#1031677 (C++17) No.2990 Interval XOR

提出ソース

結果

問題	No.2990 Interval XOR
ユーザー	👑 Nachia
提出日時	2024-12-15 23:20:15
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	711 ms / 2,000 ms
コード長	11,967 bytes
コンパイル時間	1,146 ms
コンパイル使用メモリ	100,932 KB
実行使用メモリ	26,988 KB
最終ジャッジ日時	2024-12-15 23:20:33
合計ジャッジ時間	14,719 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,816 KB
testcase_01	AC	2 ms 6,820 KB
testcase_02	AC	2 ms 6,820 KB
testcase_03	AC	2 ms 6,820 KB
testcase_04	AC	2 ms 6,816 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	2 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	3 ms 5,248 KB
testcase_09	AC	2 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	2 ms 5,248 KB
testcase_12	AC	2 ms 5,248 KB
testcase_13	AC	2 ms 5,248 KB
testcase_14	AC	3 ms 5,248 KB
testcase_15	AC	4 ms 5,248 KB
testcase_16	AC	3 ms 5,248 KB
testcase_17	AC	3 ms 5,248 KB
testcase_18	AC	4 ms 5,248 KB
testcase_19	AC	2 ms 5,248 KB
testcase_20	AC	3 ms 5,248 KB
testcase_21	AC	2 ms 5,248 KB
testcase_22	AC	3 ms 5,248 KB
testcase_23	AC	2 ms 5,248 KB
testcase_24	AC	3 ms 5,248 KB
testcase_25	AC	44 ms 5,248 KB
testcase_26	AC	25 ms 6,824 KB
testcase_27	AC	14 ms 6,820 KB
testcase_28	AC	138 ms 7,736 KB
testcase_29	AC	48 ms 6,816 KB
testcase_30	AC	142 ms 7,884 KB
testcase_31	AC	146 ms 8,540 KB
testcase_32	AC	711 ms 26,988 KB
testcase_33	AC	694 ms 26,900 KB
testcase_34	AC	664 ms 26,860 KB
testcase_35	AC	674 ms 26,896 KB
testcase_36	AC	689 ms 26,956 KB
testcase_37	AC	678 ms 26,896 KB
testcase_38	AC	615 ms 26,880 KB
testcase_39	AC	672 ms 26,976 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;

#include <atcoder/modint>
using Modint = atcoder::static_modint<998244353>;


#include <iterator>
#include <functional>
#include <utility>
#include <type_traits>

template<class Elem> struct vec;

template<class Iter>
struct seq_view{
    using Ref = typename std::iterator_traits<Iter>::reference;
    using Elem = typename std::iterator_traits<Iter>::value_type;
    Iter a, b;
    Iter begin() const { return a; }
    Iter end() const { return b; }
    int size() const { return (int)(b-a); }
    seq_view(Iter first, Iter last) : a(first), b(last) {}
    seq_view sort() const { std::sort(a, b); return *this; }
    Ref& operator[](int x) const { return *(a+x); }
    template<class F = std::less<Elem>, class ret = vec<int>> ret sorti(F f = F()) const {
        ret x(size()); for(int i=0; i<size(); i++) x[i] = i;
        x().sort([&](int l, int r){ return f(a[l],a[r]); });
        return x;
    }
    template<class ret = vec<Elem>> ret col() const { return ret(begin(), end()); }
    template<class ret = vec<Elem>> ret cumsum() const {
        auto res = ret(size() + 1, Elem(0));
        for(int i=0; i<size(); i++) res[i+1] = res[i] + operator[](i);
        return res;
    }
    template<class F = std::equal_to<Elem>, class ret = vec<std::pair<Elem, int>>>
    ret rle(F eq = F()) const {
        auto x = ret();
        for(auto& a : (*this)){
            if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++;
        } return x;
    }
    template<class F> seq_view sort(F f) const { std::sort(a, b, f); return *this; }
    Iter uni() const { return std::unique(a, b); }
    Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); }
    Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); }
    int lbi(const Elem& x) const { return lb(x) - a; }
    int ubi(const Elem& x) const { return ub(x) - a; }
    seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; }
    template<class F> Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); }
    template<class F> Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); }
    template<class F> Iter when_true_to_false(F f) const {
        if(a == b) return a;
        return std::lower_bound(a, b, *a,
            [&](const Elem& x, const Elem&){ return f(x); });
    }
    seq_view same(Elem x) const { return { lb(x), ub(x) }; }
    template<class F> auto map(F f) const {
        vec<decltype(f(std::declval<const typename Iter::value_type&>()))> r;
        for(auto& x : *this) r.emp(f(x));
        return r;
    }
    Iter max() const { return std::max_element(a, b); }
    Iter min() const { return std::min_element(a, b); }
    template<class F = std::less<Elem>>
    Iter min(F f) const { return std::min_element(a, b, f); }
    seq_view rev() const { std::reverse(a, b); return *this; }
};

template<class Elem>
struct vec {
public:
    using Base = typename std::vector<Elem>;
    using Iter = typename Base::iterator;
    using CIter = typename Base::const_iterator;
    using View = seq_view<Iter>;
    using CView = seq_view<CIter>;

    vec(){}
    explicit vec(int n, const Elem& value = Elem()) : a(0<n?n:0, value) {}
    template <class I2> vec(I2 first, I2 last) : a(first, last) {}
    vec(std::initializer_list<Elem> il) : a(std::move(il)) {}
    vec(Base b) : a(std::move(b)) {}
    operator Base() const { return a; }

