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#include <bits/stdc++.h> #pragma GCC optimize("O3") #pragma GCC target("sse4") using namespace std; using ii = pair<int, int>; using ll = long long; const int N = 1e5 + 5; const int mod = 1e9 + 7; void kill() { cout << "No solution\n"; exit(0); } int n, m; set<int> adj[N]; int dfs(int u) { vector<int> out; while (adj[u].size()) { int v = *adj[u].begin(); adj[v].erase(u); adj[u].erase(v); int w = dfs(v); if (~w) { cout << u << ' ' << v << ' ' << w << '\n'; } else { out.push_back(v); } } for (int i = out.size() & 1; i < out.size(); i += 2) { cout << out[i] << ' ' << u << ' ' << out[i + 1] << '\n'; } if (out.size() & 1) return out[0]; return -1; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> n >> m; if (m & 1) { kill(); } for (int i = 0, u, v; i < m; i++) { cin >> u >> v; adj[u].insert(v); adj[v].insert(u); } dfs(1); return 0; }
#include <bits/stdc++.h> #pragma GCC target("avx2") #pragma GCC optimization("O3") #pragma GCC optimization("unroll-loops") using namespace std; template <typename T> void DBG(const char* name, T&& H) { cerr << name << " = " << H << ')' << '\n'; } template <typename T, typename... Args> void DBG(const char* names, T&& H, Args&&... args) { const char* NEXT = strchr(names + 1, ','); cerr.write(names, NEXT - names) << " = " << H << " |"; DBG(NEXT + 1, args...); } using ll = long long; using ld = long double; const long long mod = 1e9 + 7; const long double PI = acos(-1.0); const long long INF = 1e18; const int maxN = 1e5 + 1; int N, M; vector<vector<pair<int, int>>> graph(maxN); vector<bool> blocked(maxN, false); void bad() { cout << "No solution\n"; exit(0); } int dfs(int node) { vector<int> freeedge, toVis; for (auto i : graph[node]) { if (blocked[i.second]) continue; toVis.push_back(i.first); blocked[i.second] = 1; } for (auto i : toVis) { int end = dfs(i); if (end != -1) { cout << node << " " << i << " " << end << '\n'; } else freeedge.push_back(i); } while (freeedge.size() >= 2) { cout << freeedge.back() << " " << node << " " << freeedge[freeedge.size() - 2] << '\n'; freeedge.pop_back(); freeedge.pop_back(); } if (freeedge.size()) return freeedge.back(); else return -1; } void Solve() { cin >> N >> M; for (int i = 0; i < M; i++) { int a, b; cin >> a >> b; graph[a].push_back({b, i}); graph[b].push_back({a, i}); } if (M % 2) bad(); dfs(1); } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int tt = 1; while (tt--) { Solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; int n, m, a[100005], b[100005], te[100005], dir[100005]; int summ[100005]; bool vis[100005]; vector<pair<int, int> > V[100005]; vector<int> res[100005]; void dfs(int id, int pv) { vis[id] = 1; for (int i = (0); i <= ((int)V[id].size() - 1); i++) { pair<int, int> to = V[id][i]; if (to.first == pv || vis[to.first]) continue; te[to.second] = 1; dfs(to.first, id); } return; } void dfs2(int id, int pv, int fe) { for (int i = (0); i <= ((int)V[id].size() - 1); i++) { pair<int, int> to = V[id][i]; if (to.first == pv || !te[to.second]) continue; dfs2(to.first, id, to.second); } if (summ[id] & 1) { dir[fe] = id; summ[id]++; } else if (fe != -1) { dir[fe] = a[fe] + b[fe] - id; summ[dir[fe]]++; } return; } int main() { scanf("%d %d", &n, &m); if (m & 1) { printf("No solution\n"); return 0; } for (int i = (1); i <= (m); i++) { scanf("%d %d", &a[i], &b[i]); V[a[i]].push_back(make_pair(b[i], i)); V[b[i]].push_back(make_pair(a[i], i)); } dfs(1, -1); for (int i = (1); i <= (m); i++) if (!te[i]) summ[a[i]]++, dir[i] = a[i]; dfs2(1, -1, -1); for (int i = (1); i <= (m); i++) res[dir[i]].push_back(a[i] + b[i] - dir[i]); for (int i = (1); i <= (n); i++) { for (int j = 0; j < res[i].size(); j += 2) printf("%d %d %d\n", res[i][j], i, res[i][j + 1]); } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") #pragma GCC target("avx,avx2,fma") using namespace std; const int N = (int)1e5 + 5; const int INF = 0x3f3f3f3f; vector<int> g[N]; vector<int> bad[N]; vector<vector<int>> ans; bool used[N]; int h[N]; int dfs(int v) { if (used[v]) { return bad[v][0]; } used[v] = true; for (int to : g[v]) { if (used[to] && h[to] < h[v]) { continue; } if (!used[to]) { h[to] = h[v] + 1; } int q = dfs(to); if (q == -1) { bad[v].push_back(to); } else { ans.push_back({v, to, q}); bad[to].clear(); bad[to].push_back(-1); } } while (bad[v].size() >= 2) { int to = bad[v].back(); bad[v].pop_back(); int q = bad[v].back(); bad[v].pop_back(); ans.push_back({to, v, q}); } if (bad[v].empty()) { bad[v].push_back(-1); } return bad[v][0]; } int main() { int n, m; cin >> n >> m; for (int i = 1; i <= m; i++) { int u, v; scanf("%d %d", &u, &v); g[u].push_back(v); g[v].push_back(u); } dfs(1); if (ans.size() != m / 2 || m % 2) { return cout << "No solution", 0; } for (auto vec : ans) { for (int to : vec) { printf("%d ", to); } puts(""); } }
#include <bits/stdc++.h> using namespace std; int mod = 100000000; set<int> adj[100005]; int n, m; int dfs(int node) { vector<int> lef; while (adj[node].size()) { int mm = *(adj[node].begin()); adj[mm].erase(node); adj[node].erase(mm); int t = dfs(mm); if (t != -1) { printf("%d %d %d\n", node, mm, t); } else lef.push_back(mm); } for (int i = (lef.size() % 2); i < lef.size(); i += 2) { printf("%d %d %d\n", lef[i], node, lef[i + 1]); } if (lef.size() % 2) return lef[0]; else return -1; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int TESTS = 1; while (TESTS--) { scanf("%d %d", &n, &m); for (int i = 0; i < m; i++) { int a, b; scanf("%d %d", &a, &b); adj[a].insert(b); adj[b].insert(a); } if (m % 2 == 1) puts("No solution"); else dfs(1); } return 0; }
#include <bits/stdc++.h> using namespace std; const int NMAX = 100000 + 5; int N, M, S; set<int> V[NMAX]; bool Viz[NMAX]; void DFS(int nod, int tata) { set<int>::iterator it; set<int> W = V[nod]; Viz[nod] = 1; for (it = W.begin(); it != W.end(); it++) { if (Viz[*it]) continue; DFS(*it, nod); } if (V[nod].size() % 2) V[nod].erase(tata); for (it = V[nod].begin(); it != V[nod].end(); it++) { printf("%d %d ", *it, nod); V[*it].erase(nod); it++; printf("%d\n", *it); V[*it].erase(nod); } } int main() { int x, y; scanf("%d%d", &N, &M); if (M % 2) { printf("No solution\n"); return 0; } for (; M; --M) { scanf("%d%d", &x, &y); V[x].insert(y); V[y].insert(x); } DFS(1, 0); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 100020; bool ok[maxn]; int h[maxn]; bool mark[maxn]; vector<int> adj[maxn]; void dfs(int v, int par) { mark[v] = 1; vector<int> can; for (int i = 0; i < adj[v].size(); i++) { int u = adj[v][i]; if (mark[u] != 1) { h[u] = h[v] + 1; dfs(u, v); if (ok[u] != true) { can.push_back(u); } } else if (u != par && h[u] < h[v]) { can.push_back(u); } } if (can.size() % 2 != 0) { can.push_back(par); ok[v] = true; } for (int i = 0; i < can.size() / 2; i++) { cout << can[2 * i] << " " << v << " " << can[2 * i + 1]; cout << endl; } } int main() { int n, m; cin >> n >> m; if (m % 2 != 0) { cout << "No solution"; return 0; } int x, y; for (int i = 0; i < m; i++) { cin >> x >> y; adj[x].push_back(y); adj[y].push_back(x); } dfs(1, -1); }
#include <bits/stdc++.h> using namespace std; struct edge { int to, nx; } e[200050]; int head[200050]; int num = 0; bool bo[200050]; void addedge(int x, int y) { e[num].to = y; e[num].nx = head[x]; head[x] = num++; } bool ok[200050]; int gao(int now) { ok[now] = true; queue<int> q; for (int p = head[now]; p != -1; p = e[p].nx) { if (!bo[p]) { q.push(e[p].to); bo[p] = bo[p ^ 1] = true; } } queue<int> p; while (!q.empty()) { int u = q.front(); q.pop(); int w = gao(u); if (w != 0) printf("%d %d %d\n", w, u, now); else p.push(u); } while (p.size() >= 2) { int u, v; u = p.front(); p.pop(); v = p.front(); p.pop(); printf("%d %d %d\n", u, now, v); } if (!p.empty()) return p.front(); else return 0; } int main() { int i, j, k, n, m; num = 0; memset(head, -1, sizeof(head)); memset(ok, 0, sizeof(ok)); memset(bo, 0, sizeof(bo)); scanf("%d%d", &n, &m); for (i = 0; i < m; i++) { int x, y; scanf("%d%d", &x, &y); addedge(x, y); addedge(y, x); } if (m % 2) printf("No solution\n"); else { for (i = 1; i <= n; i++) if (!ok[i]) gao(i); } }
#include <bits/stdc++.h> using namespace std; inline void setmin(int &x, int y) { if (y < x) x = y; } inline void setmax(int &x, int y) { if (y > x) x = y; } inline void setmin(long long &x, long long y) { if (y < x) x = y; } inline void setmax(long long &x, long long y) { if (y > x) x = y; } const int N = 100000; const int inf = (int)1e9 + 1; const long long big = (long long)1e18 + 1; const int P = 239; const int MOD = (int)1e9 + 7; const int MOD1 = (int)1e9 + 9; const double eps = 1e-9; const double pi = atan2(0, -1); const int ABC = 26; vector<int> g[N]; bool used[N]; int height[N]; bool dfs(int u, int p, int h) { used[u] = true; height[u] = h; vector<int> todo; for (int v : g[u]) if (v != p) { if (!used[v]) { if (dfs(v, u, h + 1)) todo.push_back(v); } else if (height[v] < height[u]) todo.push_back(v); } bool res = true; if ((int)todo.size() % 2 == 1) { todo.push_back(p); res = false; } for (int i = 0; i < (int)todo.size() / 2; i++) cout << todo[i * 2] + 1 << " " << u + 1 << " " << todo[i * 2 + 1] + 1 << "\n"; return res; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.precision(20); cout << fixed; int n, m; cin >> n >> m; if (m % 2 == 1) { cout << "No solution\n"; return 0; } for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; u--; v--; g[u].push_back(v); g[v].push_back(u); } dfs(0, -1, 0); return 0; }
#include <bits/stdc++.h> using namespace std; bool debug = 1; int n, m, k; int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0}; long long ln, lk, lm; vector<pair<int, int>> mp[100005]; vector<pair<int, pair<int, int>>> ans; bool vis[100005 * 2]; int cnt; int dfs(int x, int pa) { vector<int> v; for (auto p : mp[x]) { int c = p.first, id = p.second; if (vis[id] || c == pa) continue; vis[id] = 1; vis[id ^ 1] = 1; int rm = dfs(c, x); if (rm != -1) { ans.push_back({c, {x, rm}}); } else { v.push_back(c); } } while (v.size() > 1) { int a = v.back(); v.pop_back(); int b = v.back(); v.pop_back(); ans.push_back({x, {a, b}}); } if (v.empty()) return -1; return v[0]; } int main() { scanf("%d%d", &n, &m); int u, v; if (m & 1) { puts("No solution"); return 0; } for (int(i) = 0; (i) < (int)(m); (i)++) { scanf("%d%d", &u, &v); mp[u].push_back({v, cnt++}); mp[v].push_back({u, cnt++}); } dfs(1, 0); for (auto p : ans) printf("%d %d %d\n", p.second.first, p.first, p.second.second); return 0; }
#include <bits/stdc++.h> using namespace std; bool endline = false; template <class T> istream& operator>>(istream& inp, vector<T>& v) { for (auto& it : v) inp >> it; return inp; } template <class T> ostream& operator<<(ostream& out, vector<T>& v) { for (auto& it : v) out << it << (endline ? "\n" : " "); return out; } template <class T, class U> istream& operator>>(istream& inp, pair<T, U>& v) { inp >> v.first >> v.second; return inp; } template <class T, class U> ostream& operator<<(ostream& out, pair<T, U>& v) { out << v.first << ' ' << v.second; return out; } void debug() { cout << endl; } template <typename H, typename... T> void debug(H a, T... b) { cout << a << ' '; debug(b...); } void FAST_IO(string filein = "", string fileout = "", string fileerr = "") { if (fopen(filein.c_str(), "r")) { freopen(filein.c_str(), "r", stdin); freopen(fileout.c_str(), "w", stdout); } cin.tie(0), cout.tie(0)->sync_with_stdio(0); } void Hollwo_Pelw(); signed main() { FAST_IO(".inp", ".out"); int testcases = 1; for (int test = 1; test <= testcases; test++) { Hollwo_Pelw(); } return 0; } const int allmod[3] = {(int)1e9 + 7, 998244353, (int)1e9 + 9}; const int mod = allmod[0]; const int MAXN = 1e5 + 5; const int inf = 2e9; const long long linf = 1e18; const long double eps = 1e-9; int n, m, vis[MAXN], evis[MAXN]; vector<pair<int, int>> adj[MAXN]; int dfs(int u) { vis[u] = 1; int last = -1; for (auto vi : adj[u]) { int v = vi.first, id = vi.second; if (evis[id]) continue; evis[id] = 1; int w = (vis[v] == 1 ? -1 : dfs(v)); if (w == -1) { if (last != -1) cout << v << " " << u << " " << last << "\n"; last = (last == -1 ? v : -1); } else { cout << u << ' ' << v << ' ' << w << "\n"; } } return last; } void Hollwo_Pelw() { cin >> n >> m; if (m & 1) { cout << "No solution"; return; } for (int i = 1, u, v; i <= m; i++) { cin >> u >> v, adj[u].emplace_back(v, i), adj[v].emplace_back(u, i); } dfs(1); }
