tests/ds/segment_tree_lazy.test.cpp

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• Last update: 2021-09-12 23:20:08-04:00
• Problem: https://judge.yosupo.jp/problem/range_affine_range_sum

Depends on

• ds/segment_tree_lazy.hpp
• math/eea.hpp
• math/mod.hpp
• template.hpp
• tests/test_utils.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#include "../../template.hpp"
#include "../test_utils.hpp"
#include "../../ds/segment_tree_lazy.hpp"
#include "../../math/mod.hpp"

// A = (ax+b), B = (cx+d)
// c(ax+b)+d = acx + bc + d
using MI = ModInt<int, 998244353>;
using pm = pair<MI, MI>;
struct AffineComp {
    using Data = MI;
    using Lazy = pm;
    const Data vdef = 0;
    const Lazy ldef = {1, 0};
    Data merge(Data l, Data r) const { return l + r; }
    Lazy mergeLazy(Lazy to, Lazy v) const {
        auto [a, b] = to;
        auto [c, d] = v;
        return {a * c, b * c + d};
    }
    void applyLazy(Data &to, Lazy &v, int l, int r) { to = v.first * to + (r - l + 1) * v.second; }
};

int main() {
    fast_io();
    int N = readi(), Q = readi();
    LazySegmentTree<AffineComp> seg; seg.init(N);
    for (auto [i, v] : enumerate(readv<int>(N), 1))
        seg.setPoint(i, v);
    while (Q--) {
        if (readi() == 0) {
            int l = readi() + 1, r = readi(), b = readi(), c = readi();
            seg.update(l, r, {b, c});
        }
        else {
            int l = readi()+1, r = readi();
            print(seg.query(l, r));
        }
    }
}

#line 1 "tests/ds/segment_tree_lazy.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#line 2 "template.hpp"
#include <bits/stdc++.h>
#define DEBUG 1
using namespace std;

// Defines
#define fs first
#define sn second
#define pb push_back
#define eb emplace_back
#define mpr make_pair
#define mtp make_tuple
#define all(x) (x).begin(), (x).end()
// Basic type definitions
#if __cplusplus == 201703L // CPP17 only things
template <typename T> using opt_ref = optional<reference_wrapper<T>>; // for some templates
#endif
using ll = long long; using ull = unsigned long long; using ld = long double;
using pii = pair<int, int>; using pll = pair<long long, long long>;
#ifdef __GNUG__
// PBDS order statistic tree
#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template <typename T, class comp = less<T>> using os_tree = tree<T, null_type, comp, rb_tree_tag, tree_order_statistics_node_update>;
template <typename K, typename V, class comp = less<K>> using treemap = tree<K, V, comp, rb_tree_tag, tree_order_statistics_node_update>;
// HashSet
#include <ext/pb_ds/assoc_container.hpp>
template <typename T, class Hash> using hashset = gp_hash_table<T, null_type, Hash>;
template <typename K, typename V, class Hash> using hashmap = gp_hash_table<K, V, Hash>;
const ll RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash { ll operator()(ll x) const { return x ^ RANDOM; } };
#endif
// More utilities
int SZ(string &v) { return v.length(); }
template <typename C> int SZ(C &v) { return v.size(); }
template <typename C> void UNIQUE(vector<C> &v) { sort(v.begin(), v.end()); v.resize(unique(v.begin(), v.end()) - v.begin()); }
template <typename T, typename U> void maxa(T &a, U b) { a = max(a, b); }
template <typename T, typename U> void mina(T &a, U b) { a = min(a, b); }
const ll INF = 0x3f3f3f3f, LLINF = 0x3f3f3f3f3f3f3f3f;
#line 3 "tests/test_utils.hpp"

// I/O
template <typename T> void print(T v) {
    cout << v << '\n';
}

template <typename T, typename... Rest> void print(T v, Rest... vs) {
    cout << v << ' ';
    print(vs...);
}

void fast_io() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
}

// Reading operators
template <typename T, typename U> istream& operator>>(istream& in, pair<T, U> &o) {
    return in >> o.first >> o.second;
}

// Read helpers
int readi() {
    int x; cin >> x;
    return x;
}

ll readl() {
    ll x; cin >> x;
    return x;
}

template <typename T> vector<T> readv(int n) {
    vector<T> res(n);
    for (auto &x : res) cin >> x;
    return res;
}

// Functional stuff
template <typename T> vector<pair<int, T>> enumerate(vector<T> v, int start = 0) {
    vector<pair<int, T>> res;
    for (auto &x : v)
        res.emplace_back(start++, x);
    return res;
}

#line 3 "ds/segment_tree_lazy.hpp"

