結果

問題 No.1813 Magical Stones
コンテスト
ユーザー hitonanode
提出日時 2022-01-14 21:56:09
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 173 ms / 2,000 ms
コード長 10,733 bytes
コンパイル時間 2,714 ms
コンパイル使用メモリ 187,644 KB
実行使用メモリ 21,184 KB
最終ジャッジ日時 2024-11-20 09:53:36
合計ジャッジ時間 6,386 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 4
other AC * 40
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 <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
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 ALL(x) (x).begin(), (x).end()
#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)
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; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
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> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind {
    std::vector<int> par, cou;
    UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }
    int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
    bool unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y) return false;
        if (cou[x] < cou[y]) std::swap(x, y);
        par[y] = x, cou[x] += cou[y];
        return true;
    }
    int count(int x) { return cou[find(x)]; }
    bool same(int x, int y) { return find(x) == find(y); }
};

// Directed graph library to find strongly connected components （強連結成分分解）
// 0-indexed directed graph
// Complexity: O(V + E)
struct DirectedGraphSCC {
    int V; // # of Vertices
    std::vector<std::vector<int>> to, from;
    std::vector<int> used; // Only true/false
    std::vector<int> vs;
    std::vector<int> cmp;
    int scc_num = -1;

    DirectedGraphSCC(int V = 0) : V(V), to(V), from(V), cmp(V) {}

    void _dfs(int v) {
        used[v] = true;
        for (auto t : to[v])
            if (!used[t]) _dfs(t);
        vs.push_back(v);
    }
    void _rdfs(int v, int k) {
        used[v] = true;
        cmp[v] = k;
        for (auto t : from[v])
            if (!used[t]) _rdfs(t, k);
    }

    void add_edge(int from_, int to_) {
        assert(from_ >= 0 and from_ < V and to_ >= 0 and to_ < V);
        to[from_].push_back(to_);
        from[to_].push_back(from_);
    }

    // Detect strongly connected components and return # of them.
    // Also, assign each vertex `v` the scc id `cmp[v]` (0-indexed)
    int FindStronglyConnectedComponents() {
        used.assign(V, false);
        vs.clear();
        for (int v = 0; v < V; v++)
            if (!used[v]) _dfs(v);
        used.assign(V, false);
        scc_num = 0;
        for (int i = (int)vs.size() - 1; i >= 0; i--)
            if (!used[vs[i]]) _rdfs(vs[i], scc_num++);
        return scc_num;
    }

    // Find and output the vertices that form a closed cycle.
    // output: {v_1, ..., v_C}, where C is the length of cycle,
    //         {} if there's NO cycle (graph is DAG)
    int _c, _init;
    std::vector<int> _ret_cycle;
    bool _dfs_detectcycle(int now, bool b0) {
        if (now == _init and b0) return true;
        for (auto nxt : to[now])
            if (cmp[nxt] == _c and !used[nxt]) {
                _ret_cycle.emplace_back(nxt), used[nxt] = 1;
                if (_dfs_detectcycle(nxt, true)) return true;
                _ret_cycle.pop_back();
            }
        return false;
    }
    std::vector<int> DetectCycle() {
        int ns = FindStronglyConnectedComponents();
        if (ns == V) return {};
        std::vector<int> cnt(ns);
        for (auto x : cmp) cnt[x]++;
        _c = std::find_if(cnt.begin(), cnt.end(), [](int x) { return x > 1; }) - cnt.begin();
        _init = std::find(cmp.begin(), cmp.end(), _c) - cmp.begin();
        used.assign(V, false);
        _ret_cycle.clear();
        _dfs_detectcycle(_init, false);
        return _ret_cycle;
    }

    // After calling `FindStronglyConnectedComponents()`, generate a new graph by uniting all
    // vertices belonging to the same component(The resultant graph is DAG).
    DirectedGraphSCC GenerateTopologicalGraph() {
        DirectedGraphSCC newgraph(scc_num);
        for (int s = 0; s < V; s++)
            for (auto t : to[s]) {
                if (cmp[s] != cmp[t]) newgraph.add_edge(cmp[s], cmp[t]);
            }
        return newgraph;
    }
};

// 2-SAT solver: Find a solution for  `(Ai v Aj) ^ (Ak v Al) ^ ... = true`
// - `nb_sat_vars`: Number of variables
// - Considering a graph with `2 * nb_sat_vars` vertices
// - Vertices [0, nb_sat_vars) means `Ai`
// - vertices [nb_sat_vars, 2 * nb_sat_vars) means `not Ai`
struct SATSolver : DirectedGraphSCC {
    int nb_sat_vars;
    std::vector<int> solution;
    SATSolver(int nb_variables = 0)
        : DirectedGraphSCC(nb_variables * 2), nb_sat_vars(nb_variables), solution(nb_sat_vars) {}
    void add_x_or_y_constraint(bool is_x_true, int x, bool is_y_true, int y) {
        assert(x >= 0 and x < nb_sat_vars);
        assert(y >= 0 and y < nb_sat_vars);
        if (!is_x_true) x += nb_sat_vars;
        if (!is_y_true) y += nb_sat_vars;
        add_edge((x + nb_sat_vars) % (nb_sat_vars * 2), y);
        add_edge((y + nb_sat_vars) % (nb_sat_vars * 2), x);
    }
    // Solve the 2-SAT problem. If no solution exists, return `false`.
    // Otherwise, dump one solution to `solution` and return `true`.
    bool run() {
        FindStronglyConnectedComponents();
        for (int i = 0; i < nb_sat_vars; i++) {
            if (cmp[i] == cmp[i + nb_sat_vars]) return false;
            solution[i] = cmp[i] > cmp[i + nb_sat_vars];
        }
        return true;
    }
};

int main() {
    int N, M;
    cin >> N >> M;
    UnionFind uf(N);
    DirectedGraphSCC graph(N);
    while (M--) {
        int a, b;
        cin >> a >> b;
        --a, --b;
        uf.unite(a, b);
        graph.add_edge(a, b);
    }
    set<int> se;
    REP(i, N) se.insert(uf.find(i));
    dbg(se.size());
    const int V = graph.FindStronglyConnectedComponents();
    auto g = graph.GenerateTopologicalGraph();

    vector<int> in(V), out(V);
    dbgif(V <= 10, g.to);
    REP(i, V) {
        for (auto j : g.to[i]) {
            in[i]++;
            out[j]++;
        }
    }

    if (V == 1) puts("0");
    else {
        cout << max<int>(count(ALL(in), 0), count(ALL(out), 0)) << endl;
    }
}
0