tests/Eulerian_Trail_Undirected.test.cpp

View this file on GitHub
Last update: 2025-11-28 02:09:51+07:00
Problem: https://judge.yosupo.jp/problem/eulerian_trail_undirected

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_undirected"

#include "../misc/macros.h"
#include "../graph/EulerWalk.h"

void solve() {
  int n, m;
  cin >> n >> m;
  vector<vector<pii>> g(n);
  for (int i = 0; i < m; ++i) {
    int u, v;
    cin >> u >> v;
    g[u].eb(v, i), g[v].eb(u, i);
  }
  auto [nodes, edges] = EulerWalk(n, g, m, false, false);
  if (!nodes.empty()) {
    cout << "Yes\n";
    for (auto u : nodes) cout << u << ' ';
    cout << '\n';
    for (auto e : edges) cout << e << ' ';
    cout << '\n';
  } else {
    cout << "No\n";
  }
}

int main() {
  int tc;
  cin >> tc;
  while (tc--) solve();
}

#line 1 "tests/Eulerian_Trail_Undirected.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_undirected"

#line 1 "misc/macros.h"
// #pragma GCC optimize("Ofast,unroll-loops")       // unroll long, simple loops
// #pragma GCC target("avx2,fma")                   // vectorizing code
// #pragma GCC target("lzcnt,popcnt,abm,bmi,bmi2")  // for fast bitset operation

#include <bits/extc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace __gnu_pbds;  // ordered_set, gp_hash_table
// using namespace __gnu_cxx; // rope

// for templates to work
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define pb push_back
#define eb emplace_back
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using pii = pair<i32, i32>;
using vi = vector<i32>;

// fast map
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {  // customize hash function for gp_hash_table
  int operator()(int x) const { return x ^ RANDOM; }
};
gp_hash_table<int, int, chash> table;

/* ordered set
    find_by_order(k): returns an iterator to the k-th element (0-based)
    order_of_key(k): returns the number of elements in the set that are strictly less than k
*/
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

/*  rope
    rope <int> cur = v.substr(l, r - l + 1);
    v.erase(l, r - l + 1);
    v.insert(v.mutable_begin(), cur);
*/
#line 1 "graph/EulerWalk.h"
pair<vi, vi> EulerWalk(int n, vector<vector<pii>>& adj, int m, bool dir, bool cyc) {
  vi D(n), ptr(n), used(m), nodes, edges;
  vector<pii> st;
  int src = 0, bad = 0;
  for (int i = 0; i < n; ++i) {
    if (dir) for (auto& p : adj[i]) D[i]++, D[p.first]--;
    else D[i] = sz(adj[i]) & 1;
  }
  for (int i = 0; i < n; ++i) {
    if (sz(adj[i]) && adj[src].empty()) src = i;
    if (D[i]) {
      bad++;
      if ((dir && D[i] > 0) || (!dir)) src = i;
    }
  }
  if (bad > 2 || (cyc && bad) || (dir && bad && D[src] != 1)) return {};
  st.pb({src, -1});
  while (!st.empty()) {
    int u = st.back().first;
    if (ptr[u] < sz(adj[u])) {
      auto [v, id] = adj[u][ptr[u]++];
      if (!used[id]) used[id] = 1, st.pb({v, id});
    } else {
      auto [v, id] = st.back();
      st.pop_back();
      nodes.pb(v);
      if (id != -1) edges.pb(id);
    }
  }
  if (sz(edges) != m) return {};
  reverse(all(nodes)), reverse(all(edges));
  return {nodes, edges};
}
#line 5 "tests/Eulerian_Trail_Undirected.test.cpp"

void solve() {
  int n, m;
  cin >> n >> m;
  vector<vector<pii>> g(n);
  for (int i = 0; i < m; ++i) {
    int u, v;
    cin >> u >> v;
    g[u].eb(v, i), g[v].eb(u, i);
  }
  auto [nodes, edges] = EulerWalk(n, g, m, false, false);
  if (!nodes.empty()) {
    cout << "Yes\n";
    for (auto u : nodes) cout << u << ' ';
    cout << '\n';
    for (auto e : edges) cout << e << ' ';
    cout << '\n';
  } else {
    cout << "No\n";
  }
}

int main() {
  int tc;
  cin >> tc;
  while (tc--) solve();
}