// Example comparator: Range min + Range increment
// In the functions mergeLazy and applyLazy, objects are merged from `v` to `to`.  In the function merge, data is merged from left to right
struct Comp {
    using Data = int;
    using Lazy = int;
    const Data vdef = INF;
    const Lazy ldef = 0;
    Data merge(Data l, Data r) const { return min(l, r); }
    Lazy mergeLazy(Lazy to, Lazy v) const { return to + v; }
    void applyLazy(Data &to, Lazy &v, int l, int r) { to += v; }
};
#define MID int mid = (l + r) / 2, lhs = i + 1, rhs = i + (mid - l + 1) * 2;
template <class Comp> struct LazySegmentTree {
    using Data = typename Comp::Data; using Lazy = typename Comp::Lazy; Comp C;
    int N;
    vector<Data> seg; vector<Lazy> lazy;
    void init(int n0) {
        N = n0;
        seg.assign(2 * N + 2, C.vdef);
        lazy.assign(2 * N + 2, C.ldef);
    }
    void push(int i, int l, int r) {
        if (lazy[i] != C.ldef) {
            MID;
            C.applyLazy(seg[i], lazy[i], l, r);
            if (l != r) {
                lazy[lhs] = C.mergeLazy(lazy[lhs], lazy[i]);
                lazy[rhs] = C.mergeLazy(lazy[rhs], lazy[i]);
            }
            lazy[i] = C.ldef;
        }
    }
    Data _query(int ql, int qr, int i, int l, int r) {
        if (ql > r || qr < l) return C.vdef;
        push(i, l, r);
        if (l >= ql && r <= qr) return seg[i];
        MID;
        return C.merge(_query(ql, qr, lhs, l, mid), _query(ql, qr, rhs, mid + 1, r));
    }
    Data _update(int ql, int qr, Lazy v, int i, int l, int r) {
        push(i, l, r);
        if (ql > r || qr < l) return seg[i];
        if (l >= ql && r <= qr) {
            lazy[i] = v;
            push(i, l, r);
            return seg[i];
        }
        MID;
        return seg[i] = C.merge(_update(ql, qr, v, lhs, l, mid), _update(ql, qr, v, rhs, mid + 1, r));
    }
    Data _setPoint(int q, Data v, int i, int l, int r) {
        push(i, l, r);
        if (q > r || q < l) return seg[i];
        if (l >= q && r <= q) return seg[i] = v;
        MID;
        return seg[i] = C.merge(_setPoint(q, v, lhs, l, mid), _setPoint(q, v, rhs, mid + 1, r));
    }
    Data query(int ql, int qr) { return _query(ql, qr, 1, 1, N); }
    void update(int ql, int qr, Lazy v) { _update(ql, qr, v, 1, 1, N); }
    void setPoint(int q, Data v) { _setPoint(q, v, 1, 1, N); }
};
#line 3 "math/eea.hpp"

/*
 * ax + by = gcd(a, b)
 *
 * we know
 * bx' + (a%b)y' = gcd(a, b)
 *
 * bx' + (a-b*(a//b))y' = gcd(a, b)
 * bx' + ay' - b*(a//b)y' = gcd(a, b)
 * ay' + b(x' - (a//b)y') = gcd(a, b)
 */
template <typename T> T extgcd(T a, T b, T &x, T &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    T x0, y0, res = extgcd(b, a%b, x0, y0);
    x = y0;
    y = x0 - (a / b) * y0;
    return res;
}
#line 4 "math/mod.hpp"

// based on Tourist modInt orz
template <typename MD> struct _ModInt {
    using T = typename decay<decltype(MD::value)>::type;
    static_assert(sizeof(T) >= 4, "size of T must be at least 32 bits");
    static_assert(sizeof(T) <= 8, "size of T must be at most 64 bits");
    static_assert(is_integral<T>::value, "T must be an integral type");
#ifdef __SIZEOF_INT128__
    using mul_t = typename conditional<sizeof(T) <= 4, int64_t, __int128>::type;
#else
    using mul_t = int64_t;
    static_assert(sizeof(T) <= 4, "int128 not available, cannot use 64-bit size of T");
#endif

    constexpr static T mod() { return MD::value; }

    template <typename U> static T normalize(const U& x) {
        T res = x;
        res %= mod();
        if (res < 0) res += mod();
        return res;
    }

    T value;
    constexpr _ModInt() : value() {}
    template <typename U> _ModInt(const U& x) { value = normalize(x); }
    const T& operator()() const { return value; }
    template <typename U> operator U() const { return static_cast<U>(value); }

    // FastPow
    template <typename U> static _ModInt pow(_ModInt x, U y) {
        _ModInt res(1);
        for (; y; y /= 2) {
            if (y & 1) res *= x;
            x *= x;
        }
        return res;
    }
    static _ModInt inv(const _ModInt &x) {
        T inv, _; extgcd(x.value, mod(), inv, _);
        return _ModInt(inv);
    }