#include <bits/stdc++.h> using namespace std; long n, m, a, b; vector<long> g[200000]; set<pair<long, long> > done; vector<pair<long, pair<long, long> > > ans; long ptr[300000]; long dfs(long v) { vector<long> dd; dd.reserve(16); for (; ptr[v] < g[v].size(); ptr[v]++) { long q = g[v][ptr[v]]; pair<long, long> p = make_pair(min(v, q), max(v, q)); if (done.find(p) != done.end()) continue; if (p.first > p.second) swap(p.first, p.second); done.insert(p); long t = dfs(q); if (t == 0) dd.push_back(q); else { ans.push_back(make_pair(v, make_pair(q, t))); } } long t = dd.size() % 2; for (int i = t; i < dd.size(); i += 2) { long a, b; a = dd[i]; b = dd[i + 1]; ans.push_back(make_pair(a, make_pair(v, b))); done.insert(make_pair(min(a, v), max(a, v))); done.insert(make_pair(min(b, v), max(b, v))); } if (dd.size() % 2 == 0) return 0; done.insert(make_pair(min(dd[0], v), max(dd[0], v))); return dd[0]; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> n >> m; if (m % 2) { cout << "No solution" << endl; return 0; } for (int i = 1; i <= m; i++) { cin >> a >> b; g[a].push_back(b); g[b].push_back(a); } dfs(1); for (int i = 0; i < ans.size(); i++) { cout << ans[i].first << " " << ans[i].second.first << " " << ans[i].second.second << endl; } cin.get(); cin.get(); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAX_N = 100000 + 20; vector<int> adj[MAX_N]; int mark[MAX_N]; int lvl[MAX_N]; vector<pair<int, pair<int, int> > > ans; int n, m; void readInput() { cin >> n >> m; for (int i = 0; i < m; i++) { int v, u; cin >> v >> u; --v, u--; adj[v].push_back(u); adj[u].push_back(v); } for (int i = 0; i < n; ++i) lvl[i] = MAX_N; } int dfs(int v) { if (mark[v]) return -1; mark[v] = 1; vector<int> seq; for (int i = 0; i < adj[v].size(); ++i) { int u = adj[v][i]; if (lvl[u] < lvl[v]) continue; lvl[u] = (lvl[u] == MAX_N ? lvl[v] + 1 : lvl[u]); int ver = dfs(u); if (ver != -1) ans.push_back(make_pair(v, make_pair(u, ver))); else seq.push_back(u); } while (seq.size() > 1) { int u = seq.back(); seq.pop_back(); int ver = seq.back(); seq.pop_back(); ans.push_back(make_pair(u, make_pair(v, ver))); } return (seq.size() == 1 ? seq.back() : -1); } int main() { readInput(); if (m % 2) { cout << "No solution" << endl; return 0; } lvl[0] = 0; dfs(0); for (int i = 0; i < ans.size(); ++i) cout << ans[i].first + 1 << ' ' << ans[i].second.first + 1 << ' ' << ans[i].second.second + 1 << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long int pw(long long int a, long long int b, long long int mod) { if (!b) return 1; if (b & 1) return a * pw(a * a % mod, b / 2, mod) % mod; return pw(a * a % mod, b / 2, mod) % mod; } const long long int MAXN = 2e5 + 10; const long long int INF = 8e18; const long long int MOD = 1e9 + 7; int n, m, mark[MAXN], last[MAXN]; vector<int> adj[MAXN]; vector<pair<int, pair<int, int>>> ans; void DFS(int u, int p = -1) { mark[u] = 1; vector<int> now; for (int v : adj[u]) { if (mark[v] == 2 || v == p) continue; if (mark[v] == 1) { now.push_back(v); continue; } DFS(v, u); if (last[v]) ans.push_back({last[v], {v, u}}); else now.push_back(v); } for (int i = 0; i + 1 < now.size(); i += 2) { ans.push_back({now[i], {u, now[i + 1]}}); } if (now.size() % 2 == 1) last[u] = now[now.size() - 1]; mark[u] = 2; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cin >> n >> m; if (m % 2 == 1) return cout << "No solution" << '\n', 0; ; for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } for (int i = 1; i <= n; i++) if (mark[i] == 0) { DFS(i); } if (ans.size() != m / 2) return cout << "No solution" << '\n', 0; ; for (auto p : ans) { cout << p.first << ' ' << p.second.first << ' ' << p.second.second << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; int n, m, u, v, flag, num, vis[100100]; vector<int> edge[100100]; queue<int> sk[100100]; struct G { int a, b, c; } ans[100100]; void dfs(int u, int father) { vis[u] = true; for (int i = 0; i < edge[u].size(); ++i) { int v = edge[u][i]; if (vis[v] == false) dfs(v, u); else if (v != father && vis[v] == true) sk[v].push(u); } while (sk[u].size() >= 2) { int x = sk[u].front(); sk[u].pop(); int y = sk[u].front(); sk[u].pop(); ans[++num] = {x, u, y}; } if (sk[u].size() == 1) { if (father == 0) flag = 1; int x = sk[u].front(); sk[u].pop(); ans[++num] = {x, u, father}; } else sk[father].push(u); } int main() { cin >> n >> m; if (m % 2 == 1) { cout << "No solution" << endl; return 0; } for (int i = 1; i <= m; ++i) { cin >> u >> v; edge[u].push_back(v); edge[v].push_back(u); } dfs(1, 0); if (flag == 1) cout << "No solution" << endl; else { for (int i = 1; i <= num; ++i) { cout << ans[i].a << " " << ans[i].b << " " << ans[i].c << endl; } } return 0; }
#include <bits/stdc++.h> double pi = acos(-1); using namespace std; vector<int> g[100010]; bool visited[100010]; map<pair<int, int>, int> blocked; int get(int u) { if (visited[u]) return -1; visited[u] = true; stack<int> unpaired; vector<int> vs; for (int i = 0; i < g[u].size(); i++) { int v = g[u][i]; if (!blocked.count(pair<int, int>(u, v)) && !blocked.count(pair<int, int>(v, u))) { vs.push_back(v); blocked[pair<int, int>(u, v)]; blocked[pair<int, int>(v, u)]; } } if (!vs.size()) return -1; for (int i = 0; i < vs.size(); i++) { int v = vs[i]; int res = get(v); if (res != -1) { printf("%d %d %d\n", u + 1, v + 1, res + 1); } else { unpaired.push(v); } } while (unpaired.size()) { if (unpaired.size() == 1) return unpaired.top(); printf("%d ", unpaired.top() + 1); unpaired.pop(); printf("%d ", u + 1); printf("%d\n", unpaired.top() + 1); unpaired.pop(); } return -1; } int main() { int n, m; scanf("%d %d", &n, &m); if (m % 2 == 1) { cout << "No solution" << endl; return 0; } for (int i = 0; i < m; i++) { int a, b; scanf("%d %d", &a, &b); a--, b--; g[a].push_back(b); g[b].push_back(a); } get(0); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 20; int h[maxn], e; vector<pair<int, int> > adj[maxn]; vector<pair<pair<int, int>, pair<int, int> > > ans; bool visited[maxn], evisited[maxn]; void dfs(int v) { e += adj[v].size(); visited[v] = 1; for (auto u : adj[v]) if (!visited[u.first]) h[u.first] = h[v] + 1, dfs(u.first); vector<pair<int, int> > backedge, down, p; for (auto u : adj[v]) { if (evisited[u.second]) continue; if (h[u.first] > h[v]) down.push_back(u); else if (h[u.first] == h[v] - 1) p.push_back(u); else backedge.push_back(u); } if (down.size()) { for (int i = (int)down.size() - 2; i > -1; i -= 2) { pair<int, int> a = down[i], b = down[i + 1]; down.pop_back(); down.pop_back(); ans.push_back({{a.first, v}, {v, b.first}}); evisited[a.second] = evisited[b.second] = 1; } if (down.size()) { if (backedge.size()) { pair<int, int> a = backedge.back(), b = down.back(); ans.push_back({{a.first, v}, {v, b.first}}); evisited[a.second] = evisited[b.second] = 1; backedge.pop_back(); down.pop_back(); } else if (p.size()) { pair<int, int> a = p.back(), b = down.back(); ans.push_back({{a.first, v}, {v, b.first}}); evisited[a.second] = evisited[b.second] = 1; p.pop_back(); down.pop_back(); } } } while (backedge.size() > 1) { pair<int, int> a = backedge.back(); backedge.pop_back(); pair<int, int> b = backedge.back(); backedge.pop_back(); evisited[a.second] = evisited[b.second] = 1; ans.push_back({{a.first, v}, {v, b.first}}); } if (backedge.size()) { pair<int, int> a = backedge.back(), b = p.back(); ans.push_back({{a.first, v}, {v, b.first}}); evisited[a.second] = evisited[b.second] = 1; p.pop_back(); backedge.pop_back(); } } int main() { int n, m; cin >> n >> m; for (int i = 0; i < m; i++) { int a, b; cin >> a >> b; adj[--a].push_back({--b, i}); adj[b].push_back({a, i}); } for (int i = 0; i < n; i++) if (!visited[i]) { e = 0; dfs(i); e /= 2; if (e & 1) { cout << "No solution\n"; return 0; } } for (auto u : ans) cout << u.first.first + 1 << " " << u.first.second + 1 << " " << u.second.second + 1 << endl; }
#include <bits/stdc++.h> using namespace std; struct node { int t, nxt; bool block; } edge[110000 << 1]; int headline[110000], E; inline void add(int f, int t) { edge[E].t = t; edge[E].nxt = headline[f]; edge[E].block = false; headline[f] = E++; } int n, m; int dfs(int u) { vector<int> adj; for (int i = headline[u]; ~i; i = edge[i].nxt) { if (edge[i].block) continue; edge[i].block = edge[i ^ 1].block = true; adj.push_back(edge[i].t); } int ss = adj.size(); queue<int> q; for (int i = 0; i < ss; i++) { int ww = dfs(adj[i]); if (ww == 0) { q.push(adj[i]); } else { printf("%d %d %d\n", u, adj[i], ww); } } int x = -1, y = -1; while (!q.empty()) { if (x == -1) { x = q.front(); q.pop(); } else { y = q.front(); q.pop(); printf("%d %d %d\n", x, u, y); x = y = -1; } } if (x == -1) return 0; return x; } void solve(void) { memset(headline, -1, sizeof(headline)); E = 0; for (int i = 0; i < (m); i++) { int a, b; scanf("%d%d", &a, &b); add(a, b); add(b, a); } if (m % 2) { printf("No solution\n"); return; } dfs(1); } int main(void) { while (2 == scanf("%d%d", &n, &m)) solve(); }
#include <bits/stdc++.h> using namespace std; const int MAXN = 100010; int N, M; set<int> adj[MAXN]; bool vis[MAXN]; void dfs(int u, int p) { vis[u] = true; set<int> s = adj[u]; for (typeof(s.begin()) it = s.begin(); it != s.end(); it++) { int t = (*it); if (!vis[t]) { dfs(t, u); } } if (adj[u].size() & 1) { adj[u].erase(p); } for (typeof(adj[u].begin()) it = adj[u].begin(); it != adj[u].end(); it++) { cout << (*it) << ' ' << u << ' '; adj[*it].erase(u); it++; cout << (*it) << '\n'; adj[*it].erase(u); } } int main() { cin >> N >> M; if (M & 1) { cout << "No solution\n"; return 0; } for (int i = 0; i < M; i++) { int a, b; cin >> a >> b; adj[a].insert(b); adj[b].insert(a); } dfs(1, 0); }
#include <bits/stdc++.h> using namespace std; const long long inf = 2e18; const long long mod = 1e9 + 7; const double Pi = acos(-1); int n, m; set<int> v[100009]; int dfs(int node) { vector<int> out; while (v[node].size()) { int u = *v[node].begin(); v[node].erase(u); v[u].erase(node); int ret = dfs(u); if (ret != -1) { cout << node + 1 << " " << u + 1 << " " << ret + 1 << endl; } else { out.push_back(u); } } for (int i = (out.size()) % 2; i < out.size(); i += 2) { cout << out[i] + 1 << " " << node + 1 << " " << out[i + 1] + 1 << endl; } return (out.size() % 2 ? out[0] : -1); } int main() { cin >> n >> m; for (int i = 0; i < m; i++) { int a, b; cin >> a >> b; a--, b--; v[a].insert(b); v[b].insert(a); } if (m % 2) { cout << "No solution" << endl; return 0; } dfs(0); }
#include <bits/stdc++.h> using namespace std; const long long mod = 1e9 + 7; const long long maxn = 1e5 + 500; vector<long long> ger[maxn]; bool vis[maxn]; long long mond[maxn]; long long h[maxn]; long long jad[maxn][3]; long long j = 0; void dfs(long long a, long long hh) { vis[a] = 1; long long v; h[a] = hh; for (long long i = 0; i < ger[a].size(); i++) { v = ger[a][i]; if (!vis[v]) { dfs(v, hh + 1); } } } void dfss(long long a) { vis[a] = 1; long long v; vector<long long> vec; for (long long i = 0; i < ger[a].size(); i++) { v = ger[a][i]; if (!vis[v]) { dfss(v); if (mond[v] != -1) { jad[j][0] = a; jad[j][1] = v; jad[j][2] = mond[v]; j++; } else { vec.push_back(v); } } else { if (h[v] > h[a]) { vec.push_back(v); } } } for (long long i = 1; i < vec.size(); i += 2) { jad[j][0] = vec[i]; jad[j][1] = a; jad[j][2] = vec[i - 1]; j++; } if (vec.size() & 1) { mond[a] = vec.back(); } else { mond[a] = -1; } } int main() { long long n, m, v, u; cin >> n >> m; if (m & 1) { cout << "No solution"; return 0; } for (long long i = 0; i < m; i++) { cin >> v >> u; ger[--v].push_back(--u); ger[u].push_back(v); } dfs(0, 0); memset(&vis[0], 0, maxn); dfss(0); for (long long i = 0; i < j; i++) { for (long long o = 0; o < 3; o++) { cout << jad[i][o] + 1 << ' '; } cout << endl; } }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e5 + 10; vector<int> child[MAXN], adj[MAXN]; bitset<MAXN> b; vector<array<int, 3>> ans; array<int, 3> o; void build(int v, int par) { b[v] = true; for (auto i : adj[v]) if (i != par && !b[i]) { child[v].push_back(i); build(i, v); } } int dfs(int v, int par) { b[v] = true; vector<int> k; for (auto i : adj[v]) if (b[i] && i != par) k.push_back(i); for (auto i : child[v]) if (!b[i]) { int now = dfs(i, v); if (now) { o[0] = v; o[1] = i; o[2] = now; ans.push_back(o); } else k.push_back(i); } int t = k.size(); for (int i = 0; i + 1 < t; i += 2) { o[0] = k[i]; o[1] = v; o[2] = k[i + 1]; ans.push_back(o); } return (t % 2 ? k[t - 1] : 0); } int main() { ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0); int n, m; cin >> n >> m; int a1, a2; for (int i = 0; i < m; ++i) { cin >> a1 >> a2; adj[a1].push_back(a2); adj[a2].push_back(a1); } build(1, 0); for (int i = 0; i < MAXN; ++i) b[i] = false; if (dfs(1, 0)) return cout << "No solution", 0; for (auto i : ans) cout << i[0] << ' ' << i[1] << ' ' << i[2] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; struct edg { int v, nxt; } E[100004 * 2]; int hd[100004], ide; int s[100004]; void adde(int u, int v) { E[ide].v = v; E[ide].nxt = hd[u]; hd[u] = ide++; } void init() { memset(hd, -1, sizeof(hd)); memset(s, 0, sizeof(s)); ide = 0; } int dfs(int u, int f) { s[u] = 1; int pre = 0; for (int i = hd[u]; ~i; i = E[i].nxt) { int v; if ((v = E[i].v) != f && s[v] < 2) { int q = (s[v] == 1) ? 0 : dfs(v, u); if (q) printf("%d %d %d\n", u, v, q); else if (pre) printf("%d %d %d\n", pre, u, v), pre = 0; else pre = v; } } s[u] = 2; return pre; } int n, m; int main() { while (~scanf("%d%d", &n, &m)) { init(); for (int i = 0; i < m; ++i) { int u, v; scanf("%d%d", &u, &v); adde(u, v); adde(v, u); } if (m % 2) puts("No solution"); else dfs(1, -1); } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAX = 1e5 + 5; set<int> adj[MAX]; int n, m; int dfs(int source) { vector<int> unpaired; while (!adj[source].empty()) { int each = *adj[source].begin(); adj[source].erase(each); adj[each].erase(source); int u = dfs(each); if (u == 0) { unpaired.push_back(each); } else { printf("%d %d %d\n", u, each, source); } } while (unpaired.size() >= 2) { int u = unpaired.back(); unpaired.pop_back(); int v = unpaired.back(); unpaired.pop_back(); printf("%d %d %d\n", u, source, v); } if (!unpaired.empty()) { return unpaired.back(); } return 0; } int main() { scanf("%d %d", &n, &m); if (m & 1) { puts("No solution"); return 0; } for (int i = int(0); i < int(m); i++) { int u, v; scanf("%d %d", &u, &v); adj[u].insert(v); adj[v].insert(u); } dfs(1); return 0; }
#include <bits/stdc++.h> using namespace std; long long read() { char ch = getchar(); long long f = 1, x = 0; while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); } return f * x; } const long long maxn = 1e5 + 10; long long n, h[maxn], cnt, m; struct edge { long long v, next; } e[maxn << 1]; void addedge(long long u, long long v) { e[++cnt].v = v; e[cnt].next = h[u]; h[u] = cnt; } void insert(long long u, long long v) { addedge(u, v); addedge(v, u); } stack<long long> g[maxn]; struct answers { long long a, b, c; } ans[maxn]; long long vis[maxn], tot; bool no; void dfs(long long u, long long fa) { vis[u] = 1; for (long long i = h[u]; i; i = e[i].next) { long long v = e[i].v; if (!vis[v]) dfs(v, u); else if (v != fa) { g[v].push(u); } } while (g[u].size() >= 2) { ans[++tot].a = g[u].top(); ans[tot].b = u; g[u].pop(); ans[tot].c = g[u].top(); g[u].pop(); } if (g[u].size() == 1) { if (fa == 0) { no = 1; return; } long long x = g[u].top(); ans[++tot].a = x; ans[tot].b = u; ans[tot].c = fa; g[u].pop(); } else { g[fa].push(u); } } signed main() { n = read(); m = read(); if (m & 1) { cout << "No solution\n"; return 0; } for (long long i = 1; i <= m; i++) { insert(read(), read()); } dfs(1, 0); if (no) { cout << "No solution\n"; return 0; } for (long long i = 1; i <= tot; i++) { cout << ans[i].a << " " << ans[i].b << " " << ans[i].c << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e5 + 1; vector<int> g[MAXN]; vector<int> reverse_idx[MAXN]; vector<bool> blocked[MAXN]; int partition(const int v) { vector<bool>::iterator is_blocked = blocked[v].begin(); vector<int>::iterator reverse = reverse_idx[v].begin(); int unpaired = false; for (int u : g[v]) { if (*is_blocked) { ++is_blocked; ++reverse; continue; } *is_blocked = true; blocked[u][*reverse] = true; int w = partition(u); if (w) { printf("%d %d %d\n", v, u, w); } else { if (unpaired) { printf("%d %d %d\n", unpaired, v, u); unpaired = false; } else { unpaired = u; } } ++is_blocked; ++reverse; } return unpaired; } int main() { int n, m; scanf("%d %d ", &n, &m); if (m % 2) { printf("No solution\n"); return 0; } for (int i = 0; i < m; ++i) { int a, b; scanf("%d %d ", &a, &b); reverse_idx[a].push_back(g[b].size()); reverse_idx[b].push_back(g[a].size()); g[a].push_back(b); g[b].push_back(a); } for (int i = 1; i <= n; ++i) { blocked[i].resize(g[i].size(), false); } partition(1); return 0; }