    Iter begin(){ return a.begin(); }
    CIter begin() const { return a.begin(); }
    Iter end(){ return a.end(); }
    CIter end() const { return a.end(); }
    int size() const { return a.size(); }
    bool empty() const { return a.empty(); }
    Elem& back(){ return a.back(); }
    const Elem& back() const { return a.back(); }
    vec& sortuni(){ (*this)().sort(); a.erase((*this)().uni(), end()); return *this; }
    vec sortunied(){ vec x = *this; x.sortuni(); return x; }
    Iter operator()(int x){ return a.begin() + x; }
    CIter operator()(int x) const { return a.begin() + x; }
    View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; }
    CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; }
    View operator()(){ return (*this)(0,size()); }
    CView operator()() const { return (*this)(0,size()); }
    Elem& operator[](int x){ return a[x]; }
    const Elem& operator[](int x) const { return a[x]; }
    Base& operator*(){ return a; }
    const Base& operator*() const { return a; }
    vec& push(Elem args){
        a.push_back(std::move(args));
        return *this;
    }
    template<class... Args>
    vec& emp(Args &&... args){
        a.emplace_back(std::forward<Args>(args) ...);
        return *this;
    }
    template<class Range>
    vec& app(Range& x){ for(auto& v : x){ emp(v); } return *this; }
    Elem pop(){ Elem x = std::move(a.back()); a.pop_back(); return x; }
    void resize(int sz){ a.resize(sz); }
    void reserve(int sz){ a.reserve(sz); }
    bool operator==(const vec& r) const { return a == r.a; }
    bool operator!=(const vec& r) const { return a != r.a; }
    bool operator<(const vec& r) const { return a < r.a; }
    bool operator<=(const vec& r) const { return a <= r.a; }
    bool operator>(const vec& r) const { return a > r.a; }
    bool operator>=(const vec& r) const { return a >= r.a; }
    vec<vec<Elem>> pile(int n) const { return vec<vec<Elem>>(n, *this); }
    template<class F> vec& filter(F f){
        int p = 0;
        for(auto& x : a) if(f(x)) std::swap(a[p++],x);
        resize(p); return *this;
    }
    vec& operator+=(const vec& r){ return app(r); }
    vec operator+(const vec& r) const { vec x = *this; x += r; return x; }
    vec operator*(int t) const { vec res; while(t--){ res += *this; } return res; }
private: Base a;
};

template<class IStr, class U, class T>
IStr& operator>>(IStr& is, vec<std::pair<U,T>>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; }
template<class IStr, class T>
IStr& operator>>(IStr& is, vec<T>& v){ for(auto& x:v){ is >> x; } return is; }
template<class OStr, class T>
OStr& operator<<(OStr& os, const vec<T>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << v[i];
    } return os;
}
template<class OStr, class U, class T>
OStr& operator<<(OStr& os, const vec<std::pair<U,T>>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << '(' << v[i].first << ',' << v[i].second << ')';
    } return os;
}

void Hadamard(i64 n, vec<Modint>& a, i64 i){
    i64 I = 1 << i;
    rep(j,1<<n) if(!(j&I)){
        auto p = a[j];
        auto q = a[j+I];
        a[j] = p + q;
        a[j+I] = p - q;
    }
}

void Hadamard2(i64 n, vec<Modint>& a, vec<Modint>& b){
    rep(j,1<<n){
        auto p = a[j];
        auto q = b[j];
        a[j] = p + q;
        b[j] = p - q;
    }
}

void LayerSkip(i64 n, vec<Modint>& a, i64 i){
    i64 I = 1 << i;
    rep(j,1<<n) if(!(j&I)){
        auto p = a[j];
        auto q = a[j+I];
        a[j] = p * q;
        a[j+I] = - p * q;
    }
}

void LayerSkip0(i64 n, vec<Modint>& a, i64 i){
    i64 I = 1 << i;
    rep(j,1<<n) if(!(j&I)){
        auto p = a[j];
        auto q = a[j+I];
        a[j] = p * q;
        a[j+I] = p * q;
    }
}

