data_structure/test/range_affine_range_sum.test.cpp

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Last update: 2023-05-04 19:50:45+09:00
Problem: https://judge.yosupo.jp/problem/range_affine_range_sum

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Code

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

#define FAST_IO

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

using Mint = ModInt<mod998244353>;

struct Node {
    i32 len;
    Mint sum;
};

struct Fn {
    Mint a, b;
};

struct Ops {
    using Value = Node;
    using Func = Fn;
    static Value id() {
        return Node{0, Mint()};
    }
    static Value op(const Value &x, const Value &y) {
        return Node{x.len + y.len, x.sum + y.sum};
    }
    static Func func_id() {
        return Fn{Mint(1), Mint()};
    }
    static Func composite(const Func &f, const Func &g) {
        return Fn{f.a * g.a, f.a * g.b + f.b};
    }
    static Value apply(const Func &f, const Value &x) {
        return Node{x.len, x.sum * f.a + Mint(x.len) * f.b};
    }
};

int main() {
    i32 n, q;
    cin >> n >> q;
    Vec<Node> a(n);
    REP(i, n) {
        a[i].len = 1;
        cin >> a[i].sum;
    }
    LazySegmentTree<Ops> seg(a);
    REP(qi, q) {
        i32 type;
        cin >> type;
        if (type == 0) {
            i32 l, r;
            Fn f;
            cin >> l >> r >> f.a >> f.b;
            seg.apply(l, r, f);
        } else {
            i32 l, r;
            cin >> l >> r;
            cout << seg.prod(l, r).sum << '\n';
        }
    }
}

#line 1 "data_structure/test/range_affine_range_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"

#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/lazy_segment_tree.hpp"

#line 6 "data_structure/lazy_segment_tree.hpp"

template <typename MonoidFunc>
class LazySegmentTree {
public:
    using Value = typename MonoidFunc::Value;
    using Func = typename MonoidFunc::Func;

private:
    int old_length;
    int lg;
    int length;
    std::vector<Value> values;
    std::vector<Func> funcs;

    static int lg2(int n) {
        int x = 1;
        int l = 0;
        while (x < n) {
            x <<= 1;
            ++l;
        }
        return l;
    }

    void _apply(int idx, const Func &func) {
        values[idx] = MonoidFunc::apply(func, values[idx]);
        funcs[idx] = MonoidFunc::composite(func, funcs[idx]);
    }

    void push(int idx) {
        _apply(idx << 1, funcs[idx]);
        _apply(idx << 1 | 1, funcs[idx]);
        funcs[idx] = MonoidFunc::func_id();
    }

    void recalc_values(int idx) {
        values[idx] = MonoidFunc::op(values[idx << 1], values[idx << 1 | 1]);
    }

public:
    LazySegmentTree(int n) :
        old_length(n),
        lg(lg2(n)),
        length(1 << lg),
        values(length << 1, MonoidFunc::id()),
        funcs(length << 1, MonoidFunc::func_id()) {
        assert(n >= 0);    
    }

    LazySegmentTree(const std::vector<Value> &v) :
        old_length((int) v.size()),
        lg(lg2(old_length)),
        length(1 << lg),
        values(length << 1, MonoidFunc::id()),
        funcs(length << 1, MonoidFunc::func_id()) {
        for (int i = 0; i < old_length; ++i) {
            values[i + length] = v[i];
        }
        for (int i = length - 1; i > 0; --i) {
            recalc_values(i);
        }
    }

    template <typename F>
    LazySegmentTree(int n, const F &f) :
        old_length(n),
        lg(lg2(n)),
        length(1 << lg),
        values(length << 1, MonoidFunc::id()),
        funcs(length << 1, MonoidFunc::func_id()) {
        for (int i = 0; i < old_length; ++i) {
            values[i + length] = f(i);
        }
        for (int i = length - 1; i > 0; --i) {
            recalc_values(i);
        }
    }

    void update(int idx, Value val) {
        assert(idx >= 0 && idx < old_length);
        idx += length;
        for (int i = lg; i > 0; --i) {
            push(idx >> i);
        }
        values[idx] = std::move(val);
        while (idx >>= 1) {
            recalc_values(idx);
        }
    }

    void apply(int l, int r, const Func &func) {
        assert(l >= 0 && l <= r && r <= old_length);
        if (l == r) {
            return;
        }
        l += length;
        r += length;
        int _l = l;
        int _r = r;
        for (int i = lg; i > 0; --i) {
            push(_l >> i);
            push((_r - 1) >> i);
        }
        while (l < r) {
            if (l & 1) {
                _apply(l++, func);
            }
            if (r & 1) {
                _apply(--r, func);
            }
            l >>= 1;
            r >>= 1;
        }
        for (int i = 1; i <= lg; ++i) {
            if ((_l >> i << i) != _l) {
                recalc_values(_l >> i);
            }
            if ((_r >> i << i) != _r) {
                recalc_values((_r - 1) >> i);
            }
        }
    }

    Value prod(int l, int r) {
        assert(l >= 0 && l <= r && r <= old_length);
        if (l == r) {
            return MonoidFunc::id();
        }
        l += length;
        r += length;
        for (int i = lg; i > 0; --i) {
            push(l >> i);
            push((r - 1) >> i);
        }
        Value lp = MonoidFunc::id();
        Value rp = MonoidFunc::id();
        while (l < r) {
            if (l & 1) {
                lp = MonoidFunc::op(lp, values[l++]);
            }
            if (r & 1) {
                rp = MonoidFunc::op(values[--r], rp);
            }
            l >>= 1;
            r >>= 1;
        }
        return MonoidFunc::op(lp, rp);
    }
    
    Value all_prod() const {
        return values[1];
    }
};

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

using Mint = ModInt<mod998244353>;

struct Node {
    i32 len;
    Mint sum;
};

struct Fn {
    Mint a, b;
};

struct Ops {
    using Value = Node;
    using Func = Fn;
    static Value id() {
        return Node{0, Mint()};
    }
    static Value op(const Value &x, const Value &y) {
        return Node{x.len + y.len, x.sum + y.sum};
    }
    static Func func_id() {
        return Fn{Mint(1), Mint()};
    }
    static Func composite(const Func &f, const Func &g) {
        return Fn{f.a * g.a, f.a * g.b + f.b};
    }
    static Value apply(const Func &f, const Value &x) {
        return Node{x.len, x.sum * f.a + Mint(x.len) * f.b};
    }
};

int main() {
    i32 n, q;
    cin >> n >> q;
    Vec<Node> a(n);
    REP(i, n) {
        a[i].len = 1;
        cin >> a[i].sum;
    }
    LazySegmentTree<Ops> seg(a);
    REP(qi, q) {
        i32 type;
        cin >> type;
        if (type == 0) {
            i32 l, r;
            Fn f;
            cin >> l >> r >> f.a >> f.b;
            seg.apply(l, r, f);
        } else {
            i32 l, r;
            cin >> l >> r;
            cout << seg.prod(l, r).sum << '\n';
        }
    }
}