#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; 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##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template 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 pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &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 // 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> to, from; std::vector used; // Only true/false std::vector vs; std::vector 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 _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 DetectCycle() { int ns = FindStronglyConnectedComponents(); if (ns == V) return {}; std::vector 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; } }; // UnionFind Tree (0-indexed), based on size of each disjoint set struct UnionFind { std::vector 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); } }; int main() { int N, M; cin >> N >> M; vector> to(N); DirectedGraphSCC graph(N); REP(e, M) { int s, t; cin >> s >> t; s--, t--; to[s].push_back(t); graph.add_edge(s, t); } const int G = graph.FindStronglyConnectedComponents(); auto g2 = graph.GenerateTopologicalGraph(); vector> c2i(G); REP(i, N) c2i[graph.cmp[i]].push_back(i); UnionFind uf(G); REP(i, N) for (auto j : to[i]) { uf.unite(graph.cmp[i], graph.cmp[j]); } vector> grps(G); REP(g, G) grps[uf.find(g)].push_back(g); vector ret; int prv = -1; REP(g, G) { if (c2i[g].size() > 1) { REP(d, c2i[g].size()) { ret.emplace_back(c2i[g][d], c2i[g][d % c2i[g].size()]); } } } for (auto v : grps) { if (v.size() > 1) { REP(i, int(v.size()) - 1) ret.emplace_back(v[i], v[i + 1]); } } cout << ret.size() << '\n'; for (auto [s, t] : ret) cout << s + 1 << ' ' << t + 1 << '\n'; }