raybbian's CP Algos

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:heavy_check_mark: verify/ds/lazy_segtree.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#include "algo/common.h"

/* #include */
#include "algo/ds/lazy_segtree.h"
#include "algo/math/modint.h"

using namespace std;
using namespace algo;
using ds::lazy_segtree;

using mint = math::static_modint<998244353>;

struct affine_sum {
    using Value = mint;
    using Update = pair<mint, mint>;
    static Value op(Value a, Value b) {
        return a + b;
    }
    static Value e() {
        return 0;
    }
    static Update id() {
        return {1, 0};
    }
    static Update composition(Update f, Update g) {
        return {f.first * g.first, f.first * g.second + f.second};
    }
    static Value mapping(Update f, Value x, index_t len) {
        return f.first * x + f.second * len;
    }
};

void solve() {
    int n, q;
    cin >> n >> q;
    vector<mint> a(n);
    for (int i = 0; i < n; i++)
        cin >> a[i];
    lazy_segtree<affine_sum> st(a);
    for (int i = 0; i < q; i++) {
        int typ, l, r;
        cin >> typ >> l >> r;
        if (typ == 0) {
            int b, c;
            cin >> b >> c;
            st.apply(l, r - 1, {b, c});
        } else {
            cout << st.query(l, r - 1) << '\n';
        }
    }
}

signed main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    // int t;
    // cin >> t;
    // while (t--)
    solve();
}

#line 1 "verify/ds/lazy_segtree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#line 2 "algo/common.h"
#ifndef PREPROCESS
#include <bits/stdc++.h>
#include <cassert>
#endif

namespace algo {

// Indices and sizes into library containers. Signed, so the usual "walk down to
// -1" loops still terminate; widening the whole library is a change here alone.
using index_t = int;

} // namespace algo
#line 3 "verify/ds/lazy_segtree.test.cpp"

/* #include */
#line 3 "algo/utils/bits.h"

namespace algo::utils {

// Returns number of set bits in x
constexpr int popcnt(int64_t x) {
    return __builtin_popcountll(x);
}
// Returns floor(log_2(x))
constexpr int lg2(uint64_t x) {
    return std::bit_width(x) - 1;
}

} // namespace algo::utils
#line 4 "algo/ds/lazy_segtree.h"

namespace algo::ds {

// The monoid a query folds over. repeat(x, len) is x folded with itself len
// times: what a segment of len equal cells collapses to.
template <typename T>
struct sum_monoid {
    using Value = T;
    static Value op(Value a, Value b) {
        return a + b;
    }
    static Value e() {
        return Value(0);
    }
    static Value repeat(Value x, index_t len) {
        return x * len;
    }
};

template <typename T>
struct min_monoid {
    using Value = T;
    static Value op(Value a, Value b) {
        return std::min(a, b);
    }
    static Value e() {
        return std::numeric_limits<Value>::max();
    }
    static Value repeat(Value x, index_t) {
        return x;
    }
};

template <typename T>
struct max_monoid {
    using Value = T;
    static Value op(Value a, Value b) {
        return std::max(a, b);
    }
    static Value e() {
        return std::numeric_limits<Value>::lowest();
    }
    static Value repeat(Value x, index_t) {
        return x;
    }
};

// Adds f to every cell of a segment. The + is on Value, not op, so a range add
// shifts a min or max by f instead of folding f into it.
template <typename M>
struct add_lazy : M {
    using Value = typename M::Value;
    using Update = Value;
    static Update id() {
        return Update(0);
    }
    static Update composition(Update f, Update g) {
        return f + g;
    }
    static Value mapping(Update f, Value x, index_t len) {
        return x + M::repeat(f, len);
    }
};

// Overwrites every cell of a segment. Any Value may be written, so none is free
// to mean "nothing pending" and Update needs the extra nullopt. A write
// discards what it lands on, so of two writes the later wins.
template <typename M>
struct assign_lazy : M {
    using Value = typename M::Value;
    using Update = std::optional<Value>;
    static Update id() {
        return std::nullopt;
    }
    static Update composition(Update f, Update g) {
        return f ? f : g;
    }
    static Value mapping(Update f, Value x, index_t len) {
        return f ? M::repeat(*f, len) : x;
    }
};

// P supplies the monoid (Value, op, e) that queries fold over, the monoid of
// pending updates (Update, composition, id) where composition(f, g) applies g
// first, and mapping(f, x), which applies an update to a whole fold rather than
// to one cell. mapping may take the number of cells x covers as a third
// argument, for updates that scale with segment length. Inheriting P is free
// and keeps its names reachable.
template <typename P>
struct lazy_segtree : P {
    using Value = typename P::Value;
    using Update = typename P::Update;

