/abc357/tasks/abc357_f
    test1_sample1();
    test2_sample2();
    int a, b;
    std::cin >> a >> b;
    std::cout << a + b << '\n';
    return 0;
}
#line 1 "segment_tree/test/lazy_segment_tree_product_sum_add2.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include <iostream>

#line 2 "algebra/acted_monoid/acted_monoid_product_sum_add2.hpp"

// https://atcoder.jp/contests/abc357/tasks/abc357_f
template <class T> struct ProductSum {
    T ab, a, b;
};

template <class T> struct MonoidProductSum {
    using value_type = ProductSum<T>;
    static constexpr value_type operation(const value_type& a,
                                          const value_type& b) {
        return {a.ab + b.ab, a.a + b.a, a.b + b.b};
    }
    static constexpr value_type identity() { return {T(0), T(0), T(0)}; }
};

template <class T> struct Add2 {
    T a, b;
};

template <class T> struct MonoidAdd2 {
    using value_type = Add2<T>;
    static constexpr value_type operation(const value_type& f,
                                          const value_type& g) {
        return {f.a + g.a, f.b + g.b};
    }
    static constexpr value_type identity() { return {T(0), T(0)}; }
};

template <class T> struct ActedMonoidProductSumAdd2 {
    using MS = MonoidProductSum<T>;
    using MF = MonoidAdd2<T>;
    using S = typename MS::value_type;
    using F = typename MF::value_type;
    static constexpr S mapping(const F f, const S x, const int size) {
        return {x.ab + f.a * x.b + f.b * x.a + f.a * f.b * T(size),
                x.a + f.a * T(size), x.b + f.b * T(size)};
    }
};
#line 2 "segment_tree/lazy_segment_tree.hpp"

#line 2 "misc/bit_ceil.hpp"

#include <cassert>

#if __cplusplus >= 202002L
#include <bit>
#endif

// bit_ceil
// (0, 1, 2, 3, 4) -> (1, 1, 2, 4, 4)
#if __cplusplus >= 202002L
using std::bit_ceil;
#else
unsigned int bit_ceil(unsigned int x) {
    unsigned int p = 1;
    while (p < x) p *= 2;
    return p;
}
unsigned long long int bit_ceil(unsigned long long int x) {
    unsigned long long int p = 1;
    while (p < x) p *= 2;
    return p;
}
#endif
int bit_ceil(int x) {
    assert(x >= 0);
    return bit_ceil((unsigned int)(x));
}
long long int bit_ceil(long long int x) {
    assert(x >= 0);
    return bit_ceil((unsigned long long int)(x));
}
#line 2 "misc/countr_zero.hpp"

#if __cplusplus >= 202002L
#include <bit>
#endif

// countr_zero
// (000, 001, 010, 011, 100) -> (32, 0, 1, 0, 2)
#if __cplusplus >= 202002L
using std::countr_zero;
#else
int countr_zero(unsigned int x) {
    return x == 0 ? 32 : __builtin_ctz(x);
}
int countr_zero(unsigned long long int x) {
    return x == 0 ? 64 : __builtin_ctzll(x);
}
#endif
int countr_zero(int x) { return countr_zero((unsigned int)(x)); }
int countr_zero(long long int x) {
    return countr_zero((unsigned long long int)(x));
}
#line 2 "misc/topbit.hpp"

#line 2 "misc/countl_zero.hpp"

#if __cplusplus >= 202002L
#include <bit>
#endif

// countl_zero
// (000, 001, 010, 011, 100) -> (32, 31, 30, 30, 29)
#if __cplusplus >= 202002L
using std::countl_zero;
#else
int countl_zero(unsigned int x) {
    return x == 0 ? 32 : __builtin_clz(x);
}
int countl_zero(unsigned long long int x) {
    return x == 0 ? 64 : __builtin_clzll(x);
}
#endif
int countl_zero(int x) { return countl_zero((unsigned int)(x)); }
int countl_zero(long long int x) {
    return countl_zero((unsigned long long int)(x));
}
#line 4 "misc/topbit.hpp"