#include <bits/stdc++.h> using namespace std; int edge[100000 + 10], first[100000 + 10], nxt[100000 + 10 << 1]; bool v[100000 + 10]; int mark[100000 + 10], vv[100000 + 10 << 1]; void dfs(int n, int fa) { v[n] = 1; for (int e = first[n]; e; e = nxt[e]) if (vv[e] != fa && !v[vv[e]]) dfs(vv[e], n); int top = 0; for (int e = first[n]; e; e = nxt[e]) if (vv[e] != fa && mark[vv[e]] != 1) edge[top++] = vv[e]; if (top & 1) edge[top++] = fa, mark[n] = 1; else mark[n] = 2; for (int i = 0; i < top; i += 2) { printf("%d %d %d\n", edge[i], n, edge[i + 1]); if (mark[edge[i]] == 2) mark[edge[i]] = 1; if (mark[edge[i + 1]] == 2) mark[edge[i + 1]] = 1; } } int main(void) { int e = 1; int n, m; scanf("%d %d", &n, &m); for (int i = 0; i < m; i++) { int u, v; scanf("%d%d", &u, &v); nxt[e] = first[u], vv[e] = v; first[u] = e++; nxt[e] = first[v], vv[e] = u; first[v] = e++; } if (m & 1) printf("No solution\n"); else dfs(1, 0); return 0; }
#include <bits/stdc++.h> using namespace std; const long long Maxn = 1e5 + 7; const long long Inf = 1e9 + 7; vector<long long> V[Maxn]; vector<pair<long long, pair<long long, long long> > > ans; map<pair<long long, long long>, bool> mark; bool vis[Maxn]; void True(long long u, long long v) { mark[make_pair(u, v)] = mark[make_pair(v, u)] = true; } long long dfs(long long u, long long dad) { if (vis[u]) return mark[make_pair(u, dad)]; vis[u] = true; long long son = -1; for (long long i = 0; i < V[u].size(); i++) { long long v = V[u][i]; if (v == dad || mark[make_pair(u, v)]) continue; bool t = dfs(v, u); if (t) continue; else if (son != -1 && !mark[make_pair(son, u)]) { ans.push_back(make_pair(son, make_pair(u, v))); True(u, v); True(u, son); son = -1; } else son = v; } if (son == -1) return 0; ans.push_back(make_pair(son, make_pair(u, dad))); True(u, son); True(u, dad); return 1; } int main() { long long n, m; cin >> n >> m; for (long long i = 1; i <= m; i++) { long long u, v; cin >> u >> v; V[u].push_back(v), V[v].push_back(u); } if (m % 2) { cout << "No solution" << endl; return 0; } dfs(1, -1); for (long long i = 0; i < ans.size(); i++) cout << ans[i].first << " " << ans[i].second.first << " " << ans[i].second.second << endl; }
#include <bits/stdc++.h> bool aa[100000 << 1]; int a[100000], ab[100000], b[100000 << 1], c[100000 << 1], h[100000], n, m, i, x, y, na, ma; int go(int k) { int ta = na, pa = ma, i, t; for (i = h[k]; ~i; i = b[i]) if (!aa[i]) a[na++] = c[i], aa[i] = 1, aa[i >= m ? i - m : i + m] = 1; for (i = ta; i < na; i++) { t = go(a[i]); if (!~t) ab[ma++] = a[i]; else printf("%d %d %d\n", k + 1, a[i] + 1, t + 1); } while (ma - pa >= 2) { i = ab[--ma]; t = ab[--ma]; printf("%d %d %d\n", i + 1, k + 1, t + 1); } na = ta; return ma > pa ? ab[--ma] : -1; } int main() { scanf("%d%d", &n, &m); if (m & 1) { puts("No solution"); return 0; } for (i = 0; i < m * 2; i++) c[i] = -1; for (i = 0; i < n; i++) h[i] = -1; for (i = 0; i < m; ++i) { scanf("%d%d", &x, &y); --x, --y; b[i] = h[x]; c[i] = y; h[x] = i; b[i + m] = h[y]; c[i + m] = x; h[y] = i + m; } go(0); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 10; int a[maxn], b[maxn]; vector<pair<int, int>> G[maxn]; bool v[maxn], use[maxn]; struct data { int a, b, c; }; vector<data> ans; void dfs(int now, int fa, int edge) { v[now] = true; int nxt = -1, cid = -1; for (auto u : G[now]) if (u.first != fa) { if (!v[u.first]) dfs(u.first, now, u.second); if (use[u.second]) continue; if (nxt == -1) nxt = u.second, cid = u.first; else if (nxt != -1) { ans.emplace_back((data){u.first, now, cid}); use[nxt] = use[u.second] = true; nxt = -1; cid = -1; } } if (nxt != -1) { if (edge && !use[edge] && !use[nxt]) { ans.emplace_back((data){cid, now, fa}); use[edge] = use[nxt] = true; } } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int n, m; cin >> n >> m; if (m & 1) return cout << "No solution" << endl, 0; for (int i = 1; i <= m; ++i) { cin >> a[i] >> b[i]; G[a[i]].emplace_back(b[i], i); G[b[i]].emplace_back(a[i], i); } for (int i = 1; i <= n; ++i) { if (!v[i]) dfs(i, 0, 0); } if (ans.size() < m / 2) return cout << "No solution" << endl, 0; for (auto e : ans) cout << e.a << ' ' << e.b << ' ' << e.c << endl; return 0; }
#include <bits/stdc++.h> const int inf = 1 << 30; const long long INF = 1ll << 61; using namespace std; int n, m; typedef struct Node { int fro, to; int nex; int val; }; Node edge[100000 * 2 + 55]; int head[100000 * 2 + 55]; bool vis[100000 * 2 + 55]; int tot; void init() { memset(vis, 0, sizeof(vis)); memset(head, -1, sizeof(head)); tot = 0; } void add(int u, int v) { edge[tot].fro = u; edge[tot].to = v; edge[tot].nex = head[u]; head[u] = tot++; } bool input() { while (cin >> n >> m) { int q = m; while (q--) { int u, v; scanf("%d %d", &u, &v); add(u, v); add(v, u); } return false; } return true; } int dfs(int u, int pre) { queue<int> q; for (int i = head[u]; i != -1; i = edge[i].nex) { int v = edge[i].to; if (vis[i] || v == pre) continue; vis[i] = true; vis[i ^ 1] = true; int tmp = dfs(v, u); if (tmp) printf("%d %d %d\n", u, v, tmp); else q.push(v); } int len = q.size(); if (len & 1) { while (q.size() > 1) { int aa = q.front(); q.pop(); int bb = q.front(); q.pop(); printf("%d %d %d\n", aa, u, bb); } int aa = q.front(); q.pop(); return aa; } else { while (q.size()) { int aa = q.front(); q.pop(); int bb = q.front(); q.pop(); printf("%d %d %d\n", aa, u, bb); } } return 0; } void cal() { if (m & 1) { puts("No solution"); return; } dfs(1, -1); } void output() {} int main() { while (true) { init(); if (input()) return 0; cal(); output(); } return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); const int MXN = 100005; int depth[MXN]; vector<int> ups[MXN]; set<int> children[MXN]; int parent[MXN]; vector<int> adj[MXN]; vector<pair<int, int>> cur_component; int cur_edges = 0; bool dealt_with[MXN]; bool weird[MXN]; void dfs(int v, int par) { depth[v] = 1 + depth[par]; cur_component.push_back({depth[v], v}); children[par].insert(v); parent[v] = par; for (auto u : adj[v]) { if (depth[u] > depth[v]) ups[u].push_back(v); if (depth[u] == 0) dfs(u, v); if (depth[u] < depth[v]) cur_edges++; } } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n, m; cin >> n >> m; for (int i = 0; i < m; i++) { int a, b; cin >> a >> b; adj[a].push_back(b); adj[b].push_back(a); } vector<tuple<int, int, int>> ans; for (int v = 1; v <= n; v++) { if (depth[v] != 0) continue; while (!cur_component.empty()) cur_component.pop_back(); dfs(v, 0); if (cur_edges % 2 != 0) { cout << "No solution\n"; return 0; } sort(cur_component.rbegin(), cur_component.rend()); for (auto thing : cur_component) { int u = thing.second; while (int((ups[u]).size()) > 1) { ans.push_back({ups[u][int((ups[u]).size()) - 1], u, ups[u][int((ups[u]).size()) - 2]}); ups[u].pop_back(); ups[u].pop_back(); } } priority_queue<tuple<int, int, int>> cur_components2; for (auto c : cur_component) { cur_components2.push({c.first, int((ups[c.second]).size()), c.second}); } while (!cur_components2.empty()) { int u = get<2>(cur_components2.top()); if (weird[u] && get<1>(cur_components2.top()) == 1) { cur_components2.pop(); continue; } cur_components2.pop(); if (dealt_with[u] || u == v) continue; if (int((ups[u]).size()) == 1) { ans.push_back({parent[u], u, ups[u].back()}); ups[u].pop_back(); children[parent[u]].erase(u); continue; } if (int((children[parent[u]]).size()) >= 2) { children[parent[u]].erase(u); int u2; for (auto uu : children[parent[u]]) { u2 = uu; break; } children[parent[u]].erase(u2); dealt_with[u2] = 1; ans.push_back({u, parent[u], u2}); } else { if (!ups[parent[u]].empty()) { children[parent[u]].erase(u); ans.push_back({u, parent[u], ups[parent[u]].back()}); ups[parent[u]].pop_back(); cur_components2.push({depth[parent[u]], 0, parent[u]}); weird[parent[u]] = 1; } else { ans.push_back({u, parent[u], parent[parent[u]]}); dealt_with[parent[u]] = 1; children[parent[parent[u]]].erase(parent[u]); } } } } for (auto a : ans) cout << get<0>(a) << " " << get<1>(a) << " " << get<2>(a) << endl; }
#include <bits/stdc++.h> using namespace std; const int maxn = 100 * 1000 + 10; int n, m; vector<pair<int, int> > vertex[maxn]; bool mark[maxn]; stack<int> f[maxn]; stack<int> adj[maxn]; int build(int v) { for (int i = 0; i < ((int(vertex[v].size()))); i++) { int u = vertex[v][i].first, e = vertex[v][i].second; if (!mark[e]) { adj[v].push(u); mark[e] = true; } } while (!adj[v].empty()) { int u = adj[v].top(); adj[v].pop(); int w = build(u); if (w == 0) f[v].push(u); else printf("%d %d %d\n", v, u, w); } while (((int(f[v].size()))) >= 2) { int u = f[v].top(); f[v].pop(); int w = f[v].top(); f[v].pop(); printf("%d %d %d\n", u, v, w); } if (!f[v].empty()) { int w = f[v].top(); f[v].pop(); return w; } else return 0; } int main() { scanf("%d%d", &n, &m); for (int i = 1; i <= m; i++) { int u, v; scanf("%d%d", &u, &v); vertex[u].push_back(make_pair(v, i)); vertex[v].push_back(make_pair(u, i)); } if (m & 1) { printf("No solution"); return 0; } build(1); return 0; }
#include <bits/stdc++.h> using namespace std; const long long mod7 = 1000000007; int gcd(int a, int b) { while (b) { a %= b; swap(a, b); } return a; } vector<int> gr[1000001]; pair<long long, long long> data[1000001]; bool used1[1000001]; bool used2[1000001]; int dfs(int v) { vector<int> ch, ch2; used2[v] = true; for (int i = 0; i < gr[v].size(); ++i) { int m = gr[v][i]; if (used1[m]) continue; used1[m] = true; int fr = data[m].first; int to = data[m].second; if (to == v) swap(fr, to); ch2.push_back(to); } for (int i = 0; i < ch2.size(); ++i) { if (!used2[ch2[i]]) { int ret = dfs(ch2[i]); if (ret) { printf("%d %d %d\n", ret, ch2[i], v); } else { ch.push_back(ch2[i]); } } else ch.push_back(ch2[i]); } for (int i = 0; i + 1 < ch.size(); i += 2) { printf("%d %d %d\n", ch[i], v, ch[i + 1]); } if (ch.size() & 1) return ch.back(); return 0; } int main() { int n, m; scanf("%d%d", &n, &m); if (m & 1) { printf("No solution"); return 0; } for (int i = 0; i < m; ++i) { scanf("%d%d", &data[i].first, &data[i].second); gr[data[i].first].push_back(i); gr[data[i].second].push_back(i); } dfs(1); return 0; }
#include <bits/stdc++.h> using namespace std; vector<pair<int, int> > adjlist[100005]; int num[100005]; bool visited[100005]; int n, m, u, v, d; int dfs(int u) { int c1 = -1, c2 = 0; for (int i = 0; i < adjlist[u].size(); i++) { pair<int, int> next = adjlist[u][i]; if (visited[next.second]) continue; visited[next.second] = 1; int res = dfs(next.first); if (res > -1) { printf("%d %d %d\n", res + 1, next.first + 1, u + 1); } else { if (c2 == 0) { c1 = next.first; c2 = 1; } else { printf("%d %d %d\n", next.first + 1, u + 1, c1 + 1); c2 = 0; } } } if (c2 == 0) return -1; return c1; } int main() { scanf("%d %d", &n, &m); for (int i = 0; i < n; i++) visited[i] = false; for (int i = 0; i < m; i++) { int u, v; scanf("%d %d", &u, &v); u--; v--; adjlist[u].push_back(pair<int, int>(v, i)); adjlist[v].push_back(pair<int, int>(u, i)); } if (m % 2) { printf("No solution\n"); return 0; } dfs(0); }
#include <bits/stdc++.h> using namespace std; vector<int> con[110000]; int vis[110000], visE[110000], chk[110000]; int prv[110000], arr[110000][5]; int R[110000], RN; int rn, q[110000 * 2]; int n, m; int st, en; struct Edge { int x, y; Edge(int x = 0, int y = 0) : x(x), y(y) {} } E[110000]; void Push(int a, int b) { arr[rn][0] = E[a].x; arr[rn][1] = E[a].y; arr[rn][2] = E[b].x; arr[rn][3] = E[b].y; sort(arr[rn], arr[rn] + 4); rn++; } bool connect(int a, int b) { if (E[a].x == E[b].x || E[a].x == E[b].y || E[a].y == E[b].x || E[a].y == E[b].y) { Push(a, b); return true; } return false; } void Chk(int e, int x) { if (vis[x]) return; vis[x] = 1; for (int i = 0; i < con[x].size(); i++) { int id = con[x][i]; if (visE[id]) continue; visE[id] = 1; q[en++] = id; prv[id] = e; } } int main() { int i, k, j, x, y; int a, b; scanf("%d%d", &n, &m); for (i = 0; i < m; i++) { scanf("%d%d", &x, &y); E[i].x = --x; E[i].y = --y; con[x].push_back(i); con[y].push_back(i); } if (m & 1) { puts("No solution"); return 0; } q[en++] = 0, visE[0] = 1, prv[0] = -1; while (st < en) { int e = q[st++]; Chk(e, E[e].x); Chk(e, E[e].y); } rn = 0; for (i = m - 1; i >= 1; i--) { RN = 0; for (k = i; prv[q[k]] == prv[q[i]]; k--) if (!chk[q[k]]) R[RN++] = q[k]; i = k + 1; if (!prv[q[i]]) break; for (j = 0; j < RN; j += 2) if (j + 1 < RN) Push(R[j], R[j + 1]); if (RN & 1) { chk[prv[R[RN - 1]]] = 1; Push(R[RN - 1], prv[R[RN - 1]]); } } while (RN > 2) { int a = R[--RN]; int b = R[--RN]; int c = R[--RN]; if (connect(a, b)) R[RN++] = c; else if (connect(a, c)) R[RN++] = b; else if (connect(b, c)) R[RN++] = a; } if (RN == 1) Push(R[0], 0); else if (RN == 2) { puts("No solution"); return 0; } for (i = 0; i < rn; i++) { for (k = 0; k < 3; k++) if (arr[i][k] == arr[i][k + 1]) break; int tmp[4], tn(0); for (j = 0; j < 4; j++) if (j != k && j != k + 1) tmp[tn++] = arr[i][j]; printf("%d %d %d\n", tmp[0] + 1, arr[i][k] + 1, tmp[1] + 1); } }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e5 + 100; vector<int> V[MAXN]; int N, M; int pass[MAXN], instack[MAXN]; vector<int> atdep[MAXN], extra[MAXN]; void dfs(int u, int parr, int dep) { pass[u] = true; instack[u] = true; atdep[dep].push_back(u); for (int i = 0; i < V[u].size(); i++) { if (instack[V[u][i]]) extra[u].push_back(V[u][i]); if (V[u][i] != parr && !pass[V[u][i]]) dfs(V[u][i], u, dep + 1); } instack[u] = false; } int main() { scanf("%d %d", &N, &M); if (M % 2 == 1) { printf("No solution\n"); return 0; } for (int i = 1; i <= M; i++) { int a, b; scanf("%d %d", &a, &b); V[a].push_back(b); V[b].push_back(a); } dfs(1, -1, 0); for (int dep = N - 1; dep >= 0; dep--) { for (int i = 0; i < atdep[dep].size(); i++) { while (extra[atdep[dep][i]].size() >= 2) { int x = extra[atdep[dep][i]].back(); extra[atdep[dep][i]].pop_back(); int y = extra[atdep[dep][i]].back(); extra[atdep[dep][i]].pop_back(); printf("%d %d %d\n", x, atdep[dep][i], y); } if (!extra[atdep[dep][i]].empty()) { int x = extra[atdep[dep][i]].back(); extra[atdep[dep][i]].pop_back(); extra[x].push_back(atdep[dep][i]); } } } return 0; }