vec<Modint> subx(i64 N, vec<Modint> F, vec<Modint> G){
    //cout << "subx(" << N << ")" << endl;
    //cout << "   F : "; rep(i,1<<N){ cout << F[i].val() << " "; } cout << endl;
    //cout << "   G : "; rep(i,1<<N){ cout << G[i].val() << " "; } cout << endl;
    Modint inv2 = Modint(2).inv();
    rep(b,N){
        i64 B = 1 << b;
        rep(i,1<<N) if(!(i&B)){
            auto gp = G[i];
            auto gq = G[i+B];
            auto fp = F[i];
            auto fq = F[i+B];
            auto gpx = (gp + fp) * (gq + fq);
            auto gqx = (gp + fp) * (gq - fq);
            auto fpx = (gp - fp) * (gq - fq);
            auto fqx = (gp - fp) * (gq + fq);
            G[i] = (gpx + fpx) * inv2;
            G[i+B] = (gqx + fqx) * inv2;
            F[i] = (gpx - fpx) * inv2;
            F[i+B] = (gqx - fqx) * inv2;
        }
    }
    //cout << "   F : "; rep(i,1<<N){ cout << F[i].val() << " "; } cout << endl;
    //cout << "   G : "; rep(i,1<<N){ cout << G[i].val() << " "; } cout << endl;
    rep(b,N){
        Hadamard(N, F, b);
        Hadamard(N, G, b);
    }
    Modint inv = Modint(2).pow(N).inv();
    //cout << "   F : "; rep(i,1<<N){ cout << (F[i]*inv).val() << " "; } cout << endl;
    //cout << "   G : "; rep(i,1<<N){ cout << (G[i]*inv).val() << " "; } cout << endl;
    vec<Modint> res(1<<N);
    rep(i,1<<N) res[i] = (F[i] + G[i]) * inv;
    //cout << "return subx(" << N << ")" << endl;
    //cout << "   X : "; rep(i,1<<N){ cout << res[i].val() << " "; } cout << endl;
    return res;
}

vec<Modint> sub(i64 N, vec<i64> A, vec<Modint> CA, vec<i64> B, vec<Modint> CB){
    //cout << "sub(" << N << ")" << endl;
    //cout << "   A = " << A << endl;
    //cout << "   CA = "; for(auto a : CA){ cout << a.val() << " "; } cout << endl;
    //cout << "   B = " << B << endl;
    //cout << "   CB = "; for(auto a : CB){ cout << a.val() << " "; } cout << endl;
    i64 M = A.size();
    rep(i,M) B[i] ^= A[i];
    i64 NN = 1 << N;
    vec<Modint> F(NN, 0);
    vec<Modint> G(NN, 1);
    rep(i,M){
        i64 b = B[i];
        Modint p = F[b] * CA[i] + G[b] * CB[i];
        Modint q = F[b] * CB[i] + G[b] * CA[i];
        F[b] = p;
        G[b] = q;
    }
    auto res = subx(N, move(F), move(G));
    vec<Modint> ans(1<<N);
    i64 a = 0;
    for(auto v : A) a ^= v;
    rep(i,1<<N) ans[a^i] = res[i];
    //cout << "return sub(" << N << ")" << endl;
    return ans;
}

void testcase(){
    i64 N, M; cin >> N >> M;
    vec<i64> L(M), R(M);
    rep(i,M){ cin >> L[i] >> R[i]; R[i]++; }

    auto solve = [&](auto& solve, i64 b) -> vec<Modint> {
        //cout << "solve(" << b << ")" << endl;
        if(b == N){
            Modint q = 1;
            rep(i,M) q *= R[i] - L[i];
            return vec<Modint>(1, q);
        }
        auto rough = solve(solve, b+1);
        vec<i64> A(M), B(M);
        vec<Modint> CA(M), CB(M);
        rep(i,M){
            if((L[i] >> b) == ((R[i]-1) >> b)){
                A[i] = (L[i] >> b);
                CA[i] = L[i] - R[i];
                B[i] = (L[i] >> b);
                CB[i] = 0;
            } else {
                if((L[i] >> b) & 1){
                    A[i] = (L[i] >> b);
                    CA[i] = L[i] - ((A[i] + 1) << b);
                } else {
                    A[i] = (L[i] >> b);
                    CA[i] = L[i] - (A[i] << b);
                }
                if(((R[i]-1) >> b) & 1){
                    B[i] = ((R[i]-1) >> b);
                    CB[i] = ((B[i] + 1) << b) - R[i];
                } else {
                    B[i] = ((R[i]-1) >> b);
                    CB[i] = (B[i] << b) - R[i];
                }
            }
        }
        auto diff = sub(N-b, move(A), move(CA), move(B), move(CB));
        vec<Modint> res(1<<(N-b));
        Modint inv2 = Modint(2).inv();
        rep(i,1<<(N-b-1)){
            res[i*2+(M%2)^0] = (rough[i] + diff[i*2+0] - diff[i*2+1]) * inv2;
            res[i*2+(M%2)^1] = (rough[i] + diff[i*2+1] - diff[i*2+0]) * inv2;
        }
        //cout << "return solve(" << b << ")" << endl;
        //cout << "   X : "; rep(i,1<<(N-b)){ cout << res[i].val() << " "; } cout << endl;
        return res;
    };
    auto ans = solve(solve, 0);
    rep(i,1<<N){
        cout << ans[i].val() << "\n";
    }
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}

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結果

テストケース

ソースコード