    // If the default value for leaf elements is not identical (e.g. in the case
    // that indices are stored) then you must use the alternative constructor
    lazy_segtree(index_t _n) : lazy_segtree(std::vector<Value>(_n, P::e())) {
    }
    lazy_segtree(const std::vector<Value> &a)
        : n((index_t)a.size()), sz((index_t)std::bit_ceil((uint32_t)n)),
          lg(utils::lg2(sz)), d(2 * sz, P::e()), lz(sz, P::id()) {
        std::copy(a.begin(), a.end(), d.begin() + sz);
        for (index_t i = sz - 1; i >= 1; i--)
            pull(i);
    }
    Value get(index_t p) {
        assert(0 <= p && p < n);
        p += sz;
        push_down(p);
        return d[p];
    }
    void set(index_t p, Value x) {
        assert(0 <= p && p < n);
        p += sz;
        push_down(p);
        d[p] = x;
        for (index_t i = 1; i <= lg; i++)
            pull(p >> i);
    }
    // Inclusive on [l, r]
    Value query(index_t l, index_t r) {
        assert(0 <= l && r < n);
        if (l > r) return P::e();
        l += sz, r += sz + 1;
        push_down(l, r);
        // Two accumulators keep the fold in index order, which ops that are
        // not commutative need.
        Value ml = P::e(), mr = P::e();
        for (; l < r; l >>= 1, r >>= 1) {
            if (l & 1) ml = P::op(ml, d[l++]);
            if (r & 1) mr = P::op(d[--r], mr);
        }
        return P::op(ml, mr);
    }
    Value all() {
        return d[1];
    }
    // Inclusive on [l, r]
    void apply(index_t l, index_t r, Update f) {
        assert(0 <= l && r < n);
        if (l > r) return;
        l += sz, r += sz + 1;
        push_down(l, r);
        index_t l0 = l, r0 = r;
        for (index_t len = 1; l < r; l >>= 1, r >>= 1, len <<= 1) {
            if (l & 1) all_apply(l++, f, len);
            if (r & 1) all_apply(--r, f, len);
        }
        for (index_t i = 1; i <= lg; i++) {
            if (((l0 >> i) << i) != l0) pull(l0 >> i);
            if (((r0 >> i) << i) != r0) pull((r0 - 1) >> i);
        }
    }
    friend std::ostream &operator<<(std::ostream &os, lazy_segtree t) {
        // A parent precedes its children in index order, so one increasing
        // sweep pushes every pending update out to the leaves.
        for (index_t k = 1; k < t.sz; k++)
            t.push(k, t.sz >> (utils::lg2(k) + 1));
        os << "[";
        bool first = true;
        for (index_t i = 0; i < t.n; i++) {
            if (!first) os << ", ";
            first = false;
            os << t.d[t.sz + i];
        }
        return os << "]";
    }

private:
    // A 1-indexed heap of 2 * sz nodes, the cells past n padded with e(). d[k]
    // is always current; lz[k] is owed to k's children, never to k itself.
    index_t n, sz, lg;
    std::vector<Value> d;
    std::vector<Update> lz;

    void pull(index_t k) {
        d[k] = P::op(d[2 * k], d[2 * k + 1]);
    }
    // len is the number of cells node k covers. Policies whose updates ignore
    // segment length may leave the third parameter of mapping off.
    void all_apply(index_t k, const Update &f, index_t len) {
        if constexpr (requires { P::mapping(f, d[k], len); }) {
            d[k] = P::mapping(f, d[k], len);
        } else {
            d[k] = P::mapping(f, d[k]);
        }
        if (k < sz) lz[k] = P::composition(f, lz[k]);
    }
    // len is the number of cells each child of node k covers
    void push(index_t k, index_t len) {
        all_apply(2 * k, lz[k], len);
        all_apply(2 * k + 1, lz[k], len);
        lz[k] = P::id();
    }
    // Clears every pending update above leaf p
    void push_down(index_t p) {
        for (index_t i = lg; i >= 1; i--)
            push(p >> i, index_t(1) << (i - 1));
    }
    // Same for the two boundary paths of [l, r). A node wholly inside the range
    // is used as a whole and its own value is already current, so nothing below
    // it needs clearing.
    void push_down(index_t l, index_t r) {
        for (index_t i = lg; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i, index_t(1) << (i - 1));
            if (((r >> i) << i) != r) push((r - 1) >> i, index_t(1) << (i - 1));
        }
    }
};

template <typename T>
using add_sum = add_lazy<sum_monoid<T>>;
template <typename T>
using add_min = add_lazy<min_monoid<T>>;
template <typename T>
using add_max = add_lazy<max_monoid<T>>;
template <typename T>
using assign_sum = assign_lazy<sum_monoid<T>>;
template <typename T>
using assign_min = assign_lazy<min_monoid<T>>;
template <typename T>
using assign_max = assign_lazy<max_monoid<T>>;