#include <bits/stdc++.h> using namespace std; const int inf = 2000000000; static inline int Rint() { struct X { int dig[256]; X() { for (int i = '0'; i <= '9'; ++i) dig[i] = 1; dig['-'] = 1; } }; static X fuck; int s = 1, v = 0, c; for (; !fuck.dig[c = getchar()];) ; if (c == '-') s = 0; else if (fuck.dig[c]) v = c ^ 48; for (; fuck.dig[c = getchar()]; v = v * 10 + (c ^ 48)) ; return s ? v : -v; } template <typename T> static inline void cmax(T& a, const T& b) { if (b > a) a = b; } template <typename T> static inline void cmin(T& a, const T& b) { if (b < a) a = b; } vector<int> adj[100005]; int visited[100005]; int av[100005]; int xid; void dfs(int curr, int prev) { vector<int>& vec = adj[curr]; const int size = ((int)(vec).size()); visited[curr] = ++xid; vector<int> orz; for (int i = 0; i < size; ++i) { int to = vec[i]; if (to == prev) continue; if (visited[to]) { if (visited[to] < visited[curr]) { orz.push_back(to); } } else { dfs(to, curr); if (av[to] != 0) { printf("%d %d %d\n", curr, to, av[to]); } else { orz.push_back(to); } } } int now = 0; while (now + 1 < orz.size()) { printf("%d %d %d\n", orz[now], curr, orz[now + 1]); now += 2; } if (now < orz.size()) { av[curr] = orz[now]; } } int main() { int n = Rint(), m = Rint(); if (m & 1) { puts("No solution"); return 0; } for (int i = 0; i < m; ++i) { int s = Rint(), t = Rint(); adj[s].push_back(t), adj[t].push_back(s); } dfs(1, -1); return 0; }
#include <bits/stdc++.h> using namespace std; int n, m, ok[200050]; vector<pair<int, int> > grafo[200050]; set<pair<int, int> > vis; vector<pair<int, pair<int, int> > > ans; bool possivel = true; int dfs(int x) { vector<int> filhos, exposed; ok[x] = 1; for (auto v : grafo[x]) { int a = min(x, v.first), b = max(x, v.first); if (vis.count({a, b})) continue; vis.insert({a, b}); filhos.push_back(v.first); } for (auto v : filhos) { int u = (ok[v] ? -1 : dfs(v)); if (u == -1) exposed.push_back(v); else ans.push_back({x, {v, u}}); } for (int i = 0; i < (int)exposed.size(); i += 2) { if (i == (int)exposed.size() - 1) return exposed[i]; ans.push_back({exposed[i], {x, exposed[i + 1]}}); } return -1; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m; for (int i = 1, a, b; i <= m; i++) { cin >> a >> b; grafo[a].push_back({b, i}); grafo[b].push_back({a, i}); } dfs(1); if (2 * ans.size() == m) { for (auto w : ans) cout << w.first << " " << w.second.first << " " << w.second.second << "\n"; } else cout << "No solution\n"; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 3; int n, m, p[N], d[N]; bool vis[N]; vector<int> g[N], backw[N], vec[N]; void dfs(int x) { for (int i : g[x]) { if (p[i] == 0) { d[i] = d[x] + 1; p[i] = x; dfs(i); } else if (p[x] != i && d[x] > d[i]) { backw[x].push_back(i); } } } void solve(int x) { vis[x] = 1; for (int i : g[x]) { if (!vis[i]) { solve(i); } } while (vec[x].size() >= 2) { int a = vec[x].back(); vec[x].pop_back(); int b = vec[x].back(); vec[x].pop_back(); cout << a << ' ' << x << ' ' << b << '\n'; } if (vec[x].size() == 1) { int a = vec[x].back(); vec[x].pop_back(); backw[x].push_back(a); } while (backw[x].size() >= 2) { int a = backw[x].back(); backw[x].pop_back(); int b = backw[x].back(); backw[x].pop_back(); cout << a << ' ' << x << ' ' << b << '\n'; } if (backw[x].size() == 1) { int a = backw[x].back(); backw[x].pop_back(); cout << a << ' ' << x << ' ' << p[x] << '\n'; } else { vec[p[x]].push_back(x); } } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n >> m; if (m % 2 == 1) { cout << "No solution"; return 0; } for (int i = 0; i < m; ++i) { int a, b; cin >> a >> b; g[a].push_back(b); g[b].push_back(a); } p[1] = 1; dfs(1); solve(1); }
#include <bits/stdc++.h> using namespace std; const int maxn = 100010; int first[maxn], nxt[maxn << 1], vv[maxn << 1]; bool vis[maxn]; int mark[maxn]; int edge[maxn]; void dfs(int n, int fa) { vis[n] = true; for (int e = first[n]; e; e = nxt[e]) if (vv[e] != fa && !vis[vv[e]]) dfs(vv[e], n); int top = 0; for (int e = first[n]; e; e = nxt[e]) if (vv[e] != fa && mark[vv[e]] != 1) edge[top++] = vv[e]; if (top & 1) edge[top++] = fa, mark[n] = 1; else mark[n] = 2; for (int i = 0; i < top; i += 2) { printf("%d %d %d\n", edge[i], n, edge[i + 1]); if (mark[edge[i]] == 2) mark[edge[i]] = 1; if (mark[edge[i + 1]] == 2) mark[edge[i + 1]] = 1; } } int main() { int e = 2; int n, m; scanf("%d%d", &n, &m); for (int i = 0; i < m; i++) { int u, v; scanf("%d%d", &u, &v); nxt[e] = first[u], vv[e] = v, first[u] = e++; nxt[e] = first[v], vv[e] = u, first[v] = e++; } if (m & 1) puts("No solution"); else dfs(1, 0); }
#include <bits/stdc++.h> using namespace std; const long long MAX_N = 1e5 + 10, INF = 1e9; int n, m, from[MAX_N], to[MAX_N], tkhor[MAX_N], tvor[MAX_N], d[MAX_N]; vector<int> adj[MAX_N], khor[MAX_N], vor[MAX_N], fard, efkhor[MAX_N]; bool vis[MAX_N], avaz[MAX_N], mar[MAX_N]; int tyal(int v) { vis[v] = 1; int ret = adj[v].size(); for (int k : adj[v]) { int u = from[k] ^ to[k] ^ v; if (!vis[u]) { ret += tyal(u); } } return ret; } void ffar(int v) { vis[v] = 1; if (tkhor[v] % 2 == 1) fard.push_back(v); for (int k : adj[v]) { int u = from[k] ^ to[k] ^ v; if (!vis[u]) { ffar(u); } } } void avyal(int v, int yp = 0) { mar[v] = 1; for (int k : adj[v]) { int u = from[k] ^ to[k] ^ v; if (!mar[u]) { avyal(u, k); d[v] += d[u]; } } if (d[v] % 2 == 1) avaz[yp] = 1; } void hal(int v) { fard.clear(); ffar(v); memset(mar, 0, sizeof mar); for (int i = 0; i < fard.size(); i++) { d[fard[i]]++; } avyal(v); } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m; for (int i = 0; i < m; i++) { int a, b; cin >> a >> b; tkhor[a]++; from[i] = a; to[i] = b; adj[a].push_back(i); adj[b].push_back(i); } for (int i = 1; i <= n; i++) { if (!vis[i]) { if ((tyal(i) / 2) % 2 == 1) { cout << "No solution" << endl; return 0; } } } memset(vis, 0, sizeof vis); for (int i = 1; i <= n; i++) { if (!vis[i]) { hal(i); } } for (int i = 0; i < m; i++) { if (avaz[i] == 1) { efkhor[to[i]].push_back(from[i]); } else { efkhor[from[i]].push_back(to[i]); } } for (int i = 1; i <= n; i++) { for (int j = 0; j < efkhor[i].size(); j += 2) { cout << efkhor[i][j] << " " << i << " " << efkhor[i][j + 1] << endl; } } }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e5 + 5; int N, M; vector<int> adj[maxn]; int cnt = 0, num[maxn]; vector<pair<int, pair<int, int>>> res; bool dfs(int u, int p = 0) { num[u] = ++cnt; int cur = 0; for (int v : adj[u]) { if (v == p) continue; if ((num[v] != 0 && num[v] < num[u]) || (num[v] == 0 && dfs(v, u))) { if (cur == 0) cur = v; else res.push_back(make_pair(cur, make_pair(u, v))), cur = 0; } } if (cur == 0) return true; else { if (p != 0) res.push_back(make_pair(p, make_pair(u, cur))); return false; } } signed main(void) { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> N >> M; for (int i = 1; i <= M; ++i) { int u, v; cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } if (M & 1) { cout << "No solution"; return 0; } for (int i = 1; i <= N; ++i) { if (num[i] == 0) dfs(i); } for (auto& x : res) cout << x.first << ' ' << x.second.first << ' ' << x.second.second << '\n'; }
#include <bits/stdc++.h> using namespace std; vector<int> G[(int)(1e5 + 500)]; map<pair<int, int>, int> block, done; int process[(int)(1e5 + 500)]; void print(int x, int y, int z) { printf("%d", x); printf(" "); printf("%d", y); printf(" "); printf("%d", z); printf(" "); done[make_pair(x, y)] = done[make_pair(y, x)] = 1; done[make_pair(y, z)] = done[make_pair(z, y)] = 1; } int cut(int x) { vector<int> adj; for (int i = 0; i < G[x].size(); i++) { int to = G[x][i]; if (block.find(make_pair(x, to)) == block.end()) { block[make_pair(x, to)] = block[make_pair(to, x)] = 1; adj.push_back(to); } } for (int i = 0; i < adj.size(); i++) { int to = adj[i]; if (!process[to]) { int z = cut(to); if (z) { print(x, to, z); } } } int other = 0; for (int i = 0; i < adj.size(); i++) { int to = adj[i]; if (!done[make_pair(x, to)]) { if (other == 0) { other = to; } else { print(other, x, to); other = 0; } } } process[x] = 1; return other; } void solve() { int n, m; scanf("%d", &n); scanf("%d", &m); if (m % 2) { printf("No solution"); return; } for (int i = 1; i <= m; i++) { int x, y; scanf("%d", &x); scanf("%d", &y); G[x].push_back(y); G[y].push_back(x); } cut(1); } int main() { int t = 1; for (int i = 1; i <= t; i++) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1000 * 100 + 5; int n, m, t = -1; vector<pair<int, int> > adj[MAXN]; bool mark[MAXN]; void DMP(int v) { queue<int> q; while (!q.empty()) { q.pop(); } for (int i = 0; i < adj[v].size(); i++) { if (!mark[adj[v][i].second]) { q.push(adj[v][i].first); mark[adj[v][i].second] = true; } } int siz = q.size(); for (int i = 0; i < siz; i++) { int u = q.front(); DMP(u); if (t == -1) q.push(u); else cout << v + 1 << " " << u + 1 << " " << t + 1 << endl; q.pop(); } int s = q.size(); for (int i = 0; i < s - 1; i += 2) { cout << q.front() + 1 << " "; q.pop(); cout << v + 1 << " "; cout << q.front() + 1 << endl; q.pop(); } if (s % 2 == 0) t = -1; else t = q.back(); return; } int main() { cin >> n >> m; for (int i = 0, u, v; i < m; i++) { cin >> u >> v; u--; v--; adj[u].push_back(make_pair(v, i)); adj[v].push_back(make_pair(u, i)); } if (m % 2 == 1) { cout << "No solution" << endl; return 0; } DMP(0); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 100000 + 10; const int inf = 522133279; const int mod = 1000000007; struct edge { int s; int t; int next; int vis; } e[100100 * 2]; int n, m; int cnt, head[100100]; int color[100100]; void add(int s, int t) { e[cnt].s = s; e[cnt].t = t; e[cnt].next = head[s]; e[cnt].vis = 0; head[s] = cnt++; } int dfs(int cur) { queue<int> adjacent; for (int i = head[cur]; ~i; i = e[i].next) { if (!e[i].vis) { adjacent.push(e[i].t); e[i].vis = e[i ^ 1].vis = 1; } } queue<int> unpair; while (!adjacent.empty()) { int u = adjacent.front(); adjacent.pop(); int w = dfs(u); if (w == 0) unpair.push(u); else printf("%d %d %d\n", cur, u, w); } while (unpair.size() >= 2) { int u = unpair.front(); unpair.pop(); int v = unpair.front(); unpair.pop(); printf("%d %d %d\n", u, cur, v); } if (unpair.size()) return unpair.front(); return 0; } int main() { scanf("%d%d", &n, &m); memset(head, -1, sizeof(head)); for (int i = 0; i < m; i++) { int a, b; scanf("%d%d", &a, &b); add(a, b); add(b, a); } if (m % 2) puts("No solution"); else dfs(1); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAX = 1e5 + 10; vector<vector<int>> G(MAX); vector<int> odd(MAX, 0), lef(MAX, 0), vis(MAX, 0), par(MAX); vector<tuple<int, int, int>> ans; void dfs(int node, int p) { vis[node] = 1; par[node] = p; for (int nxt : G[node]) { if (!vis[nxt]) { dfs(nxt, node); } } vector<int> Ve; for (int nxt : G[node]) { if (nxt != p) { if (par[nxt] == node && odd[nxt]) { ans.push_back({node + 1, nxt + 1, lef[nxt] + 1}); } else if (vis[nxt] == 1 || par[nxt] == node) Ve.push_back(nxt); } } int sz = Ve.size(); if (sz & 1) { odd[node] = 1; lef[node] = Ve[sz - 1]; } for (int i = 0; i + 1 < sz; i += 2) { ans.push_back({Ve[i] + 1, node + 1, Ve[i + 1] + 1}); } vis[node] = 2; } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, m; cin >> n >> m; for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; u--, v--; G[u].push_back(v); G[v].push_back(u); } if (m & 1) { cout << "No solution\n"; return 0; } dfs(0, -1); for (auto x : ans) { int a, b, c; tie(a, b, c) = x; cout << a << ' ' << b << ' ' << c << '\n'; } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") using namespace std; const long long MAX = (long long)1e6 + 10; long long inf = (long long)2e9; long long mod = (long long)1e9 + 7; ; long long m, n, q, used[MAX], parity[MAX], par[MAX]; set<long long> gr[MAX], useless[MAX]; vector<pair<long long, long long>> edg[MAX]; long long t = 0; vector<long long> perm; void dfs(long long v, long long p) { par[v] = p; used[v] = ++t; set<long long> del; del.insert(p); for (auto u : gr[v]) { if (u == p) continue; if (used[u] && used[u] < used[v]) { useless[v].insert(u); del.insert(u); } else if (used[u]) { del.insert(u); } else { dfs(u, v); } } for (auto u : del) gr[v].erase(u); } void tour(long long v, long long p) { for (auto u : gr[v]) { tour(u, v); } perm.push_back(v); } void solve() { cin >> n >> m; if (m % 2) { cout << "No solution\n"; return; } for (int i = 0; i < m; i++) { long long a, b; cin >> a >> b; gr[a].insert(b); gr[b].insert(a); } dfs(1, 0); tour(1, 0); for (int i = 0; i < perm.size() - 1; i++) { long long v = perm[i]; for (auto u : useless[v]) { edg[v].push_back({u, v}); } long long u = par[v]; if (edg[v].size() % 2) { edg[v].push_back({u, v}); } else edg[u].push_back({v, u}); } for (int i = 1; i <= n; i++) { for (int j = 0; j < edg[i].size(); j += 2) { long long a = edg[i][j].first, b = edg[i][j + 1].first; cout << a << " " << i << " " << b << "\n"; } } } int main() { ios::sync_with_stdio(0); long long q; q = 1; while (q--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 100010; int n, m; bool mark[MAXN]; vector<int> adj[MAXN]; vector<int> boom[MAXN]; bool DFS(int cur, int p) { mark[cur] = true; for (int i = 0; i < (int)adj[cur].size(); i++) { int viz = adj[cur][i]; if (mark[viz]) { if (viz != p) boom[viz].push_back(cur); continue; } if (!DFS(viz, cur)) boom[cur].push_back(viz); } while ((int)boom[cur].size() > 1) { int A = boom[cur].back(); boom[cur].pop_back(); int B = boom[cur].back(); boom[cur].pop_back(); printf("%d %d %d\n", A, cur, B); } if (boom[cur].empty()) return false; printf("%d %d %d\n", p, cur, boom[cur].back()); return true; } int main() { scanf("%d %d", &n, &m); for (int i = 1; i <= m; i++) { int U, V; scanf("%d %d", &U, &V); adj[U].push_back(V); adj[V].push_back(U); } if (m % 2 == 1) { printf("No solution\n"); return 0; } DFS(1, 1); }
#include <bits/stdc++.h> using namespace std; const int N = 100100; int n, m, x[N], y[N]; vector<int> e[N], id[N], ans; bool vn[N], ve[N]; int dfs(int nd) { if (vn[nd]) return 0; vn[nd] = 1; int up = 0; for (int i = 0; i < e[nd].size(); i++) { if (!ve[id[nd][i]]) { ve[id[nd][i]] = 1; int k = dfs(e[nd][i]); if (!k) { if (up == 0) { up = id[nd][i]; } else { ans.push_back(id[nd][i]); ans.push_back(up); up = 0; } } else { ans.push_back(id[nd][i]); ans.push_back(k); } } } return up; } int main() { if (fopen("E.in", "r")) freopen("E.in", "r", stdin); cin >> n >> m; if (m % 2) { cout << "No solution"; return 0; } for (int i = 1; i <= m; i++) { scanf("%d %d", x + i, y + i); e[x[i]].push_back(y[i]); id[x[i]].push_back(i); e[y[i]].push_back(x[i]); id[y[i]].push_back(i); } dfs(1); for (int i = 0; i < ans.size() - 1; i += 2) { if (x[ans[i]] == x[ans[i + 1]]) { printf("%d %d %d\n", y[ans[i]], x[ans[i]], y[ans[i + 1]]); } else if (x[ans[i]] == y[ans[i + 1]]) { printf("%d %d %d\n", y[ans[i]], x[ans[i]], x[ans[i + 1]]); } else if (y[ans[i]] == x[ans[i + 1]]) { printf("%d %d %d\n", x[ans[i]], y[ans[i]], y[ans[i + 1]]); } else if (y[ans[i]] == y[ans[i + 1]]) { printf("%d %d %d\n", x[ans[i]], y[ans[i]], x[ans[i + 1]]); } } return 0; }