// topbit
// (000, 001, 010, 011, 100) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return 31 - countl_zero(x); }
int topbit(unsigned int x) { return 31 - countl_zero(x); }
int topbit(long long int x) { return 63 - countl_zero(x); }
int topbit(unsigned long long int x) { return 63 - countl_zero(x); }
#line 6 "segment_tree/lazy_segment_tree.hpp"

#line 8 "segment_tree/lazy_segment_tree.hpp"
#include <vector>

// Lazy Segment Tree
template <class AM> struct LazySegmentTree {
  public:
    using MS = typename AM::MS;
    using MF = typename AM::MF;
    using S = typename MS::value_type;
    using F = typename MF::value_type;

    LazySegmentTree() = default;

    explicit LazySegmentTree(int n)
        : LazySegmentTree(std::vector<S>(n, MS::identity())) {}

    explicit LazySegmentTree(const std::vector<S>& v) : n((int)(v.size())) {
        size = bit_ceil(n);
        log = countr_zero(size);
        d = std::vector<S>(size << 1, MS::identity());
        lz = std::vector<F>(size, MF::identity());
        for (int i = 0; i < n; i++) d[i + size] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, const S& x) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    void add(int p, const S& x) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = MS::operation(d[p], x);
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S operator[](int p) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S get(int p) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) {
        assert(0 <= l and l <= r and r <= n);
        if (l == r) return MS::identity();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = MS::identity(), smr = MS::identity();
        while (l < r) {
            if (l & 1) sml = MS::operation(sml, d[l++]);
            if (r & 1) smr = MS::operation(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return MS::operation(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, const F& f) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = AM::mapping(f, d[p], 1);
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    void apply(int l, int r, const F& f) {
        assert(0 <= l and l <= r and r <= n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <class G> int max_right(int l, G& g) {
        assert(0 <= l and l <= n);
        assert(g(MS::identity()));
        if (l == n) return n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = MS::identity();
        do {
            while ((l & 1) == 0) l >>= 1;
            if (!g(MS::operation(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l <<= 1;
                    if (g(MS::operation(sm, d[l]))) {
                        sm = MS::operation(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = MS::operation(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return n;
    }

    template <class G> int min_left(int r, G& g) {
        assert(0 <= r and r <= n);
        assert(g(MS::identity()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = MS::identity();
        do {
            r--;
            while (r > 1 and (r & 1)) r >>= 1;
            if (!g(MS::operation(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (r << 1) | 1;
                    if (g(MS::operation(d[r], sm))) {
                        sm = MS::operation(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = MS::operation(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

    std::vector<S> make_vector() {
        std::vector<S> vec(n);
        for (int i = 0; i < n; i++) vec[i] = get(i);
        return vec;
    }

  private:
    int n, log, size;
    std::vector<S> d;
    std::vector<F> lz;

    inline void update(int k) {
        d[k] = MS::operation(d[k << 1], d[(k << 1) | 1]);
    }

    void all_apply(int k, const F& f) {
        d[k] = AM::mapping(f, d[k], 1 << (log - topbit(k)));
        // MF::operation(f, g), g(f(x))
        if (k < size) lz[k] = MF::operation(lz[k], f);
    }

    void push(int k) {
        all_apply(k << 1, lz[k]);
        all_apply((k << 1) | 1, lz[k]);
        lz[k] = MF::identity();
    }
};
#line 2 "math/static_modint.hpp"

#include <utility>
#line 5 "math/static_modint.hpp"