} // namespace algo::ds
#line 3 "algo/math/common.h"

namespace algo::math {

constexpr int64_t safe_mod(int64_t x, int64_t m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Returns (x ** n) % m
constexpr int64_t pow_mod_constexpr(int64_t x, int64_t n, int m) {
    assert(0 <= n);
    assert(1 <= m);
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    uint64_t r = 1;
    uint64_t y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

struct barrett {
    constexpr explicit barrett(uint64_t _m) : m(_m), im(-1ULL / _m) {
        assert(1 <= _m);
    }
    uint64_t mod() const {
        return m;
    };
    uint64_t reduce(uint64_t a) const {
        uint64_t q = (uint64_t)((__uint128_t(im) * a) >> 64);
        uint64_t r = a - q * m;
        return r - (r >= m) * m;
    }

private:
    uint64_t m, im;
};

constexpr int64_t c_div(int64_t a, int64_t b) {
    return a / b + ((a ^ b) > 0 && a % b);
}
constexpr int64_t f_div(int64_t a, int64_t b) {
    return a / b - ((a ^ b) < 0 && a % b);
}

auto bpow(auto const &x, auto n, auto const &one, auto op) {
    if (n == 0) {
        return one;
    } else {
        auto t = bpow(x, n / 2, one, op);
        t = op(t, t);
        if (n % 2) {
            t = op(t, x);
        }
        return t;
    }
}
auto bpow(auto x, auto n, auto ans) {
    return bpow(x, n, ans, std::multiplies{});
}
template <typename T>
T bpow(T const &x, auto n) {
    return bpow(x, n, T(1));
}

// Returns a pair(g, x) s.t. g = gcd(a, n), xa = g (mod n), 0 <= x < n/g
// If r > 1 then a is not invertible mod n
constexpr std::pair<int64_t, int64_t> inv_gcd(int64_t a, int64_t n) {
    a = safe_mod(a, n);
    if (a == 0) return {n, 0};

    int64_t t = 0, newt = 1;
    int64_t r = n, newr = a;

    while (newr) {
        int64_t quotient = r / newr;
        r -= newr * quotient;
        t -= newt * quotient;

        std::swap(r, newr);
        std::swap(t, newt);
    }
    if (t < 0) t += n / r;
    return {r, t};
}

} // namespace algo::math
#line 4 "algo/math/modint.h"

namespace algo::math {

// A modulus fixed at compile time: no state, and the division folds into a
// multiply-shift.
template <int Mod>
struct static_mod {
    static constexpr int mod() {
        return Mod;
    }
    static int reduce(uint64_t x) {
        return (int)(x % (uint64_t)Mod);
    }
};

// A modulus known only at run time, held for the extent of with_mod. Nesting is
// rejected: values built under the outer modulus would survive into the inner
// one. Use a second id to hold two moduli at once.
template <int id>
struct dynamic_mod {
    static int mod() {
        assert(armed);
        return bt.mod();
    }
    static int reduce(uint64_t x) {
        return (int)bt.reduce(x);
    }
    static auto with_mod(int m, auto callback) {
        assert(1 <= m && !armed);
        struct scoped {
            ~scoped() {
                armed = false;
            }
        } _;
        bt = barrett(m), armed = true;
        return callback();
    }

private:
    static inline barrett bt{1};
    static inline bool armed = false;
};