#include <bits/stdc++.h> bool a[100000 << 1], aa[100000]; int b[100000 << 1], c[100000 << 1], h[100000], n, m, i, x, y; int go(int k) { if (aa[k]) return -1; int i, t, x = -1; for (i = h[k]; ~i; i = b[i]) if (!a[i]) { aa[k] = 1; a[i] = 1, a[i >= m ? i - m : i + m] = 1; t = go(c[i]); if (~t) printf("%d %d %d\n", k + 1, c[i] + 1, t + 1); else if (~x) printf("%d %d %d\n", x + 1, k + 1, c[i] + 1), x = -1; else x = c[i]; } return ~x ? x : -1; } int main() { scanf("%d%d", &n, &m); if (m & 1) { puts("No solution"); return 0; } for (i = 0; i < m * 2; i++) c[i] = -1; for (i = 0; i < n; i++) h[i] = -1; for (i = 0; i < m; ++i) { scanf("%d%d", &x, &y); --x, --y; b[i] = h[x]; c[i] = y; h[x] = i; b[i + m] = h[y]; c[i + m] = x; h[y] = i + m; } go(0); return 0; }
#include <bits/stdc++.h> using namespace std; vector<long long int> fact(100005); vector<long long int> prime_check(1e7 + 2); vector<long long int> primes; long long powmod(long long x, long long y, long long m) { long long res = 1LL; while (y) { if (y & 1) res = (res * x) % m; x = (x * x) % m; y /= 2; } return res; } void init_fact() { fact[0] = 1; for (long long int i = 1; i < 100005; i++) { fact[i] = (fact[i - 1] * i) % 1000000009; } } long long int C(long long int n, long long int r) { if (n < r) return 0; long long int temp = fact[n] * powmod(fact[r], 1000000009 - 2, 1000000009) % 1000000009; temp *= powmod(fact[n - r], 1000000009 - 2, 1000000009); temp %= 1000000009; return temp; } void Sieve() { for (long long int i = 2; i <= 1e7 + 1; i++) { if (prime_check[i]) continue; primes.push_back(i); for (long long int j = 2 * i; j <= 1e7 + 1; j += i) prime_check[j] = i; } } long long int phi(long long int n) { long long int i, res = n; for (i = 2; i * i <= n; i++) if (n % i == 0) { while (n % i == 0) n /= i; res -= res / i; } if (n > 1) res -= res / n; return res; } long long int n, m; vector<vector<pair<long long int, long long int>>> adj(100005); vector<long long int> visited(100005); vector<long long int> vis(100005); long long int part(long long int u) { vector<long long int> unpaired; visited[u] = 1; for (auto y : adj[u]) { long long int x = y.first; if (!visited[x]) { vis[y.second] = 1; long long int w = part(x); if (w != 0) cout << u << " " << x << " " << w << "\n"; else unpaired.push_back(x); } else if (!vis[y.second]) unpaired.push_back(x), vis[y.second] = 1; } while (unpaired.size() >= 2) { cout << unpaired.back() << " " << u << " "; unpaired.pop_back(); cout << unpaired.back() << "\n"; unpaired.pop_back(); } if (unpaired.size() > 0) return unpaired.back(); return 0; } void input_adj(long long int n) { for (long long int i = 0; i < n - 1; i++) { long long int u, vector; cin >> u >> vector; adj[u].push_back({vector, i}); adj[vector].push_back({u, i}); } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> n >> m; input_adj(m + 1); if (m % 2) { cout << "No solution\n"; return 0; } part(1); }
#include <bits/stdc++.h> using namespace std; const int MAX = 1e5 + 10, mod = 1e9 + 7, base = 41, INF = 99999999999, sq = 502; struct A { int a, b, c; }; vector<A> ans; int q, n, m, h[MAX]; bool used[MAX], mark[MAX]; vector<int> adj[MAX]; inline void hdfs(int v) { mark[v] = 1; for (int i = 0; i < adj[v].size(); i++) { int u = adj[v][i]; if (!mark[u]) { h[u] = h[v] + 1; hdfs(u); } } } inline void dfs(int v, int p) { mark[v] = 1; queue<int> second; for (int i = 0; i < adj[v].size(); i++) { int u = adj[v][i]; if (!mark[u]) { dfs(u, v); } if (u != p && !used[u]) second.push(u); } while (second.size() > 1) { int x = second.front(); second.pop(); int y = second.front(); used[x] = (h[x] > h[v]), used[y] = (h[y] > h[v]); second.pop(); ans.push_back({x, v, y}); } if (second.size()) { int x = second.front(); used[x] = (h[x] > h[v]); ans.push_back({x, v, p}); used[v] = 1; } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m; if (m & 1) return cout << "No solution", -0; for (int u, v, i = 0; i < m; i++) { cin >> u >> v; adj[v].push_back(u), adj[u].push_back(v); } hdfs(1); for (int i = 1; i <= n; i++) mark[i] = 0; dfs(1, -1); for (int i = 0; i < ans.size(); i++) { cout << ans[i].a << ' ' << ans[i].b << ' ' << ans[i].c << '\n'; } return -0; }
#include <bits/stdc++.h> using namespace std; const long long maxn = 3e5 + 5; const long long mod = 1e9 + 7; const long long inf = 1e9; const long long del = 728729; long long poww(long long a, long long b, long long md) { return (!b ? 1 : (b & 1 ? a * poww(a * a % md, b / 2, md) % md : poww(a * a % md, b / 2, md) % md)); } long long n; long long m; long long visited[maxn]; vector<long long> adj[maxn]; vector<long long> back[maxn], dare[maxn]; long long par[maxn]; long long dis[maxn]; long long check[maxn]; vector<pair<pair<int, int>, long long> > ans; bool dfs(long long root) { visited[root] = 1; long long cnt = 0; long long test; for (int i = 0; i < adj[root].size(); i++) { long long u = adj[root][i]; if (!visited[u]) { par[u] = root; if (dfs(u) == false) { cnt++; if (cnt % 2 == 0) { ans.push_back({{test, root}, u}); } else { test = u; } } } } check[root] = 1; for (int i = 0; i < adj[root].size(); i++) { long long u = adj[root][i]; if (u != par[root] && check[u] == 0) { cnt++; if (cnt % 2 == 0) { ans.push_back({{test, root}, u}); } else { test = u; } } } if (cnt % 2 == 1 && par[root] != -1) { ans.push_back({{test, root}, par[root]}); return 1; } return 0; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; cin >> m; for (long long i = 0; i < m; i++) { long long x; long long y; cin >> x >> y; adj[x].push_back(y); adj[y].push_back(x); } if (m % 2 == 1) { cout << "No solution"; return 0; } for (long long i = 1; i <= n; i++) { if (!visited[i]) { par[i] = -1; dis[i] = 0; dfs(i); } } if (ans.size() != m / 2) { cout << "No solution"; return 0; } while (ans.size()) { cout << ans.back().first.first << " " << ans.back().first.second << " " << ans.back().second << endl; ans.pop_back(); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> T sqr(T x) { return x * x; } struct sa { int x, y, z; sa(int x, int y, int z) : x(x), y(y), z(z) {} sa() {} }; vector<sa> ans; vector<int> a[110000]; int v[110000], d[110000]; int n, m; int dfs(int x, int dep) { int i, y, z, last = 0; v[x] = 1; d[x] = dep; for (i = 0; i < a[x].size(); i++) { y = a[x][i]; if (v[y] && d[y] < d[x]) continue; if (!v[y] && (z = dfs(y, dep + 1)) && z) { sa t(x, y, z); ans.push_back(t); } else { sa t(last, x, y); last = last ? ans.push_back(t), 0 : y; } } return last; } int main() { int i, x, y, flag; scanf("%d%d", &n, &m); for (i = 0; i < m; i++) { scanf("%d%d", &x, &y); a[x].push_back(y); a[y].push_back(x); } flag = 1; for (i = 1; i <= n; i++) if (!v[i] && dfs(i, 0)) flag = 0; if (!flag) return puts("No solution"), 0; for (i = 0; i < ans.size(); i++) printf("%d %d %d\n", ans[i].x, ans[i].y, ans[i].z); }
#include <bits/stdc++.h> using namespace std; const int MAX_N = 1000 * 100 + 10; vector<int> v[MAX_N], a[MAX_N], b[MAX_N], javab, c; bool check[MAX_N], edge[MAX_N]; map<pair<int, int>, int> m; int parent[MAX_N]; void DFS(int x) { check[x] = true; for (int i = 0; i < v[x].size(); i++) { if (check[v[x][i]] == false) { parent[v[x][i]] = x; DFS(v[x][i]); } else if (parent[x] != v[x][i] && edge[m[make_pair(x, v[x][i])]] == false) { b[x].push_back(v[x][i]); edge[m[make_pair(x, v[x][i])]] = true; edge[m[make_pair(v[x][i], x)]] = true; } } c.push_back(x); if (parent[x] != x) a[x].push_back(parent[x]); } int main() { int n, mm, x, y; ios::sync_with_stdio(false); cin >> n >> mm; for (int i = 0; i < mm; i++) { cin >> x >> y; x--; y--; v[x].push_back(y); v[y].push_back(x); m[make_pair(x, y)] = i; m[make_pair(y, x)] = i; } if (mm % 2 == 1) { cout << "No solution" << endl; return 0; } DFS(0); for (int i = 0; i < c.size(); i++) { int ras = c[i]; if ((a[ras].size() + b[ras].size()) % 2 == 0) { if (a[ras].size() % 2 == 0) { for (int j = 0; j < b[ras].size(); j += 2) { javab.push_back(b[ras][j] + 1); javab.push_back(ras + 1); javab.push_back(b[ras][j + 1] + 1); } for (int j = 0; j < a[ras].size(); j += 2) { javab.push_back(a[ras][j] + 1); javab.push_back(ras + 1); javab.push_back(a[ras][j + 1] + 1); } } else { for (int j = 0; j < b[ras].size() - 1; j += 2) { javab.push_back(b[ras][j] + 1); javab.push_back(ras + 1); javab.push_back(b[ras][j + 1] + 1); } for (int j = 0; j < a[ras].size() - 1; j += 2) { javab.push_back(a[ras][j] + 1); javab.push_back(ras + 1); javab.push_back(a[ras][j + 1] + 1); } javab.push_back(b[ras][b[ras].size() - 1] + 1); javab.push_back(ras + 1); javab.push_back(a[ras][a[ras].size() - 1] + 1); } } else { if (b[ras].size() % 2 == 0) for (int j = 0; j < b[ras].size(); j += 2) { javab.push_back(b[ras][j] + 1); javab.push_back(ras + 1); javab.push_back(b[ras][j + 1] + 1); } if (b[ras].size() % 2 == 1) { for (int j = 0; j < b[ras].size() - 1; j += 2) { javab.push_back(b[ras][j] + 1); javab.push_back(ras + 1); javab.push_back(b[ras][j + 1] + 1); } javab.push_back(b[ras][b[ras].size() - 1] + 1); javab.push_back(ras + 1); javab.push_back(a[ras][a[ras].size() - 1] + 1); a[ras].pop_back(); } if (a[ras].size() % 2 == 0) for (int j = 0; j < a[ras].size(); j += 2) { javab.push_back(a[ras][j] + 1); javab.push_back(ras + 1); javab.push_back(a[ras][j + 1] + 1); } else for (int j = 0; j < a[ras].size() - 1; j += 2) { javab.push_back(a[ras][j] + 1); javab.push_back(ras + 1); javab.push_back(a[ras][j + 1] + 1); } b[a[ras][a[ras].size() - 1]].push_back(ras); } } for (int i = 0; i < javab.size(); i += 3) cout << javab[i] << " " << javab[i + 1] << " " << javab[i + 2] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int xx[4] = {0, 0, 1, -1}; int yy[4] = {1, -1, 0, 0}; int n, m; vector<int> a[int(1e5 + 100)]; vector<int> d[int(1e5 + 100)]; int cha[int(1e5 + 100)]; void dfs(int x) { for (int i = (0), _b = (a[x].size() - 1); i <= _b; i++) { int y = a[x][i]; if (y != cha[x]) { cha[y] = x; dfs(y); if (d[y].size() % 2 == 1) { d[y].push_back(x); } else { d[x].push_back(y); } } } } int lab[int(1e5 + 100)]; int root(int x) { while (lab[x] > 0) x = lab[x]; return x; } void uni(int x, int y) { if (lab[x] > lab[y]) swap(x, y); lab[x] += lab[y]; lab[y] = x; } int main() { scanf("%d%d", &n, &m); if (m % 2 == 1) { cout << "No solution" << endl; return 0; } for (int i = (1), _b = (n); i <= _b; i++) lab[i] = -1; for (int i = (1), _b = (m); i <= _b; i++) { int x, y; scanf("%d%d", &x, &y); int u = root(x); int v = root(y); if (u != v) { uni(u, v); a[x].push_back(y); a[y].push_back(x); } else { d[x].push_back(y); } } dfs(1); for (int i = (1), _b = (n); i <= _b; i++) for (int j = 0; j + 1 < d[i].size(); j += 2) { printf("%d %d %d\n", d[i][j], i, d[i][j + 1]); } }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; int n, m, h[N]; vector<int> e[N]; bool mark[N]; int dfs(int v, int p = 0) { vector<int> vec; mark[v] = 1; for (auto u : e[v]) { if (mark[u]) { if (h[u] > h[v]) vec.push_back(u); continue; } h[u] = h[v] + 1; int x = dfs(u, v); if (x != -1) cout << x << ' ' << u << ' ' << v << "\n"; else if (h[u] > h[v]) vec.push_back(u); } int x = -1; if (vec.size() & 1) { x = vec.back(); vec.pop_back(); } for (int i = 0; i < vec.size(); i += 2) cout << vec[i] << ' ' << v << ' ' << vec[i + 1] << "\n"; return x; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m; if (m & 1) return cout << "No solution", 0; while (m--) { int u, v; cin >> u >> v; e[u].push_back(v); e[v].push_back(u); } dfs(1); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 100 * 1000 + 5; bool Mark[maxn]; vector<pair<int, int> > adj[maxn]; int decompose(int v) { queue<int> q; while (q.size()) q.pop(); for (int i = 0; i < adj[v].size(); i++) { int e = adj[v][i].second; if (!Mark[e]) { q.push(adj[v][i].first); Mark[e] = true; } } int t = q.size(); for (int i = 0; i < t; i++) { int nei = q.front(); int dc = decompose(nei); if (dc == -1) q.push(nei); else cout << v << " " << nei << " " << dc << endl; q.pop(); } t = q.size(); for (int i = 0; i < t - 1; i += 2) { cout << q.front() << " " << v << " "; q.pop(); cout << q.front() << endl; q.pop(); } if (t % 2 == 0) return -1; return q.back(); } int main() { int n, m; cin >> n >> m; for (int i = 0, u, v; i < m; i++) { cin >> u >> v; adj[u].push_back(make_pair(v, i)); adj[v].push_back(make_pair(u, i)); } if (m & 1) { cout << "No solution" << endl; return 0; } decompose(1); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; int n, m, h[N]; vector<int> e[N]; bool mark[N]; void sfd(int v, int p = 0) { mark[v] = 1; h[v] = h[p] + 1; for (auto u : e[v]) if (!mark[u]) sfd(u, v); } int dfs(int v, int p = 0) { vector<int> vec; mark[v] = 1; for (auto u : e[v]) { if (mark[u]) { if (h[u] > h[v]) vec.push_back(u); continue; } int x = dfs(u, v); if (x != -1) cout << x << ' ' << u << ' ' << v << "\n"; else if (h[u] > h[v]) vec.push_back(u); } int x = -1; if (vec.size() & 1) { x = vec.back(); vec.pop_back(); } for (int i = 0; i < vec.size(); i += 2) cout << vec[i] << ' ' << v << ' ' << vec[i + 1] << "\n"; return x; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n >> m; if (m & 1) return cout << "No solution", 0; while (m--) { int u, v; cin >> u >> v; e[u].push_back(v); e[v].push_back(u); } sfd(1); memset(mark, 0, sizeof mark); dfs(1); return 0; }
