Yosupo Library Checker - Range Affine Range Sum

これ実は ACL Practice Contest の K 問題と同じらしい

atcoder.jp

• 問題へのリンク

問題概要

長さ の数列 が与えられる。この数列に対して、次の 回のクエリに答えよ。

• クエリタイプ 1 ()：数列の区間 内の各要素の値を 倍して を足せ
• クエリタイプ 2 ()：数列の区間 内の要素の総和を 998244353 で割った余りを答えよ

制約

• 

考えたこと

遅延評価セグメント木が使える。次の記事の問題と完全に一緒。

drken1215.hatenablog.com

コード

#include <bits/stdc++.h>
using namespace std;

// Lazy Segment Tree
template<class Monoid, class Action> struct LazySegmentTree {
    // various function types
    using FuncOperator = function<Monoid(Monoid, Monoid)>;
    using FuncMapping = function<Monoid(Action, Monoid)>;
    using FuncComposition = function<Action(Action, Action)>;

    // core member
    int N;
    FuncOperator OP;
    FuncMapping MAPPING;
    FuncComposition COMPOSITION;
    Monoid IDENTITY_MONOID;
    Action IDENTITY_ACTION;
    
    // inner data
    int log, offset;
    vector<Monoid> dat;
    vector<Action> lazy;
    
    // constructor
    LazySegmentTree() {}
    LazySegmentTree(int n,
                    const FuncOperator op,
                    const FuncMapping mapping,
                    const FuncComposition composition,
                    const Monoid &identity_monoid,
                    const Action &identity_action) {
        init(n, op, mapping, composition, identity_monoid, identity_action);
    }
    LazySegmentTree(const vector<Monoid> &v,
                    const FuncOperator op,
                    const FuncMapping mapping,
                    const FuncComposition composition,
                    const Monoid &identity_monoid,
                    const Action &identity_action) {
        init(v, op, mapping, composition, identity_monoid, identity_action);
    }
    void init(int n,
              const FuncOperator op,
              const FuncMapping mapping,
              const FuncComposition composition,
              const Monoid &identity_monoid,
              const Action &identity_action) {
        N = n, OP = op, MAPPING = mapping, COMPOSITION = composition;
        IDENTITY_MONOID = identity_monoid, IDENTITY_ACTION = identity_action;
        log = 0, offset = 1;
        while (offset < N) ++log, offset <<= 1;
        dat.assign(offset * 2, IDENTITY_MONOID);
        lazy.assign(offset * 2, IDENTITY_ACTION);
    }
    void init(const vector<Monoid> &v,
              const FuncOperator op,
              const FuncMapping mapping,
              const FuncComposition composition,
              const Monoid &identity_monoid,
              const Action &identity_action) {
        init((int)v.size(), op, mapping, composition, identity_monoid, identity_action);
        build(v);
    }
    void build(const vector<Monoid> &v) {
        assert(N == (int)v.size());
        for (int i = 0; i < N; ++i) dat[i + offset] = v[i];
        for (int k = offset - 1; k > 0; --k) pull_dat(k);
    }
    int size() const {
        return N;
    }
    
    // basic functions for lazy segment tree
    void pull_dat(int k) {
        dat[k] = OP(dat[k * 2], dat[k * 2 + 1]);
    }
    void apply_lazy(int k, const Action &f) {
        dat[k] = MAPPING(f, dat[k]);
        if (k < offset) lazy[k] = COMPOSITION(f, lazy[k]);
    }
    void push_lazy(int k) {
        apply_lazy(k * 2, lazy[k]);
        apply_lazy(k * 2 + 1, lazy[k]);
        lazy[k] = IDENTITY_ACTION;
    }
    void pull_dat_deep(int k) {
        for (int h = 1; h <= log; ++h) pull_dat(k >> h);
    }
    void push_lazy_deep(int k) {
        for (int h = log; h >= 1; --h) push_lazy(k >> h);
    }
    