// P supplies mod() and reduce(). Inheriting it makes both reachable through the
// modint (as is with_mod), and an empty policy costs no space.
template <typename P>
struct modint : P {
    modint() : v(0) {
    }
    modint(int64_t _v) {
        v = (-P::mod() < _v && _v < P::mod()) ? _v : _v % P::mod();
        if (v < 0) v += P::mod();
    }
    modint &operator+=(const modint &other) {
        v += other.v;
        if (v >= P::mod()) v -= P::mod();
        return *this;
    }
    modint &operator-=(const modint &other) {
        v -= other.v;
        if (v < 0) v += P::mod();
        return *this;
    }
    modint &operator*=(const modint &other) {
        v = P::reduce((uint64_t)v * other.v);
        return *this;
    }
    modint &operator/=(const modint &other) {
        return *this = *this * other.inv();
    }
    modint &operator++() {
        v++;
        if (v == P::mod()) v = 0;
        return *this;
    }
    modint &operator--() {
        if (v == 0) v = P::mod();
        v--;
        return *this;
    }
    modint operator++(int) {
        modint result = *this;
        ++*this;
        return result;
    }
    modint operator--(int) {
        modint result = *this;
        --*this;
        return result;
    }
    friend modint operator+(modint a, const modint &b) {
        return a += b;
    }
    friend modint operator-(modint a, const modint &b) {
        return a -= b;
    }
    friend modint operator*(modint a, const modint &b) {
        return a *= b;
    }
    friend modint operator/(modint a, const modint &b) {
        return a /= b;
    }
    friend modint operator-(modint a) {
        return 0 - a;
    }
    modint inv() const {
        auto eg = inv_gcd(v, P::mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend bool operator==(const modint &a, const modint &b) {
        return a.v == b.v;
    }
    friend bool operator!=(const modint &a, const modint &b) {
        return !(a == b);
    }
    explicit operator int() const {
        return v;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &a) {
        return os << a.v;
    }
    friend std::istream &operator>>(std::istream &is, modint &a) {
        is >> a.v;
        a.v = (-P::mod() < a.v && a.v < P::mod()) ? a.v : a.v % P::mod();
        if (a.v < 0) a.v += P::mod();
        return is;
    }

private:
    int v;
};

template <int Mod>
using static_modint = modint<static_mod<Mod>>;
template <int id = 0>
using dynamic_modint = modint<dynamic_mod<id>>;

} // namespace algo::math
#line 7 "verify/ds/lazy_segtree.test.cpp"

using namespace std;
using namespace algo;
using ds::lazy_segtree;

using mint = math::static_modint<998244353>;

struct affine_sum {
    using Value = mint;
    using Update = pair<mint, mint>;
    static Value op(Value a, Value b) {
        return a + b;
    }
    static Value e() {
        return 0;
    }
    static Update id() {
        return {1, 0};
    }
    static Update composition(Update f, Update g) {
        return {f.first * g.first, f.first * g.second + f.second};
    }
    static Value mapping(Update f, Value x, index_t len) {
        return f.first * x + f.second * len;
    }
};

void solve() {
    int n, q;
    cin >> n >> q;
    vector<mint> a(n);
    for (int i = 0; i < n; i++)
        cin >> a[i];
    lazy_segtree<affine_sum> st(a);
    for (int i = 0; i < q; i++) {
        int typ, l, r;
        cin >> typ >> l >> r;
        if (typ == 0) {
            int b, c;
            cin >> b >> c;
            st.apply(l, r - 1, {b, c});
        } else {
            cout << st.query(l, r - 1) << '\n';
        }
    }
}

signed main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    // int t;
    // cin >> t;
    // while (t--)
    solve();
}

Test cases

Env Name Status Elapsed Memory
g++ example_00 :heavy_check_mark: AC 2 ms 4 MB
g++ max_random_00 :heavy_check_mark: AC 396 ms 14 MB
g++ max_random_01 :heavy_check_mark: AC 387 ms 14 MB
g++ max_random_02 :heavy_check_mark: AC 370 ms 14 MB
g++ random_00 :heavy_check_mark: AC 323 ms 13 MB
g++ random_01 :heavy_check_mark: AC 308 ms 14 MB
g++ random_02 :heavy_check_mark: AC 214 ms 5 MB
g++ small_00 :heavy_check_mark: AC 2 ms 4 MB
g++ small_01 :heavy_check_mark: AC 2 ms 4 MB
g++ small_02 :heavy_check_mark: AC 2 ms 4 MB
g++ small_03 :heavy_check_mark: AC 2 ms 4 MB
g++ small_04 :heavy_check_mark: AC 2 ms 4 MB
g++ small_05 :heavy_check_mark: AC 2 ms 4 MB
g++ small_06 :heavy_check_mark: AC 2 ms 4 MB
g++ small_07 :heavy_check_mark: AC 2 ms 4 MB
g++ small_08 :heavy_check_mark: AC 2 ms 4 MB
g++ small_09 :heavy_check_mark: AC 2 ms 4 MB
g++ small_random_00 :heavy_check_mark: AC 2 ms 4 MB
g++ small_random_01 :heavy_check_mark: AC 2 ms 4 MB
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