#include <bits/stdc++.h> using namespace std; const long long int Maxn3 = 1e3 + 10; const long long int Maxn4 = 1e4 + 10; const long long int Maxn5 = 1e5 + 10; const long long int Maxn6 = 1e6 + 10; const long long int Maxn7 = 1e7 + 10; const long long int Maxn8 = 1e8 + 10; const long long int Maxn9 = 1e9 + 10; const long long int Maxn18 = 1e18 + 10; const long long int Mod1 = 1e7 + 7; const long long int Mod2 = 1e9 + 7; const long long int LLMax = LLONG_MAX; const long long int LLMin = LLONG_MIN; const long long int INTMax = INT_MAX; const long long int INTMin = INT_MIN; long long int mn = LLMax, mx = LLMin; vector<long long int> g[Maxn6]; long long int h[Maxn6]; bool mark[Maxn6]; vector<pair<long long int, pair<long long int, long long int> > > res; int dfs(long long int x, long long int p) { mark[x] = 1; vector<long long int> a, child; for (long long int i = 0; i < g[x].size(); i++) { long long int c = g[x][i]; if (c == p) continue; if (mark[c]) { if (h[c] < h[x]) a.push_back(c); continue; } h[c] = h[x] + 1; long long int t = dfs(c, x); if (t == 1) child.push_back(c); } bool m = ((a.size() % 2) == 1), mm = ((child.size() % 2) == 1); for (long long int i = 1; i < child.size(); i += 2) { long long int u = child[i], v = child[i - 1]; res.push_back(make_pair(x, make_pair(u, v))); } for (long long int i = 1; i < a.size(); i += 2) { long long int u = a[i], v = a[i - 1]; res.push_back(make_pair(x, make_pair(u, v))); } if (m and mm) { res.push_back( make_pair(x, make_pair(child[child.size() - 1], a[a.size() - 1]))); return 1; } if (m) { res.push_back(make_pair(x, make_pair(a[a.size() - 1], p))); return 0; } if (mm) { res.push_back(make_pair(x, make_pair(child[child.size() - 1], p))); return 0; } return 1; } int main() { ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL); long long int n, m; cin >> n >> m; if (m % 2 == 1) return cout << "No solution", 0; for (long long int i = 0; i < m; i++) { long long int u, v; cin >> u >> v; g[u].push_back(v), g[v].push_back(u); } dfs(1, 1); for (long long int i = 0; i < res.size(); i++) cout << res[i].second.first << ' ' << res[i].first << ' ' << res[i].second.second << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T1, typename T2> istream& operator>>(istream& in, pair<T1, T2>& t) { return in >> t.first >> t.second; } template <typename T1, typename T2> ostream& operator<<(ostream& out, pair<T1, T2>& t) { return out << t.first << " " << t.second << endl; } template <typename T> istream& operator>>(istream& in, vector<T>& t) { for (int i = 0; i < t.size(); i++) in >> t[i]; return in; } template <typename T> ostream& operator<<(ostream& out, vector<T>& t) { for (int i = 0; i < t.size(); i++) out << t[i] << " "; return out; } vector<int> is; vector<vector<int>> answ; struct G { map<int, int> to; }; vector<G> g; int dfs1(int v, int p = -1) { for (auto i : g[v].to) { g[i.first].to.erase(v); } int last = -1; for (auto it = g[v].to.begin(); it != g[v].to.end();) { auto& i = *it; int ans = dfs1(i.first, v); if (ans != -1) { answ.push_back({v, i.first, ans}); int t = i.first; g[i.first].to.erase(ans); g[v].to.erase(i.first); it = g[v].to.upper_bound(t); continue; } if (last == -1) { last = i.first; it++; } else { answ.push_back({last, v, i.first}); int t = i.first; g[v].to.erase(last); g[v].to.erase(i.first); it = g[v].to.upper_bound(t); last = -1; continue; } } return last; } int main() { int n, m; scanf( "%" "d", &n); scanf( "%" "d", &m); g.resize(n); is.resize(m); for (int i = 0; i < m; i++) { int a, b; scanf( "%" "d", &a); scanf( "%" "d", &b); a--; b--; g[a].to[b] = i; g[b].to[a] = i; } if (dfs1(0) != -1) { puts("No solution"); return 0; } for (int i = 0; i < answ.size(); i++) { printf("%d %d %d\n", answ[i][0] + 1, answ[i][1] + 1, answ[i][2] + 1); } return 0; }
#include <bits/stdc++.h> using namespace std; int getint() { unsigned int c; int x = 0; while (((c = getchar()) - '0') >= 10) { if (c == '-') return -getint(); if (!~c) exit(0); } do { x = (x << 3) + (x << 1) + (c - '0'); } while (((c = getchar()) - '0') < 10); return x; } int getstr(char* s) { int c, n = 0; while ((c = getchar()) <= ' ') { if (!~c) exit(0); } do { s[n++] = c; } while ((c = getchar()) > ' '); s[n] = 0; return n; } template <class T> inline bool chmin(T& a, T b) { return a > b ? a = b, 1 : 0; } template <class T> inline bool chmax(T& a, T b) { return a < b ? a = b, 1 : 0; } template <class S, class T, class U> struct Tuple { S s; T t; U u; Tuple() {} Tuple(S s, T t, U u) : s(s), t(t), u(u) {} bool operator==(const Tuple<S, T, U>& a) const { return (s == a.s and t == a.t and u == a.u) ? 1 : 0; } bool operator!=(const Tuple<S, T, U>& a) const { return !this->operator==(a); } }; template <class S> struct Compare { bool operator()(const S& a, const S& b) const { if (a.s != b.s) return a.s < b.s; if (a.t != b.t) return a.t < b.t; if (a.u != b.u) return a.u < b.u; return 0; } }; template <class S, class T, class U> ostream& operator<<(ostream& os, const Tuple<S, T, U>& a) { os << '(' << a.s << ' ' << a.t << ' ' << a.u << ')'; return os; } struct edge { int to, rev, used; edge(int to, int rev, int used) : to(to), rev(rev), used(used){}; edge() { used = 0; } }; int n, m; vector<edge> graph[100100]; vector<Tuple<int, int, int> > res; void add_edge(int u, int v) { int us = graph[u].size(); int vs = graph[v].size(); graph[u].push_back(edge(v, vs, 0)); graph[v].push_back(edge(u, us, 0)); } int dfs(int u, int par) { int i, j; vector<int> child; for (i = 0; i < graph[u].size(); i++) { int v = graph[u][i].to; if (graph[u][i].used == 1) continue; graph[u][i].used = 1; int revidx = graph[u][i].rev; graph[v][revidx].used = 1; if (v != par) { int remu = dfs(v, u); if (remu != -1) { res.push_back(Tuple<int, int, int>(u + 1, v + 1, remu + 1)); } else { child.push_back(v); } } } for (i = 0; i + 1 < child.size(); i += 2) { res.push_back(Tuple<int, int, int>(child[i] + 1, u + 1, child[i + 1] + 1)); } if (child.size() & 1) { return child.back(); } return -1; } int main() { int i, j, tcc, tc = 1 << 28; for (tcc = 0; tcc < tc; tcc++) { n = getint(), m = getint(); for (i = 0; i < m; i++) { int u = getint() - 1; int v = getint() - 1; add_edge(u, v); } if (m & 1) { puts("No solution"); continue; } dfs(0, -1); for (i = 0; i < res.size(); i++) { cout << res[i].s << ' ' << res[i].t << ' ' << res[i].u << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; int const mxn = 2e5 + 10; int r; vector<pair<int, pair<int, int> > > ans, ans2; vector<int> adj[mxn]; vector<int> back[mxn]; int mark[mxn]; void dfs(int v, int p) { mark[v] = 1; for (auto u : adj[v]) { if (!mark[u]) { dfs(u, v); } else if (u != p) { back[u].push_back(v); } } for (int i = 0; i < back[v].size() - back[v].size() % 2; i += 2) { ans.push_back({back[v][i], {v, back[v][i + 1]}}); } if (back[v].size() % 2 == 1 and back[v][back[v].size() - 1] != r) ans.push_back({back[v][back[v].size() - 1], {v, p}}); else back[p].push_back(v); return; } int main() { int n, m; cin >> n >> m; for (int i = 1; i <= m; i++) { int a, b; cin >> a >> b; adj[a].push_back(b); adj[b].push_back(a); } for (int i = 1; i <= n; i++) { if (!mark[i]) { r = i; dfs(i, 0); } } if (m % 2 == 0) { for (auto i : ans) { if (i.first != 0 and i.second.first != 0 and i.second.second != 0) ans2.push_back(i); } for (auto i : ans2) { cout << i.first << " " << i.second.first << " " << i.second.second << endl; } } else cout << "No solution"; }
#include <bits/stdc++.h> using namespace std; const int MAX = 1e5 + 10; bool vis[MAX]; vector<int> g[MAX]; map<pair<int, int>, bool> M; void DFS(int v, int par) { vis[v] = 1; int last = -1; for (int i = 0; i < (int)g[v].size(); i++) { int u = g[v][i]; if (!vis[u]) DFS(u, v); if (M[make_pair(v, u)] == 1 && u != par) { if (last == -1) last = u; else { M[make_pair(v, u)] = M[make_pair(u, v)] = 0; M[make_pair(v, last)] = M[make_pair(last, v)] = 0; printf("%d %d %d\n", u, v, last); last = -1; } } } if (last != -1) { M[make_pair(v, par)] = M[make_pair(par, v)] = 0; M[make_pair(v, last)] = M[make_pair(last, v)] = 0; printf("%d %d %d\n", par, v, last); } } int main() { int n, m; scanf("%d%d", &n, &m); int sum = 0; while (m--) { int a, b; scanf("%d%d", &a, &b); sum++; g[a].push_back(b); g[b].push_back(a); M[make_pair(a, b)] = 1; M[make_pair(b, a)] = 1; } if (sum % 2 == 0) { DFS(1, -1); } else printf("No solution\n"); }
#include <bits/stdc++.h> using namespace std; vector<pair<int, int>> node[100001]; bool blocked[100000]; int partition(int v) { queue<int> q; for (int i = 0; i < node[v].size(); i++) { int e = node[v][i].second; if (blocked[e] == false) { blocked[e] = true; q.push(node[v][i].first); } } int t = q.size(); for (int i = 0; i < t; i++) { int top = q.front(); int neighbour = partition(top); if (neighbour == 0) q.push(top); else cout << v << " " << top << " " << neighbour << endl; q.pop(); } t = q.size(); for (int i = 0; i < t - 1; i += 2) { cout << q.front() << " " << v << " "; q.pop(); cout << q.front() << endl; ; q.pop(); } if (t % 2 == 0) return 0; else return q.front(); } int main() { std::ios_base::sync_with_stdio(false); int n, m; cin >> n >> m; if (m % 2) { cout << "No solution" << endl; return 0; } for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; node[u].push_back(make_pair(v, i)); node[v].push_back(make_pair(u, i)); } memset(blocked, false, sizeof(blocked)); partition(1); return 0; }
#include <bits/stdc++.h> using namespace std; struct edge { int to, nx; } e[200050]; int head[200050]; int num = 0; bool bo[200050]; void addedge(int x, int y) { e[num].to = y; e[num].nx = head[x]; head[x] = num++; } bool ok[200050]; int gao(int now) { ok[now] = true; queue<int> q; for (int p = head[now]; p != -1; p = e[p].nx) { if (!bo[p]) { q.push(e[p].to); bo[p] = bo[p ^ 1] = true; } } queue<int> p; while (!q.empty()) { int u = q.front(); q.pop(); int w = gao(u); if (w != 0) printf("%d %d %d\n", w, u, now); else p.push(u); } while (p.size() >= 2) { int u, v; u = p.front(); p.pop(); v = p.front(); p.pop(); printf("%d %d %d\n", u, now, v); } if (!p.empty()) return p.front(); else return 0; } int main() { int i, n, m; num = 0; memset(head, -1, sizeof(head)); memset(ok, 0, sizeof(ok)); memset(bo, 0, sizeof(bo)); scanf("%d%d", &n, &m); for (i = 0; i < m; i++) { int x, y; scanf("%d%d", &x, &y); addedge(x, y); addedge(y, x); } if (m % 2) printf("No solution\n"); else { gao(1); } }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; vector<pair<int, int>> vec[N]; bool vis[N]; int solve(int v) { vector<int> remain; for (int i = 0; i < vec[v].size(); ++i) { int u = vec[v][i].first, k; if (!vis[vec[v][i].second]) { vis[vec[v][i].second] = true; k = solve(u); if (k) printf("%d %d %d\n", k, u, v); else remain.push_back(u); } } while (remain.size() > 1) { printf("%d %d ", remain.back(), v); remain.pop_back(); printf("%d\n", remain.back()); remain.pop_back(); } if (remain.size()) return remain[0]; return 0; } int main() { int n, m, root; scanf("%d%d", &n, &m); for (int i = 1; i <= m; ++i) { int a, b; scanf("%d%d", &a, &b); vec[a].push_back({b, i}); vec[b].push_back({a, i}); if (vec[a].size() > 1) root = a; if (vec[b].size() > 1) root = b; } if (m & 1) { printf("No solution\n"); return 0; } solve(1); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 210000; struct Edge { int next, to; Edge(int to = 0, int next = -1) : to(to), next(next) {} }; int head[N], countedge; Edge edge[N]; void AddEdge(const int& s, const int& t) { edge[countedge] = Edge(t, head[s]); head[s] = countedge++; } void init() { memset(head, -1, sizeof(head)); countedge = 0; } bool vis[N]; int dfs(int u) { int temp; queue<int> que; vector<int> unpair; for (temp = head[u]; temp != -1; temp = edge[temp].next) { int v = edge[temp].to; if (vis[temp]) continue; vis[temp] = true; vis[temp ^ 1] = true; que.push(v); } while (!que.empty()) { int v = que.front(); que.pop(); int w = dfs(v); if (w) printf("%d %d %d\n", u, v, w); else unpair.push_back(v); } int len = unpair.size(); while (len >= 2) { printf("%d %d %d\n", unpair[len - 1], u, unpair[len - 2]); len -= 2; } if (len) return unpair[0]; return 0; } int main() { int n, m; scanf("%d%d", &n, &m); init(); for (int i = 0; i < m; i++) { int u, v; scanf("%d%d", &u, &v); AddEdge(u, v); AddEdge(v, u); } if (m & 1) { printf("No solution\n"); return 0; } else dfs(1); return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") using namespace std; const int N = 2e5 + 10; int mark[N]; vector<int> g[N]; vector<pair<int, pair<int, int> > > ans; bool dfs(int v, int par = 0) { mark[v] = 1; vector<int> V; for (auto u : g[v]) { if (!mark[u]) { if (dfs(u, v)) { V.push_back(u); } } else if (u != par && mark[u] == 1) V.push_back(u); } mark[v] = 2; for (int i = 1; i < V.size(); i += 2) { ans.push_back({V[i], {v, V[i - 1]}}); } if (V.size() % 2 != 0 && par != 0) { ans.push_back({V[V.size() - 1], {v, par}}); return 0; } return 1; } int main() { ios::sync_with_stdio(0), cin.tie(0), cout.tie(0); int n, m; cin >> n >> m; if (m % 2 == 1) return cout << "No solution", 0; for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; g[u].push_back(v); g[v].push_back(u); } for (int i = 1; i <= n; i++) if (!mark[i]) dfs(i); for (auto e : ans) { cout << e.first << ' ' << e.second.first << ' ' << e.second.second << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int N = int(2e5) + 5; const int inf = (int)1e9 + 7; int n, m; vector<pair<int, int> > g[N]; int ban[N]; int dfs(int v) { vector<int> to; for (pair<int, int> i : g[v]) { if (ban[i.second]) { continue; } ban[i.second] = 1; to.push_back(i.first); } vector<int> all; for (int i : to) { int w = dfs(i); if (w == 0) { all.push_back(i); } else { printf("%d %d %d\n", w, i, v); } } while ((int)all.size() >= 2) { printf("%d %d %d\n", all.back(), v, all[(int)all.size() - 2]); all.pop_back(), all.pop_back(); } return all.empty() ? 