    // setter and getter, update A[i], i is 0-indexed, O(log N)
    void set(int i, const Monoid &v) {
        assert(0 <= i && i < N);
        int k = i + offset;
        push_lazy_deep(k);
        dat[k] = v;
        pull_dat_deep(k);
    }
    Monoid get(int i) {
        assert(0 <= i && i < N);
        int k = i + offset;
        push_lazy_deep(k);
        return dat[k];
    }
    Monoid operator [] (int i) {
        return get(i);
    }
    
    // apply f for index i
    void apply(int i, const Action &f) {
        assert(0 <= i && i < N);
        int k = i + offset;
        push_lazy_deep(k);
        dat[k] = MAPPING(f, dat[k]);
        pull_dat_deep(k);
    }
    // apply f for interval [l, r)
    void apply(int l, int r, const Action &f) {
        assert(0 <= l && l <= r && r <= N);
        if (l == r) return;
        l += offset, r += offset;
        for (int h = log; h >= 1; --h) {
            if (((l >> h) << h) != l) push_lazy(l >> h);
            if (((r >> h) << h) != r) push_lazy((r - 1) >> h);
        }
        int original_l = l, original_r = r;
        for (; l < r; l >>= 1, r >>= 1) {
            if (l & 1) apply_lazy(l++, f);
            if (r & 1) apply_lazy(--r, f);
        }
        l = original_l, r = original_r;
        for (int h = 1; h <= log; ++h) {
            if (((l >> h) << h) != l) pull_dat(l >> h);
            if (((r >> h) << h) != r) pull_dat((r - 1) >> h);
        }
    }
    
    // get prod of interval [l, r)
    Monoid prod(int l, int r) {
        assert(0 <= l && l <= r && r <= N);
        if (l == r) return IDENTITY_MONOID;
        l += offset, r += offset;
        for (int h = log; h >= 1; --h) {
            if (((l >> h) << h) != l) push_lazy(l >> h);
            if (((r >> h) << h) != r) push_lazy(r >> h);
        }
        Monoid val_left = IDENTITY_MONOID, val_right = IDENTITY_MONOID;
        for (; l < r; l >>= 1, r >>= 1) {
            if (l & 1) val_left = OP(val_left, dat[l++]);
            if (r & 1) val_right = OP(dat[--r], val_right);
        }
        return OP(val_left, val_right);
    }
    Monoid all_prod() {
        return dat[1];
    }
    
    // get max r that f(get(l, r)) = True (0-indexed), O(log N)
    // f(IDENTITY) need to be True
    int max_right(const function<bool(Monoid)> f, int l = 0) {
        if (l == N) return N;
        l += offset;
        push_lazy_deep(l);
        Monoid sum = IDENTITY_MONOID;
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(OP(sum, dat[l]))) {
                while (l < offset) {
                    push_lazy(l);
                    l = l * 2;
                    if (f(OP(sum, dat[l]))) {
                        sum = OP(sum, dat[l]);
                        ++l;
                    }
                }
                return l - offset;
            }
            sum = OP(sum, dat[l]);
            ++l;
        } while ((l & -l) != l);  // stop if l = 2^e
        return N;
    }

    // get min l that f(get(l, r)) = True (0-indexed), O(log N)
    // f(IDENTITY) need to be True
    int min_left(const function<bool(Monoid)> f, int r = -1) {
        if (r == 0) return 0;
        if (r == -1) r = N;
        r += offset;
        push_lazy_deep(r - 1);
        Monoid sum = IDENTITY_MONOID;
        do {
            --r;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(OP(dat[r], sum))) {
                while (r < offset) {
                    push_lazy(r);
                    r = r * 2 + 1;
                    if (f(OP(dat[r], sum))) {
                        sum = OP(dat[r], sum);
                        --r;
                    }
                }
                return r + 1 - offset;
            }
            sum = OP(dat[r], sum);
        } while ((r & -r) != r);
        return 0;
    }
    
    // debug stream
    friend ostream& operator << (ostream &s, LazySegmentTree seg) {
        for (int i = 0; i < (int)seg.size(); ++i) {
            s << seg[i];
            if (i != (int)seg.size() - 1) s << " ";
        }
        return s;
    }
    
