結果

問題 No.1530 Permutation and Popcount
コンテスト
ユーザー rniya
提出日時 2021-06-12 20:51:53
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 40 ms / 2,000 ms
コード長 6,088 bytes
コンパイル時間 2,102 ms
コンパイル使用メモリ 201,796 KB
最終ジャッジ日時 2025-01-22 07:50:05
ジャッジサーバーID
（参考情報） 		judge2 / 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 * 41
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 # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U, typename V> ostream& operator<<(ostream& os, const tuple<T, U, V>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
    return os;
}
template <typename T, typename U, typename V, typename W> ostream& operator<<(ostream& os, const tuple<T, U, V, W>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;

int calc(int x, int y) { return !(__builtin_popcount(x * y) & 1); }

int f(int P, const vector<int>& X) {
    int res = 0;
    for (int i = 0; i < P; i++) {
        for (int j = 0; j < P; j++) {
            res += calc(X[i], X[j]);
        }
    }
    return res;
}

bool check(int N, int M, int P, int Q, const vector<int>& X, const vector<int>& Y) {
    if (P < 0 || Q < 0) return false;
    if (P + Q != N) return false;
    vector<int> used(N + 1, false);
    for (int x : X) {
        if (x < 1 || N < x) return false;
        if (used[x]) return false;
        used[x] = true;
    }
    for (int y : Y) {
        if (y < 1 || N < y) return false;
        if (used[y]) return false;
        used[y] = true;
    }
    return f(P, X) - f(Q, Y) == M;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N, M;
    cin >> N >> M;

    vector<int> cnt(N, 0);
    int sum = 0;
    for (int i = 1; i <= N; i++) {
        for (int j = 1; j <= N; j++) cnt[i - 1] += calc(i, j);
        sum += cnt[i - 1];
    }
    M = sum - M;
    if (M < 0 || (M & 1)) {
        cout << -1 << '\n';
        return 0;
    }
    M >>= 1;

    vector<vector<int>> dp(N + 1, vector<int>(M + 1, 0));
    dp[0][0] = 1;

    for (int i = 0; i < N; i++) {
        for (int j = 0; j <= M; j++) {
            if (dp[i][j] == 0) continue;
            dp[i + 1][j] = 1;
            if (j + cnt[i] <= M) dp[i + 1][j + cnt[i]] = -1;
        }
    }
    if (dp[N][M] == 0) {
        cout << -1 << '\n';
        return 0;
    }

    vector<int> X, Y;
    int cur = M;
    for (int i = N; i > 0; i--) {
        int nxt = dp[i][cur];
        if (nxt == 1)
            X.emplace_back(i);
        else {
            Y.emplace_back(i);
            cur -= cnt[i - 1];
        }
    }

    reverse(X.begin(), X.end());
    reverse(Y.begin(), Y.end());
    int P = X.size(), Q = Y.size();
    assert(check(N, sum - M * 2, P, Q, X, Y));
    cout << P << ' ' << Q << '\n';
    for (int i = 0; i < P; i++) cout << X[i] << (i + 1 == P ? '\n' : ' ');
    for (int i = 0; i < Q; i++) cout << Y[i] << (i + 1 == Q ? '\n' : ' ');
    return 0;
}
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