0 : all.back(); } int main() { scanf("%d %d", &n, &m); if (m & 1) { printf("No solution"); return 0; } for (int i = 1; i <= m; ++i) { int x, y; scanf("%d %d", &x, &y); g[x].push_back({y, i}); g[y].push_back({x, i}); } dfs(1); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1000100; const int INF = 1e9 + 10; int n, m; int u, v; bool vis[maxn]; struct Edge { int v; }; Edge e[maxn]; int en; int head[maxn], nex[maxn]; void addedge(int u, int v) { e[en].v = v; nex[en] = head[u]; head[u] = en; en++; } int dfs(int u, int f) { int p[2], pn = 0; for (int i = head[u]; ~i; i = nex[i]) { int v = e[i].v; if (v == f) continue; if (vis[i] || vis[i ^ 1]) continue; vis[i] = vis[i ^ 1] = 1; int r = dfs(v, u); if (r) printf("%d %d %d\n", u, v, r); else p[pn++] = v; if (pn == 2) printf("%d %d %d\n", p[0], u, p[1]), pn = 0; } return pn ? p[0] : 0; } void solve() { if (m % 2) { puts("No solution"); return; } memset(vis, 0, sizeof(vis)); dfs(1, 0); } int main() { while (cin >> n >> m) { memset(head, -1, sizeof(head)); memset(nex, -1, sizeof(nex)); en = 0; for (int i = 1; i <= m; i++) { scanf("%d%d", &u, &v); addedge(u, v); addedge(v, u); } solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<pair<int, int> > ans; struct Edge { int x, y, num, joft; Edge(int p, int q, int w) { x = p; y = q; num = w; } Edge() {} int other(int p) { if (p == y) return x; else return y; } }; const int MAXN = 100000 + 100; int n, m; vector<int> v[MAXN]; Edge e[MAXN]; bool mark[MAXN]; int seen[MAXN]; void Input() { cin >> n >> m; for (int i = 0; i < m; i++) { int x, y; cin >> x >> y; seen[i] = 0; e[i] = Edge(x, y, i); v[x].push_back(i); v[y].push_back(i); } } int par[MAXN]; void Dfs(int x) { mark[x] = true; for (int i = 0; i < v[x].size(); i++) { int u = e[v[x][i]].other(x); if (!mark[u]) { par[u] = x; Dfs(u); } } vector<int> w; int pp; for (int i = 0; i < v[x].size(); i++) { int u = e[v[x][i]].other(x); int t = v[x][i]; if (seen[t] == 0) if (u != par[x]) w.push_back(t); if (e[v[x][i]].other(x) == par[x]) pp = v[x][i]; } if (w.size() % 2 == 0) { for (int i = 0; i < w.size(); i += 2) { ans.push_back(make_pair(w[i], w[i + 1])); seen[w[i]] = 1; seen[w[i + 1]] = 1; } } else { for (int i = 0; i < w.size(); i += 2) { if (i == (w.size() - 1)) { ans.push_back(make_pair(w[i], pp)); seen[pp] = 1; seen[w[i]] = 1; } else { ans.push_back(make_pair(w[i], w[i + 1])); seen[w[i]] = 1; seen[w[i + 1]] = 1; } } } } bool Check() { for (int i = 0; i < m; i++) if (!seen[i]) return 0; return 1; } int main() { Input(); if (m % 2 == 1) { cout << "No solution" << endl; return 0; } Dfs(1); if (!Check() || ans.size() != (m / 2) || (m % 2) == 1) cout << "No solution" << endl; else { for (int i = 0; i < ans.size(); i++) { if (e[ans[i].first].x == e[ans[i].second].x) cout << e[ans[i].first].y << " " << e[ans[i].first].x << " " << e[ans[i].second].y << endl; else if (e[ans[i].first].x == e[ans[i].second].y) cout << e[ans[i].first].y << " " << e[ans[i].first].x << " " << e[ans[i].second].x << endl; else if (e[ans[i].first].y == e[ans[i].second].x) cout << e[ans[i].first].x << " " << e[ans[i].first].y << " " << e[ans[i].second].y << endl; else if (e[ans[i].first].y == e[ans[i].second].y) cout << e[ans[i].first].x << " " << e[ans[i].first].y << " " << e[ans[i].second].x << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int NMAX = 100005; int N, M, X, Y; set<int> S[NMAX]; vector<int> V[NMAX]; bitset<NMAX> viz; void DFS(int Node, int Father) { for (vector<int>::iterator it = V[Node].begin(); it != V[Node].end(); it++) if (!viz[*it]) { viz[*it] = 1; DFS(*it, Node); } if (S[Node].size() & 1) S[Node].erase(S[Node].find(Father)); for (set<int>::iterator it1 = S[Node].begin(); it1 != S[Node].end(); it1++) { set<int>::iterator it2 = it1; it2++; printf("%d %d %d\n", *it1, Node, *it2); S[*it1].erase(Node); S[*it2].erase(Node); it1 = it2; } } int main() { scanf("%d%d", &N, &M); if (M & 1) { printf("No solution\n"); return 0; } for (; M; M--) { scanf("%d%d", &X, &Y); V[X].push_back(Y); V[Y].push_back(X); S[X].insert(Y); S[Y].insert(X); } viz[1] = 1; DFS(1, 0); return 0; }
#include <bits/stdc++.h> using namespace std; const int inf = 0x3f3f3f3f; const int N = 100000 + 10; int u[N << 1], v[N << 1], nt[N << 1], ft[N]; int n, m, cnt; int vis[N << 1]; void add(int a, int b) { u[cnt] = a; v[cnt] = b; nt[cnt] = ft[a]; ft[a] = cnt++; } int dfs(int x, int f) { queue<int> vec; for (int i = ft[x]; i != -1; i = nt[i]) { int nx = v[i]; if (vis[i] || nx == f) continue; vis[i] = vis[i ^ 1] = 1; int r = dfs(nx, x); if (r) { printf("%d %d %d\n", x, nx, r); } else { vec.push(nx); } } while (vec.size() >= 2) { int a = vec.front(); vec.pop(); int b = vec.front(); vec.pop(); printf("%d %d %d\n", a, x, b); } if (!vec.empty()) { int a = vec.front(); vec.pop(); return a; } return 0; } int main() { while (scanf("%d%d", &n, &m) != EOF) { cnt = 0; memset(ft, -1, sizeof ft); memset(vis, 0, sizeof vis); int a, b; for (int i = 0; i < m; i++) { scanf("%d%d", &a, &b); add(a, b); add(b, a); } if (m & 1) { puts("No solution"); continue; } dfs(1, -1); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 100010; int first[maxn], nxt[maxn << 1], vv[maxn << 1]; bool vis[maxn]; int mark[maxn]; int edge[maxn]; void dfs(int n, int fa) { vis[n] = true; for (int e = first[n]; e; e = nxt[e]) if (vv[e] != fa && !vis[vv[e]]) dfs(vv[e], n); int top = 0; for (int e = first[n]; e; e = nxt[e]) if (vv[e] != fa && mark[vv[e]] != 1) edge[top++] = vv[e]; if (top & 1) edge[top++] = fa, mark[n] = 1; else mark[n] = 2; for (int i = 0; i < top; i += 2) { printf("%d %d %d\n", edge[i], n, edge[i + 1]); if (mark[edge[i]] == 2) mark[edge[i]] = 1; if (mark[edge[i + 1]] == 2) mark[edge[i + 1]] = 1; } } int main() { int e = 2; int n, m; scanf("%d%d", &n, &m); for (int i = 0; i < m; i++) { int u, v; scanf("%d%d", &u, &v); nxt[e] = first[u], vv[e] = v, first[u] = e++; nxt[e] = first[v], vv[e] = u, first[v] = e++; } if (m & 1) puts("No solution"); else dfs(1, 0); }
#include <bits/stdc++.h> using namespace std; inline int read() { int x = 0; char ch = getchar(); bool positive = 1; for (; ch < '0' || ch > '9'; ch = getchar()) if (ch == '-') positive = 0; for (; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0'; return positive ? x : -x; } inline char RC() { char c = getchar(); while (c == ' ' || c == '\n') c = getchar(); return c; } inline long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } inline long long lcm(long long a, long long b, long long MOD) { return a / gcd(a, b) * b % MOD; } inline long long Sub(long long x, long long y, long long mod) { long long res = x - y; while (res < 0) res += mod; return res; } inline long long Add(long long x, long long y, long long mod) { long long res = x + y; while (res >= mod) res -= mod; return res; } inline long long POW_MOD(long long x, long long y, long long mod) { long long ret = 1; while (y > 0) { if (y & 1) ret = ret * x % mod; x = x * x % mod; y >>= 1; } return ret; } const int N = 100000 + 50; const int inf = 2100000000; const long long INF = 1LL << 60; const double PI = 3.14159265358; int n, m; vector<int> e[N]; unordered_set<long long> mp; int dfs(int u) { vector<int> adj; queue<int> unPairs; for (int v : e[u]) { long long id = min((long long)v * N + u, (long long)u * N + v); if (mp.find(id) == mp.end()) { adj.push_back(v); mp.insert(id); } } for (int v : adj) { int w = dfs(v); if (w) printf("%d %d %d\n", u, v, w); else unPairs.push(v); } while (unPairs.size() >= 2) { int v = unPairs.front(); unPairs.pop(); int w = unPairs.front(); unPairs.pop(); printf("%d %d %d\n", v, u, w); } if (unPairs.size()) { return unPairs.front(); } else { return 0; } } int main() { cin >> n >> m; int cnt = 0; for (int i = 0; i < m; ++i) { int u, v; scanf("%d%d", &u, &v); e[u].push_back(v); e[v].push_back(u); cnt++; } if (cnt & 1) cout << "No solution" << endl; else dfs(1); return 0; }
#include <bits/stdc++.h> #pragma clang diagnostic push #pragma ide diagnostic ignored "cert-err58-cpp" #pragma ide diagnostic ignored "cppcoreguidelines-pro-type-member-init" using namespace std; const int maxiii = 100022; struct node { bool seen; vector<pair<int, bool>> Adj; vector<int> B; }; node graph[maxiii]; void dfs(int v, int p, int e) { graph[v].seen = true; for (int i = 0; i < graph[v].Adj.size(); ++i) if (!graph[v].Adj[i].second) { int u = graph[v].Adj[i].first; if (!graph[u].seen) dfs(u, v, i); else if (u != p) { graph[u].B.push_back(v); graph[v].Adj[i].second = true; } } if (graph[v].B.size() % 2 == 1) graph[v].B.push_back(p); else if (p != -1) { graph[p].B.push_back(v); graph[p].Adj[e].second = true; } for (int i = 0; i < graph[v].B.size(); i += 2) cout << graph[v].B[i] << " " << v << " " << graph[v].B[i + 1] << "\n"; } int main() { ios::sync_with_stdio(false); int n, m; cin >> n >> m; if (m % 2) { cout << "No solution"; return 0; } for (int i = 0; i < m; ++i) { int a, b; cin >> a >> b; graph[a].Adj.emplace_back(b, false); graph[b].Adj.emplace_back(a, false); } dfs(1, -1, -1); } #pragma clang diagnostic pop
#include <bits/stdc++.h> using namespace std; const int MAXN = 100100; int bio[MAXN]; vector<int> E[MAXN]; int dfs(int x, int dad) { bio[x] = 1; int unused = -1; for (int to : E[x]) { if (to == dad) continue; if (bio[to] == 0) { int t = dfs(to, x); if (t != -1) printf("%d %d %d\n", t + 1, to + 1, x + 1); else if (unused != -1) { printf("%d %d %d\n", unused + 1, x + 1, to + 1); unused = -1; } else unused = to; } else if (bio[to] == 1) { if (unused != -1) { printf("%d %d %d\n", unused + 1, x + 1, to + 1); unused = -1; } else unused = to; } } bio[x] = 2; return unused; } int main() { int n, m; scanf("%d%d", &n, &m); for (int i = 0; i < m; ++i) { int a, b; scanf("%d%d", &a, &b); --a; --b; E[a].push_back(b); E[b].push_back(a); } if (m & 1) return printf("No solution\n"), 0; dfs(0, -1); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 100005; vector<int> adj[MAXN]; vector<int> edges[MAXN]; int cnt[MAXN], vis[MAXN]; int cont = 0; int precalc(int v, int prev) { int res = 0; vis[v] = 1; for (int i = 0; i < int((adj[v]).size()); ++i) { int k = adj[v][i]; if (prev == k) continue; if (vis[k] == 2) continue; res++; if (vis[k] == 0) res += precalc(k, v); } vis[v] = 2; return cnt[v] = res; } void solve(int v, int prev) { vis[v] = 1; for (int i = 0; i < int((adj[v]).size()); ++i) { int k = adj[v][i]; if (k == prev) continue; if (vis[k] == 2) continue; if (vis[k] == 1) { edges[v].push_back(k); } else { if (cnt[k] & 1) edges[k].push_back(v); else edges[v].push_back(k); solve(k, v); } } vis[v] = 2; } int main() { int n, m; while (scanf(" %d %d", &n, &m) != EOF) { for (int i = 0; i < n; ++i) adj[i].clear(), edges[i].clear(); for (int i = 0; i < m; ++i) { int a, b; scanf(" %d %d", &a, &b); a--, b--; adj[a].push_back(b); adj[b].push_back(a); } if (m & 1) { cout << "No solution" << endl; } else { memset(vis, 0, sizeof vis); precalc(0, -1); memset(vis, 0, sizeof vis); solve(0, -1); for (int i = 0; i < n; ++i) { cont += int((edges[i]).size()); if (int((edges[i]).size()) & 1) cout << "opa" << endl; for (int j = 0; j < int((edges[i]).size()); ++j) { cout << (edges[i][j] + 1) << " " << (i + 1) << " " << (edges[i][j + 1] + 1) << endl; j++; } } } } }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e5 + 3; int who[MAXN]; int kol[MAXN]; bool odw[MAXN]; set<int> v[MAXN]; vector<int> ans; vector<int> tree[MAXN]; int ile = 0, kra = 0; void DFS(int x) { int k, me = ile; who[me] = x; odw[x] = true; while (!v[x].empty()) { k = *v[x].begin(); v[x].erase(v[x].begin()); v[k].erase(x); ile++; kra++; tree[me].push_back(ile); DFS(k); } } bool DFS2(int x) { vector<int> kat; for (auto it : tree[x]) { if (DFS2(it)) { ans.push_back(who[x]); ans.push_back(who[it]); ans.push_back(kol[it]); } else kat.push_back(who[it]); } while (kat.size() > 1) { ans.push_back(kat.back()); kat.pop_back(); ans.push_back(who[x]); ans.push_back(kat.back()); kat.pop_back(); } if (!kat.empty()) { kol[x] = kat.back(); return true; } return false; } int main() { int n, m; int x, y; scanf("%d %d", &n, &m); while (m--) { scanf("%d %d", &x, &y); v[x].insert(y); v[y].insert(x); } for (int i = 1; i <= n; i++) { if (!odw[i]) { ile++; y = ile; DFS(i); if (kra % 2 != 0) { printf("No solution"); return 0; } DFS2(y); } } for (int i = 0; i < (int)(ans.size()); i += 3) printf("%d %d %d\n", ans[i], ans[i + 1], ans[i + 2]); return 0; }
#include <bits/stdc++.h> using namespace std; typedef pair<long long, long long> ll; typedef vector<long long> vl; typedef vector<ll> vll; typedef vector<vl> vvl; template <typename T> ostream &operator<<(ostream &o, vector<T> v) { if (v.size() > 0) o << v[0]; for (unsigned i = 1; i < v.size(); i++) o << " " << v[i]; return o << "\n"; } template <typename U, typename V> ostream &operator<<(ostream &o, pair<U, V> p) { return o << "(" << p.first << ", " << p.second << ") "; } template <typename T> istream &operator>>(istream &in, vector<T> &v) { for (unsigned i = 0; i < v.size(); i++) in >> v[i]; return in; } template <typename T> istream &operator>>(istream &in, pair<T, T> &p) { in >> p.first; in >> p.second; return in; } vvl g(111000); vl ind(111000, 0), vis(111000, false); long long c = 0; bool rec(long long node, long long p) { vl ch; ind[node] = c++; vis[node] = 1; for (auto &it : g[node]) { if (it == p) continue; if (!vis[it]) { if (!rec(it, node)) ch.push_back((it)); } else if (ind[node] < ind[it]) ch.push_back((it)); } for (long long i = 0; i + 1 < ch.size(); i += 2) cout << ch[i] << " " << node << " " << ch[i + 1] << "\n"; if (ch.size() % 2 == 1) { cout << p << " " << node << " " << ch[ch.size() - 1] << "\n"; return true; } return false; } int main() { long long n, m; cin >> n >> m; if (m % 2 == 1) { cout << "No solution" << "\n"; return 0; } while (m--) { long long x, y; cin >> x >> y; g[x].push_back((y)); g[y].push_back((x)); } rec(1, -1); return 0; }
#include <bits/stdc++.h> using namespace std; long long read() { char ch = getchar(); long long f = 1, x = 0; while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); } return f * x; } const long long maxn = 1e5 + 10; long long n, h[maxn], cnt, m; struct edge { long long v, next; } e[maxn << 1]; void addedge(long long u, long long v) { e[++cnt].v = v; e[cnt].next = h[u]; h[u] = cnt; } void insert(long long u, long long v) { addedge(u, v); addedge(v, u); } stack<long long> g[maxn]; struct answers { long long a, b, c; } ans[maxn]; long long vis[maxn], tot; bool no; void dfs(long long u, long long fa) { vis[u] = 1; for (long long i = h[u]; i; i = e[i].next) { long long v = e[i].v; if (!vis[v]) dfs(v, u); else if (v != fa) { g[v].push(u); } } while (g[u].size() >= 2) { ans[++tot].a = g[u].top(); ans[tot].b = u; g[u].pop(); ans[tot].c = g[u].top(); g[u].pop(); } if (g[u].size() == 1) { if (fa == 0) { no = 1; return; } long long x = g[u].top(); ans[++tot].a = x; ans[tot].b = u; ans[tot].c = fa; g[u].pop(); } else { g[fa].push(u); } } signed main() { n = read(); m = read(); if (m & 1) { cout << "No solution\n"; return 0; } for (long long i = 1; i <= m; i++) { insert(read(), read()); } dfs(1, 0); if (no) { cout << "No solution\n"; return 0; } for (long long i = 1; i <= tot; i++) { cout << ans[i].a << " " << ans[i].b << " " << ans[i].c << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxN = 1e5 + 100; bool mark[maxN]; vector<pair<int, int> > adj[maxN]; int n, m; int decompose(int v) { queue<int> q; while (q.size()) q.pop(); for (int i = 0; i < adj[v].size(); i++) { int e = adj[v][i].second; if (!mark[e]) { q.push(adj[v][i].first); mark[e] = true; } } int t = q.size(); for (int i = 0; i < t; i++) { int nei = q.front(); int dc = decompose(nei); if (dc == -1) q.push(nei); else cout << v << " " << nei << " " << dc << endl; q.pop(); } t = q.size(); for (int i = 0; i < t - 1; i += 2) { cout << q.front() << " " << v << " "; q.pop(); cout << q.front() << endl; q.pop(); } if (t % 2 == 0) return -1; return q.back(); } void input() { cin >> n >> m; for (int i = 0, u, v; i < m; i++) { cin >> u >> v; adj[u].push_back(make_pair(v, i)); adj[v].push_back(make_pair(u, i)); } } int main() { input(); if (m & 1) { cout << "No solution" << endl; return 0; } decompose(1); return 0; }