    // dump
    void dump() {
        for (int i = 0; i <= log; ++i) {
            for (int j = (1 << i); j < (1 << (i + 1)); ++j) {
                cout << "{" << dat[j] << "," << lazy[j] << "} ";
            }
            cout << endl;
        }
    }
};

// modint
template<int MOD> struct Fp {
    // inner value
    long long val;
    
    // constructor
    constexpr Fp() : val(0) { }
    constexpr Fp(long long v) : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    
    // getter
    constexpr long long get() const {
        return val;
    }
    constexpr int get_mod() const {
        return MOD;
    }
    
    // comparison operators
    constexpr bool operator == (const Fp &r) const {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp &r) const {
        return this->val != r.val;
    }
    
    // arithmetic operators
    constexpr Fp& operator += (const Fp &r) {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp &r) {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp &r) {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp &r) {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp operator + () const { return Fp(*this); }
    constexpr Fp operator - () const { return Fp(0) - Fp(*this); }
    constexpr Fp operator + (const Fp &r) const { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp &r) const { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp &r) const { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp &r) const { return Fp(*this) /= r; }
    
    // other operators
    constexpr Fp& operator ++ () {
        ++val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -- () {
        if (val == 0) val += MOD;
        --val;
        return *this;
    }
    constexpr Fp operator ++ (int) {
        Fp res = *this;
        ++*this;
        return res;
    }
    constexpr Fp operator -- (int) {
        Fp res = *this;
        --*this;
        return res;
    }
    friend constexpr istream& operator >> (istream &is, Fp<MOD> &x) {
        is >> x.val;
        x.val %= MOD;
        if (x.val < 0) x.val += MOD;
        return is;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD> &x) {
        return os << x.val;
    }
    
    // other functions
    constexpr Fp pow(long long n) const {
        Fp res(1), mul(*this);
        while (n > 0) {
            if (n & 1) res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }
    constexpr Fp inv() const {
        Fp res(1), div(*this);
        return res / div;
    }
    friend constexpr Fp<MOD> pow(const Fp<MOD> &r, long long n) {
        return r.pow(n);
    }
    friend constexpr Fp<MOD> inv(const Fp<MOD> &r) {
        return r.inv();
    }
};

/* セグメント木のための構造体と、作用を表す構造体と、それらの単位元 */
using mint = Fp<998244353>;
struct Act {
    mint b, c;
    Act(mint b = 0, mint c = 0) : b(b), c(c) {}
};
struct Node {
    mint val;
    long long siz;
    Node(mint v = 0, long long s = 0) : val(v), siz(s) {}
};
const Node identity_monoid = Node(0, 0);
const Act identity_action = Act(1, 0);

// 二項演算
auto op = [](Node x, Node y) -> Node {
    return Node(x.val + y.val, x.siz + y.siz);
};

// 作用関数
auto mapping = [](Act f, Node x) -> Node {
    return Node(f.b * x.val + f.c * x.siz, x.siz);
};

// 作用の合成関数：g.b((f.b)x + f.c) + g.c = (g.b f.b)x + g.b f.c + g.c
auto composition = [](Act g, Act f) -> Act {
    return Act(g.b * f.b, g.b * f.c + g.c);
};

int main() {
    // 入力
    int N, Q;
    cin >> N >> Q;
    vector<Node> a(N);
    for (int i = 0; i < N; ++i) {
        int x;
        cin >> x;
        a[i] = Node(x, 1);
    }
    
    // 遅延評価セグメント木のセットアップ
    LazySegmentTree<Node, Act> seg(a, op, mapping, composition,
                                   identity_monoid, identity_action);
    
    // クエリ処理
    while (Q--) {
        int t;
        cin >> t;
        if (t == 0) {
            int l, r, c, d;
            cin >> l >> r >> c >> d;
            seg.apply(l, r, Act(c, d));
        } else {
            int l, r;
            cin >> l >> r;
            Node res = seg.prod(l, r);
            cout << res.val << endl;
        }
    }
}