// constexpr ... for constexpr bool prime()
template <int m> struct StaticModint {
    using mint = StaticModint;
    unsigned int _v;

    static constexpr int mod() { return m; }
    static constexpr unsigned int umod() { return m; }

    constexpr StaticModint() : _v(0) {}

    template <class T> constexpr StaticModint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }

    constexpr unsigned int val() const { return _v; }

    constexpr mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    constexpr mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    constexpr mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    constexpr mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    constexpr mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint &operator-=(const mint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint &operator*=(const mint &rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    constexpr mint &operator/=(const mint &rhs) { return (*this *= rhs.inv()); }

    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }

    constexpr mint pow(long long n) const {
        assert(n >= 0);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }

    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend constexpr mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
    friend constexpr mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
    friend constexpr mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
    friend constexpr mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
    friend constexpr bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
    friend constexpr bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
    friend std::ostream &operator<<(std::ostream &os, const mint &v) { return os << v.val(); }

    static constexpr bool prime = []() -> bool {
        if (m == 1) return false;
        if (m == 2 || m == 7 || m == 61) return true;
        if (m % 2 == 0) return false;
        unsigned int d = m - 1;
        while (d % 2 == 0) d /= 2;
        for (unsigned int a : {2, 7, 61}) {
            unsigned int t = d;
            mint y = mint(a).pow(t);
            while (t != m - 1 and y != 1 and y != m - 1) {
                y *= y;
                t <<= 1;
            }
            if (y != m - 1 and t % 2 == 0) {
                return false;
            }
        }
        return true;
    }();
    static constexpr std::pair<int, int> inv_gcd(int a, int b) {
        if (a == 0) return {b, 0};
        int s = b, t = a, m0 = 0, m1 = 1;
        while (t) {
            const int u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            std::swap(s, t);
            std::swap(m0, m1);
        }
        if (m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
using mint107 = StaticModint<1000000007>;
using mint998 = StaticModint<998244353>;
#line 8 "segment_tree/test/lazy_segment_tree_product_sum_add2.test.cpp"
using mint = mint998;

std::vector<int> solve(std::vector<int>& a,
                       std::vector<int>& b,
                       std::vector<std::tuple<int, int, int, int>>& query) {
    const int n = (int)(a.size());
    std::vector<ProductSum<mint>> segi(n);
    for (int i = 0; i < n; i++) {
        segi[i] = {mint(a[i]) * mint(b[i]), mint(a[i]), mint(b[i])};
    }
    LazySegmentTree<ActedMonoidProductSumAdd2<mint>> seg(segi);
    std::vector<int> ans;
    for (auto&& [type, l, r, x] : query) {
        l--;
        if (type == 1) {
            seg.apply(l, r, {x, 0});
        } else if (type == 2) {
            seg.apply(l, r, {0, x});
        } else {
            ans.push_back(seg.prod(l, r).ab.val());
        }
    }
    return ans;
}

void test1_sample1() {
    std::vector<int> a = {1, 3, 5, 6, 8};
    std::vector<int> b = {3, 1, 2, 1, 2};
    std::vector<std::tuple<int, int, int, int>> query = {
        {3, 1, 3, -1}, {1, 2, 5, 3}, {3, 1, 3, -1},
        {1, 1, 3, 1},  {2, 5, 5, 2}, {3, 1, 5, -1}};
    std::vector<int> sol = {16, 25, 84};
    assert(solve(a, b, query) == sol);
}

void test2_sample2() {
    std::vector<int> a = {1000000000, 1000000000};
    std::vector<int> b = {1000000000, 1000000000};
    std::vector<std::tuple<int, int, int, int>> query = {
        {3, 1, 1, -1}, {1, 2, 2, 1000000000}, {3, 1, 2, -1}};
    std::vector<int> sol = {716070898, 151723988};
    assert(solve(a, b, query) == sol);
}

int main() {
    // https://atcoder.jp/contests/abc357/tasks/abc357_f
    test1_sample1();
    test2_sample2();
    int a, b;
    std::cin >> a >> b;
    std::cout << a + b << '\n';
    return 0;
}
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