#include <bits/stdc++.h> using namespace std; const int T = 1e5 + 5; struct node { int num, x; } t; vector<node> p[T]; bool flag[T]; int dfs(int now) { queue<int> q; int l = p[now].size(); for (int i = 0; i < l; i++) { node k = p[now][i]; if (flag[k.num]) continue; else flag[k.num] = 1; int r = dfs(k.x); if (r) printf("%d %d %d\n", now, k.x, r); else q.push(k.x); } while (q.size() >= 2) { int v1 = q.front(); q.pop(); int v2 = q.front(); q.pop(); printf("%d %d %d\n", v1, now, v2); } while (!q.empty()) { int v3 = q.front(); q.pop(); return v3; } return 0; } int main() { int n, m, a, b; while (scanf("%d%d", &n, &m) != EOF) { for (int i = 0; i < n; i++) p[i].clear(); for (int i = 1; i <= m; i++) { scanf("%d%d", &a, &b); t.num = i; t.x = a; p[b].push_back(t); t.x = b; p[a].push_back(t); } if (m % 2 == 1) printf("No solution\n"); else { memset(flag, 0, sizeof(flag)); dfs(1); } } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 5; const long long mod = 1e9 + 7; const double pi = acos(-1); vector<vector<int> > adj(N); map<pair<int, int>, bool> mp, vis; pair<int, int> f(int x, int y) { return {min(x, y), max(x, y)}; } bool sa5eef[N]; int dfs(int u) { int ret = -1; vector<int> meh; for (int i = 0; i < adj[u].size(); i++) { int v = adj[u][i]; if (mp[f(u, v)]) continue; meh.push_back(v); mp[f(u, v)] = 1; } for (int i = 0; i < meh.size(); i++) { int v = meh[i]; if (sa5eef[v]) continue; int p = dfs(v); if (p != -1) { printf("%d %d %d\n", u, v, p); vis[f(u, v)] = vis[f(v, p)] = 1; } } for (int i = 0; i < meh.size(); i++) { int v = meh[i]; if (!vis[f(u, v)]) { if (ret == -1) ret = v; else { printf("%d %d %d\n", v, u, ret); ret = -1; } } } sa5eef[u] = 1; return ret; } int main() { int n, m; scanf("%d%d", &n, &m); int x, y; int cntr = 1; for (int i = 0; i < m; i++) { scanf("%d%d", &x, &y); adj[x].push_back(y); adj[y].push_back(x); } if (m % 2) puts("No solution"); else dfs(1); return 0; } long long fastpow(long long b, long long e) { if (!e) return 1; long long ret = fastpow(b, e / 2); ret = (ret * ret) % mod; if (e % 2) ret = (ret * b) % mod; return ret; } long long modinv(long long x) { return fastpow(x, mod - 2); } double torad(double ang) { return ang * pi / 180.0; }
#include <bits/stdc++.h> using namespace std; set<int> a[100005]; int dfs(int v) { vector<int> adj; for (auto it = a[v].begin(); it != a[v].end(); it++) { adj.push_back(*it); a[*it].erase(v); } a[v].clear(); vector<int> unpaired; for (int i = 0; i < adj.size(); i++) { int u = adj[i]; int w = dfs(u); if (w == 0) unpaired.push_back(u); else printf("%d %d %d\n", v, u, w); } adj.clear(); int i = (int)unpaired.size() - 1; while (i >= 1) { int u = unpaired[i]; int w = unpaired[i - 1]; printf("%d %d %d\n", u, v, w); i -= 2; } if (i >= 0) { unpaired.clear(); return unpaired[i]; } else { unpaired.clear(); return 0; } } int main() { int n, m; cin >> n >> m; for (int i = 0; i < m; i++) { int x, y; scanf("%d%d", &x, &y); a[x].insert(y); a[y].insert(x); } if (m % 2 == 0) dfs(1); else cout << "No solution" << endl; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 123; vector<int> v[maxn]; int n, m, High[maxn]; bool mark[maxn]; int Dfs(int Vert, int Dad) { mark[Vert] = true; vector<int> now; now.clear(); for (__typeof(v[Vert].begin()) i = v[Vert].begin(); i != v[Vert].end(); ++i) if (!mark[*i]) { High[*i] = High[Vert] + 1; if (Dfs(*i, Vert) == 1) now.push_back(*i); } else if (*i != Dad and High[*i] < High[Vert]) now.push_back(*i); while (now.size() >= 2) { int x = now.back(); now.pop_back(); int y = now.back(); now.pop_back(); printf("%d %d %d\n", x, Vert, y); } if (now.empty()) return 1; else { printf("%d %d %d\n", now[0], Vert, Dad); return 0; } } int main() { int fi, se; cin >> n >> m; if (m % 2) { puts("No solution"); return 0; } while (m--) { cin >> fi >> se; v[fi].push_back(se); v[se].push_back(fi); } Dfs(1, 0); return 0; }
#include <bits/stdc++.h> using namespace std; int edge[100000 + 10], first[100000 + 10], nxt[100000 + 10 << 1]; bool v[100000 + 10]; int mark[100000 + 10], vv[100000 + 10 << 1]; void dfs(int n, int fa) { v[n] = 1; for (int e = first[n]; e != -1; e = nxt[e]) if (vv[e] != fa && !v[vv[e]]) dfs(vv[e], n); int top = 0; for (int e = first[n]; e != -1; e = nxt[e]) if (vv[e] != fa && mark[vv[e]] != 1) edge[top++] = vv[e]; if (top & 1) edge[top++] = fa, mark[n] = 1; else mark[n] = 2; for (int i = 0; i < top; i += 2) { printf("%d %d %d\n", edge[i], n, edge[i + 1]); if (mark[edge[i]] == 2) mark[edge[i]] = 1; if (mark[edge[i + 1]] == 2) mark[edge[i + 1]] = 1; } } int main(void) { int e = 0; int n, m; scanf("%d %d", &n, &m); memset(first, -1, sizeof(first)); for (int i = 0; i < m; i++) { int u, v; scanf("%d%d", &u, &v); nxt[e] = first[u], vv[e] = v; first[u] = e++; nxt[e] = first[v], vv[e] = u; first[v] = e++; } if (m & 1) printf("No solution\n"); else dfs(1, 0); return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> g[100005], s[100005], A, B, C; int i, j, k, t, l, m, n, w, f[100005], V[10005]; int go(int v) { vector<int> V; for (int i = 0; i < g[v].size(); i++) if (!f[s[v][i]]) { f[s[v][i]] = 1; w = go(g[v][i]); if (w) { A.push_back(v); B.push_back(g[v][i]); C.push_back(w); } else V.push_back(g[v][i]); } for (int i = 1; i < V.size(); i += 2) A.push_back(V[i]), B.push_back(v), C.push_back(V[i - 1]); if (V.size() % 2) return V.back(); return 0; } int main() { scanf("%d%d", &n, &m); for (i = 1; i <= m; i++) { int x, y; scanf("%d%d", &x, &y); g[x].push_back(y); g[y].push_back(x); s[x].push_back(i); s[y].push_back(i); } for (i = 1; i <= n; i++) if (go(i)) { cout << "No solution" << endl; return 0; } for (i = 0; i < A.size(); i++) printf("%d %d %d\n", A[i], B[i], C[i]); }
#include <bits/stdc++.h> using namespace std; vector<vector<pair<int, int>>> adj(100005); map<int, int> vis; int vis2[100005], p[100005]; void DFS(int s, int edge) { vis2[s] = 1; deque<int> dq; for (auto i = adj[s].begin(); i != adj[s].end(); i++) { if (!vis2[i->first]) { p[i->first] = s; DFS(i->first, i->second); if (vis[i->second]) { vis[i->second] = 0; dq.push_back(i->first); } } else if (vis[i->second] && p[s] != i->first) { vis[i->second] = 0; dq.push_back(i->first); } } if (dq.size() % 2) { vis[edge] = 0; dq.push_back(p[s]); } while (!dq.empty()) { printf("%d %d %d\n", dq.front(), s, dq.back()); dq.pop_front(); dq.pop_back(); } } int main() { int n, m; scanf("%d %d", &n, &m); if (m % 2) { printf("No solution"); return 0; } for (int i = 1; i <= m; i++) { int x, y; scanf("%d %d", &x, &y); adj[x].push_back(make_pair(y, i)); adj[y].push_back(make_pair(x, i)); vis[i] = 1; } DFS(1, 100006); return 0; }
#include <bits/stdc++.h> using namespace std; void die() { cout << "No solution\n"; exit(0); } vector<int> edges[100005]; int ans[100005]; set<pair<int, int> > ret; bool seen[100005]; void dfs(int curr, int par = -1) { for (int out : edges[curr]) { if (out == par) continue; if (seen[out]) continue; seen[out] = true; dfs(out, curr); if (ans[out] % 2 && ret.count({curr, out})) { ans[out]++; ans[curr]--; ret.erase({curr, out}); ret.insert({out, curr}); } if (ans[out] % 2 && ret.count({out, curr})) { ans[out]--; ans[curr]++; ret.erase({out, curr}); ret.insert({curr, out}); } } } void solve() { int n, m; cin >> n >> m; for (int i = 0; i < m; i++) { int a, b; cin >> a >> b; ret.insert({a, b}); edges[a].push_back(b); edges[b].push_back(a); ans[a]++; } seen[1] = true; dfs(1); for (int i = 1; i <= n; i++) { if (ans[i] % 2) die(); } auto it = ret.begin(); while (it != ret.end()) { cout << it->second << " " << it->first << " "; it++; cout << it->second << "\n"; it++; } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); solve(); }
#include <bits/stdc++.h> using namespace std; const int maxn = 1000 * 100 + 10; vector<pair<int, bool> > g[maxn]; vector<int> ans[maxn]; int deg[2][maxn], mark[maxn]; int n, m; void input() { cin >> n >> m; for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; u--, v--; g[u].push_back(make_pair(v, 1)); g[v].push_back(make_pair(u, 0)); deg[1][u]++, deg[0][v]++; } } int dfs(int v, int par) { int res = 0; mark[v] = 1; for (int i = 0; i < g[v].size(); i++) { pair<int, bool> u = g[v][i]; if (par == u.first) res = i; if (!mark[u.first]) { int x = dfs(u.first, v); if (deg[1][u.first] % 2) { deg[u.second][v]--, deg[!u.second][v]++; g[v][i].second = !u.second, g[u.first][x].second = u.second; } } } return res; } int main() { input(); if (m % 2) { cout << "No solution"; return 0; } dfs(0, -1); for (int i = 0; i < n; i++) for (auto &u : g[i]) if (u.second) ans[i].push_back(u.first); for (int i = 0; i < n; i++) for (int j = 0; j < ans[i].size() / 2; j++) cout << ans[i][j * 2] + 1 << " " << i + 1 << " " << ans[i][j * 2 + 1] + 1 << endl; return 0; }
#include <bits/stdc++.h> bool a[100000 << 1]; int b[100000 << 1], c[100000 << 1], h[100000], n, m, i, x, y; int go(int k) { int i, t, x = -1; for (i = h[k]; ~i; i = b[i]) if (!a[i]) { a[i] = 1, a[i >= m ? i - m : i + m] = 1; t = go(c[i]); if (~t) printf("%d %d %d\n", k + 1, c[i] + 1, t + 1); else if (~x) printf("%d %d %d\n", x + 1, k + 1, c[i] + 1), x = -1; else x = c[i]; } return ~x ? x : -1; } int main() { scanf("%d%d", &n, &m); if (m & 1) { puts("No solution"); return 0; } for (i = 0; i < m * 2; i++) c[i] = -1; for (i = 0; i < n; i++) h[i] = -1; for (i = 0; i < m; ++i) { scanf("%d%d", &x, &y); --x, --y; b[i] = h[x]; c[i] = y; h[x] = i; b[i + m] = h[y]; c[i + m] = x; h[y] = i + m; } go(0); return 0; }
#include <bits/stdc++.h> using namespace std; inline int toInt(string s) { int v; istringstream sin(s); sin >> v; return v; } template <class T> inline string toString(T x) { ostringstream sout; sout << x; return sout.str(); } template <class T> inline T sqr(T x) { return x * x; } const double eps = 1e-10; const double pi = acos(-1.0); const long long INF = 1LL << 62; const int inf = 1 << 29; vector<pair<int, int> > graph[100010]; bool used[100010]; int n, m; int dfs(int cur) { int l = -1, r; for (int i = (0); i < (graph[cur].size()); ++i) { int m = graph[cur][i].first; if (used[graph[cur][i].second]) continue; used[graph[cur][i].second] = true; r = dfs(graph[cur][i].first); if (r == -1) { if (l == -1) { l = m; } else { cout << l << " " << cur << " " << m << endl; l = -1; } } else cout << cur << " " << m << " " << r << endl; } return l; } int main(void) { scanf("%d %d", &n, &m); for (int i = (0); i < (m); ++i) { int f, t; scanf("%d %d", &f, &t); pair<int, int> in; in.second = i; in.first = t; graph[f].push_back(in); in.first = f; graph[t].push_back(in); } if (m & 1) { printf("No solution\n"); return 0; } for (int i = (0); i < (100010); ++i) used[i] = false; dfs(1); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100005; struct node { int v; node* next; } E[N + N], *tot, *head[N]; int n, m, u, v, clk, dfn[N], cnt, ans[N][3]; void add(int u, int v) { tot->v = v; tot->next = head[u]; head[u] = tot++; } void pc(int a, int b, int c) { ans[cnt][0] = a; ans[cnt][1] = b; ans[cnt][2] = c; ++cnt; } int dfs(int u) { int ret = 0; dfn[u] = ++clk; for (node* p = head[u]; p; p = p->next) { int v = p->v; if (!dfn[v]) { int w = dfs(v); if (w) pc(u, v, w); else { if (ret) { pc(v, u, ret); ret = 0; } else ret = v; } } else if (dfn[v] > dfn[u]) { if (ret) { pc(v, u, ret); ret = 0; } else ret = v; } } return ret; } void print() { for (int i = 0; i < cnt; ++i) { printf("%d %d %d\n", ans[i][0], ans[i][1], ans[i][2]); } } int main() { tot = E; cin >> n >> m; for (int i = 0; i < m; ++i) { scanf("%d%d", &u, &v); add(u, v); add(v, u); } if (m & 1) printf("No solution\n"); else { dfs(1); print(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 10; int a[maxn], b[maxn]; vector<pair<int, int>> G[maxn]; bool v[maxn], use[maxn]; struct data { int a, b, c; }; vector<data> ans; void dfs(int now, int fa, int edge) { v[now] = true; int nxt = -1, cid = -1; for (auto u : G[now]) if (u.first != fa) { if (!v[u.first]) dfs(u.first, now, u.second); if (use[u.second]) continue; if (nxt == -1) nxt = u.second, cid = u.first; else if (nxt != -1) { ans.emplace_back((data){u.first, now, cid}); use[nxt] = use[u.second] = true; nxt = -1; cid = -1; } } if (nxt != -1) { if (edge && !use[edge] && !use[nxt]) { ans.emplace_back((data){cid, now, fa}); use[edge] = use[nxt] = true; } } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int n, m; cin >> n >> m; if (m & 1) return cout << "No solution" << endl, 0; for (int i = 1; i <= m; ++i) { cin >> a[i] >> b[i]; G[a[i]].emplace_back(b[i], i); G[b[i]].emplace_back(a[i], i); } for (int i = 1; i <= n; ++i) { if (!v[i]) dfs(i, 0, 0); } if (ans.size() < m / 2) return cout << "No solution" << endl, 0; for (auto e : ans) cout << e.a << ' ' << e.b << ' ' << e.c << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int max1 = 100010; long long a[max1], b[max1]; int main() { int n, x, y = 0, z = 0; cin >> n; if (n == 1) { cout << "NO\n"; } else { for (int i = 0; i < n; i++) { cin >> x; if (x == 200) { z++; } y += x; } if ((y % 200 == 0)) { if ((z == n) && (z % 2 != 0)) { cout << "NO\n"; } else { cout << "YES\n"; } } else { cout << "NO\n"; } } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(false); long long n; cin >> n; long long a[n]; long long sum = 0; map<int, int> m; for (size_t i = 0; i < n; i++) { cin >> a[i]; sum += a[i]; m[a[i]]++; } for (size_t i = 0; i <= m[100]; i++) { for (size_t j = 0; j <= m[200]; j++) { if (i * 100 + j * 200 == sum - (i * 100 + j * 200)) { cout << "YES"; return 0; } } } cout << "NO"; return 0; }
#include <bits/stdc++.h> using namespace std; void striker() { int n; cin >> n; int a1 = 0, a2 = 0; for (int i = 0; i < n; i++) { int x; cin >> x; if (x == 100) a1++; else a2++; } if (n & 1 == 1 && (a1 == 0 || a2 == 0)) cout << "NO"; else if (2 * (a1 / 2) + a2 == n) cout << "YES"; else cout << "NO"; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int t = 1; for (int i = 0; i < t; i++) { striker(); cout << endl; } return 0; }