結果

問題 No.2536 同値性と充足可能性
ユーザー kaikey
提出日時 2023-11-10 21:41:13
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 41 ms / 2,000 ms
コード長 7,367 bytes
コンパイル時間 2,455 ms
コンパイル使用メモリ 217,732 KB
最終ジャッジ日時 2025-02-17 20:33:22
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
other AC * 31
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 #
プレゼンテーションモードにする

#include "bits/stdc++.h"
#include <random>
#include <chrono>
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define SZ(x) ((lint)(x).size())
#define FOR(i, begin, end) for(lint i=(begin),i##_end_=(end);i<i##_end_;++i)
#define IFOR(i, begin, end) for(lint 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 endk '\n'
using namespace std; typedef unsigned long long _ulong; typedef long long int lint; typedef long double ld; typedef pair<lint, lint> plint; typedef 
    pair<ld, ld> pld;
struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(30); }; } fast_ios_;
template<class T> auto add = [](T a, T b) -> T { return a + b; };
template<class T> auto mul = [](T a, T b) -> T { return a * b; };
template<class T> auto f_max = [](T a, T b) -> T { return max(a, b); };
template<class T> auto f_min = [](T a, T b) -> T { return min(a, b); };
template<class T> using V = vector<T>;
using Vl = V<lint>; using VVl = V<Vl>; using VVVl = V<V<Vl>>;
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 != v.size() ? " " : "");
    return os;
}
template< typename T >istream& operator>>(istream& is, vector< T >& v) {
    for (T& in : v) is >> in;
    return is;
}
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; }
template <class T>
T div_floor(T a, T b) {
    if (b < 0) a *= -1, b *= -1;
    return a >= 0 ? a / b : (a + 1) / b - 1;
}
template <class T>
T div_ceil(T a, T b) {
    if (b < 0) a *= -1, b *= -1;
    return a > 0 ? (a - 1) / b + 1 : a / b;
}
template <class F> struct rec {
    F f;
    rec(F&& f_) : f(std::forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&... args) const {
        return f(*this, std::forward<Args>(args)...);
    }
};
lint gcd(lint a, lint b) { if (b == 0) return a; else return gcd(b, a % b); }
lint digit(lint a) { return (lint)log10(a); }
lint e_dist(plint a, plint b) { return abs(a.first - b.first) * abs(a.first - b.first) + abs(a.second - b.second) * abs(a.second - b.second); }
lint m_dist(plint a, plint b) { return abs(a.first - b.first) + abs(a.second - b.second); }
bool check_overflow(lint a, lint b, lint limit) { if (b == 0) return false; return a > limit / b; } // a * b > c => true
void Worshall_Floyd(VVl& g) { REP(k, SZ(g)) REP(i, SZ(g)) REP(j, SZ(g)) chmin(g[i][j], g[i][k] + g[k][j]); }
const lint MOD1000000007 = 1000000007, MOD998244353 = 998244353, INF = 2e18;
lint dx[8] = { 0, 1, 0, -1, 1, -1, 1, -1 }, dy[8] = { 1, 0, -1, 0, -1, -1, 1, 1 };
bool YN(bool flag) { cout << (flag ? "YES" : "NO") << endk; return flag; } bool yn(bool flag) { cout << (flag ? "Yes" : "No") << endk; return flag; }
struct Edge {
    lint from, to;
    lint cost;
    Edge() {
    }
    Edge(lint u, lint v, lint c) {
        cost = c;
        from = u;
        to = v;
    }
    bool operator<(const Edge& e) const {
        return cost < e.cost;
    }
};
struct WeightedEdge {
    lint to, _f;
    lint cost;
    WeightedEdge(lint v, lint f, lint c) {
        to = v;
        _f = f;
        cost = c;
    }
    bool operator<(const WeightedEdge& e) const {
        return cost < e.cost;
    }
};
using WeightedGraph = V<V<WeightedEdge>>;
typedef pair<plint, long long> tlint;
typedef pair<ld, ld> pld;
typedef pair<plint, plint> qlint;
typedef pair<Edge, lint> pEd;
typedef pair<plint, V<plint>> vVl;
typedef pair<string, string> pstr;
typedef pair<set<lint>, set<lint>> pset;
struct UnionFind {
public:
    UnionFind() : _n(0) {}
    UnionFind(int n) : _n(n), parent_or_size(n, -1) {}
    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        if (used_count) {
            if (count_in_set[x].size() < count_in_set[y].size()) {
                std::swap(count_in_set[x], count_in_set[y]);
            }
            for (auto p : count_in_set[y]) {
                count_in_set[x][p.first] += p.second;
            }
        }
        if (set_operate) {
            root_values[x] = f(root_values[y], root_values[x]);
        }
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }
    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }
    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }
    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }
    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }
    //update root calc
    //set by set operations
    void set_operate_and_value(std::vector<lint> array, function<lint(lint, lint)> _f) {
        f = _f;
        root_values = array;
        set_operate = true;
    }
    lint get_set_value(int a) {
        return root_values[leader(a)];
    }
    //regist count
    void regist_count(int a, int label) {
        if (!used_count) {
            used_count = true;
            count_in_set.assign(_n, std::map<int, int>());
        }
        count_in_set[leader(a)][label]++;
    }
    int get_count(int a, int label) {
        if (!used_count) return -1;
        return count_in_set[leader(a)][label];
    }
private:
    int _n;
    std::vector<int> parent_or_size;
    std::vector<std::map<int, int>> count_in_set;
    bool used_count = false;
    std::vector<lint> root_values;
    function<lint(lint, lint)> f;
    bool set_operate = false;
};
void solve() {
    lint N, M;
    cin >> N >> M;
    UnionFind ltree(N);
    UnionFind tree(N * 2);
    REP(i, M) {
        lint u, v;
        string s;
        cin >> u >> s >> v; u--; v--;
        if (s == "<==>") {
            tree.merge(u, v);
            tree.merge(u + N, v + N);
            ltree.merge(u, v);
        }
        else {
            tree.merge(u + N, v);
            tree.merge(u, v + N);
            ltree.merge(u, v);
        }
    }
    bool flag = true;
    REP(i, N) if (tree.same(i, i + N)) flag = false;
    if (yn(flag)) {
        VVl ans(2);
        REP(i, N) ans[tree.same(ltree.leader(i), i)].push_back(i + 1);
        if (SZ(ans[0]) >= div_ceil(N, 2ll)) {
            cout << SZ(ans[0]) << endk;
            cout << ans[0] << endk;
        }
        else {
            cout << SZ(ans[1]) << endk;
            cout << ans[1] << endk;
        }
    }
}
int main() {
    lint T = 1;
    //cin >> T;
    while (T--) solve();
}
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