    // Arithmetic Operators w/ _ModInt
    // Assignment operators here
    _ModInt& operator+=(const _ModInt &o) { if ((value += o.value) >= mod()) value -= mod(); return *this; }
    template <typename U> _ModInt& operator+=(const U &o) { return *this += _ModInt(o); }
    _ModInt& operator-=(const _ModInt &o) { if ((value -= o.value) < 0) value += mod(); return *this; }
    template <typename U> _ModInt& operator-=(const U &o) { return *this -= _ModInt(o); }
    _ModInt& operator++() { return *this += 1; }
    _ModInt operator++(int) { _ModInt res(*this); *this += 1; return res; }
    _ModInt& operator--() { return *this -= 1; }
    _ModInt operator--(int) { _ModInt res(*this); *this -= 1; return res; }
    _ModInt& operator*=(const _ModInt &o) { value = (mul_t)value * o.value % mod(); if (value < 0) value += mod(); return *this; } // make sure cast to mul_t!!!
    template <typename U> _ModInt& operator*=(const U &o) { return *this *= _ModInt(o); }
    _ModInt& operator/=(const _ModInt &o) { return *this *= inv(o.value); }
    template <typename U> _ModInt& operator/=(const U &o) { return *this /= _ModInt(o); }
    _ModInt operator-() const { return _ModInt(value); }
    // Other Operators
    T& operator()() { return value; }
    // Definitions of some operators
};
// Binary operators
#define OP_CMP(op) template <typename T> bool operator op(const _ModInt<T> &lhs, const _ModInt<T> &rhs) { return lhs.value op rhs.value; } \
    template <typename T, typename U> bool operator op(const _ModInt<T> &lhs, U rhs) { return lhs op _ModInt<T>(rhs); } \
    template <typename T, typename U> bool operator op(U lhs, const _ModInt<T> &rhs) { return _ModInt<T>(lhs) op rhs; }
#define OP_ARI(op) template <typename T> _ModInt<T> operator op(const _ModInt<T> &lhs, const _ModInt<T> &rhs) { return _ModInt<T>(lhs) op##= rhs; } \
    template <typename T, typename U> _ModInt<T> operator op(U lhs, const _ModInt<T> &rhs) { return _ModInt<T>(lhs) op##= rhs; } \
    template <typename T, typename U> _ModInt<T> operator op(const _ModInt<T> &lhs, U rhs) { return _ModInt<T>(lhs) op##= rhs; }
OP_CMP(==) OP_CMP(!=) OP_CMP(<) OP_CMP(>) OP_CMP(<=) OP_CMP(>=)
OP_ARI(+) OP_ARI(-) OP_ARI(*) OP_ARI(/)
#undef OP_CMP
#undef OP_ARI
template <typename T> istream& operator>>(istream& in, _ModInt<T> &o) { return in >> o(); }
template <typename T> ostream& operator<<(ostream& out, _ModInt<T> &o) { return out << o(); }

// Definitions
template <typename T, T mod> using ModInt = _ModInt<integral_constant<T, mod>>;
template <typename T> struct VarMod {
    static T value;
    static void read(istream& in) { in >> value; }
    static void set(T v0) { value = v0; }
};
template <typename T> using VarModInt = _ModInt<VarMod<T>>;
#line 6 "tests/ds/segment_tree_lazy.test.cpp"

// A = (ax+b), B = (cx+d)
// c(ax+b)+d = acx + bc + d
using MI = ModInt<int, 998244353>;
using pm = pair<MI, MI>;
struct AffineComp {
    using Data = MI;
    using Lazy = pm;
    const Data vdef = 0;
    const Lazy ldef = {1, 0};
    Data merge(Data l, Data r) const { return l + r; }
    Lazy mergeLazy(Lazy to, Lazy v) const {
        auto [a, b] = to;
        auto [c, d] = v;
        return {a * c, b * c + d};
    }
    void applyLazy(Data &to, Lazy &v, int l, int r) { to = v.first * to + (r - l + 1) * v.second; }
};

int main() {
    fast_io();
    int N = readi(), Q = readi();
    LazySegmentTree<AffineComp> seg; seg.init(N);
    for (auto [i, v] : enumerate(readv<int>(N), 1))
        seg.setPoint(i, v);
    while (Q--) {
        if (readi() == 0) {
            int l = readi() + 1, r = readi(), b = readi(), c = readi();
            seg.update(l, r, {b, c});
        }
        else {
            int l = readi()+1, r = readi();
            print(seg.query(l, r));
        }
    }
}

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