結果

問題 No.1240 Or Sum of Xor Pair
コンテスト
ユーザー hitonanode
提出日時 2020-10-03 17:09:59
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 526 ms / 2,000 ms
コード長 5,819 bytes
コンパイル時間 1,873 ms
コンパイル使用メモリ 201,700 KB
最終ジャッジ日時 2025-01-15 02:08:24
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
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

diff # 

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios {
    fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin), i##_end_ = (end); i < i##_end_; i++)
#define IFOR(i, begin, end) for (int i = (end)-1, i##_begin_ = (begin); i >= i##_begin_; i--)
#define REP(i, n) FOR(i, 0, n)
#define IREP(i, n) IFOR(i, 0, n)
#define ALL(x) (x).begin(), (x).end()
//
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args>
void ndarray(vector<T>& vec, const V& val, int len, Args... args)
{
    vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); });
}
template <typename T>
bool chmax(T& m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T>
bool chmin(T& m, const T q) { return m > q ? (m = q, true) : false; }
template <typename T1, typename T2>
pair<T1, T2> operator+(const pair<T1, T2>& l, const pair<T1, T2>& r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2>
pair<T1, T2> operator-(const pair<T1, T2>& l, const pair<T1, T2>& r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T>
vector<T> srtunq(vector<T> vec) { return sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()), vec; }
template <typename T>
istream& operator>>(istream& is, vector<T>& vec)
{
    return for_each(begin(vec), end(vec), [&](T& v) { is >> v; }), is;
}

// output
template <typename T, typename V>
ostream& dmpseq(ostream&, const T&, const string&, const string&, const string&);
#if __cplusplus >= 201703L
template <typename... T>
ostream& operator<<(ostream& os, const tuple<T...>& tpl)
{
    return apply([&os](auto&&... args) { ((os << args << ','), ...); }, tpl), os;
}
#endif
//
template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) { return os << '(' << p.first << ',' << p.second << ')'; }
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& x) { return dmpseq<vector<T>, T>(os, x, "[", ",", "]"); }
template <typename T>
ostream& operator<<(ostream& os, const deque<T>& x) { return dmpseq<deque<T>, T>(os, x, "deq[", ",", "]"); }
template <typename T>
ostream& operator<<(ostream& os, const set<T>& x) { return dmpseq<set<T>, T>(os, x, "{", ",", "}"); }
template <typename T, typename TH>
ostream& operator<<(ostream& os, const unordered_set<T, TH>& x) { return dmpseq<unordered_set<T, TH>, T>(os, x, "{", ",", "}"); }
template <typename T>
ostream& operator<<(ostream& os, const multiset<T>& x) { return dmpseq<multiset<T>, T>(os, x, "{", ",", "}"); }
template <typename TK, typename T>
ostream& operator<<(ostream& os, const map<TK, T>& x) { return dmpseq<map<TK, T>, pair<TK, T>>(os, x, "{", ",", "}"); }
template <typename TK, typename T, typename TH>
ostream& operator<<(ostream& os, const unordered_map<TK, T, TH>& x) { return dmpseq<unordered_map<TK, T, TH>, pair<TK, T>>(os, x, "{", ",", "}"); }
template <typename T, typename V>
ostream& dmpseq(ostream& os, const T& seq, const string& pre, const string& sp, const string& suf)
{
    return os << pre, for_each(begin(seq), end(seq), [&](V x) { os << x << sp; }), os << suf;
}
template <typename T>
void print(const vector<T>& x) { dmpseq<vector<T>, T>(cout, x, "", " ", "\n"); }
#ifdef HITONANODE_LOCAL
constexpr int D = 9;
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
constexpr int D = 19;
#define dbg(x) {}
#endif

template <typename T, typename F>
void walsh_hadamard(std::vector<T>& seq, F f)
{
    const int n = seq.size();
    assert(__builtin_popcount(n) == 1);
    for (int w = 1; w < n; w *= 2) {
        for (int i = 0; i < n; i += w * 2) {
            for (int j = 0; j < w; j++) {
                f(seq[i + j], seq[i + j + w]);
            }
        }
    }
}

template <typename T>
void walsh_hadamard_xor(std::vector<T>& seq)
{
    const int n = seq.size();
    assert(__builtin_popcount(n) == 1);
    for (int w = 1; w < n; w *= 2) {
        for (int i = 0; i < n; i += w * 2) {
            for (int j = 0; j < w; j++) {
                auto tmp = seq[i + j] - seq[i + j + w];
                seq[i + j] += seq[i + j + w];
                seq[i + j + w] = tmp;
                // f(seq[i + j], seq[i + j + w]);
            }
        }
    }
}

template <typename T>
std::vector<T> xor_convolution(std::vector<T> x, std::vector<T> y)
{
    const int n = x.size();
    assert(__builtin_popcount(n) == 1);
    assert(x.size() == y.size());
    auto f = [](T& a, T& b) {
        T c = a + b;
        b = a - b, a = c;
    };
    if (x == y) {
        // walsh_hadamard<T, decltype(f)>(x, f);
        walsh_hadamard_xor(x);
        y = x;
    } else {
        walsh_hadamard<T, decltype(f)>(x, f);
        walsh_hadamard<T, decltype(f)>(y, f);
    }
    for (size_t i = 0; i < x.size(); i++) {
        x[i] *= y[i];
    }
    walsh_hadamard<T, decltype(f)>(x, f);
    for (auto &v : x) v /= n;
    return x;
}


int main()
{
    int N, X;
    cin >> N >> X;

    vector<int> A(N);
    cin >> A;
    vector<lint> cnt(1 << D);
    for (auto a : A) cnt[a]++;
    cnt = xor_convolution(cnt, cnt);
    cnt[0] -= N;
    lint ret = 0;

    REP(d, D)
    {
        vector<lint> cntd(1 << D);
        int nd = 0;
        for (auto a : A) if (((a >> d) & 1) == 0) {
            cntd[a]++, nd++;
        }
        cntd = xor_convolution(cntd, cntd);
        cntd[0] -= nd;
        REP(i, X)
        {
            ret += (1LL << d) * (cnt[i] - cntd[i]) / 2;
        }
    }
    cout << ret << '\n';
}
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