euler walk first draft (#186)

* euler walk first draft

* [auto-verifier] verify commit fa84857

* nits

* [auto-verifier] verify commit f28be0d

* ni

* [auto-verifier] verify commit 36770a6

* add docs now

* [auto-verifier] verify commit f920eba

* renaming

* update

---------

Co-authored-by: GitHub <noreply@github.com>

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -63,6 +63,8 @@
 "tests/library_checker_aizu_tests/graphs/dijkstra_lib_checker.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/graphs/directed_cycle.test.cpp": "2026-01-17 13:05:42 -0700",
 "tests/library_checker_aizu_tests/graphs/enumerate_triangles.test.cpp": "2025-08-06 16:18:37 -0600",
+"tests/library_checker_aizu_tests/graphs/euler_walk_directed.test.cpp": "2026-02-26 13:17:25 -0700",
+"tests/library_checker_aizu_tests/graphs/euler_walk_undirected.test.cpp": "2026-02-26 13:17:25 -0700",
 "tests/library_checker_aizu_tests/graphs/hopcroft_karp_aizu.test.cpp": "2025-12-11 21:47:53 +0000",
 "tests/library_checker_aizu_tests/graphs/hopcroft_karp_lib_checker.test.cpp": "2025-12-11 21:47:53 +0000",
 "tests/library_checker_aizu_tests/graphs/mst.test.cpp": "2026-01-22 10:08:22 -0700",

library/graphs/euler_path.hpp

@@ -0,0 +1,28 @@
+#pragma once
+//! @code
+//!   vector<basic_string<array<int, 2>>> adj(n);
+//!   rep(i, 0, m) {
+//!     int u, v;
+//!     cin >> u >> v;
+//!     u--, v--;
+//!     adj[u] += {v, i};
+//!   }
+//!   vector<pii> path = euler_path(adj, m, source);
+//! @endcode
+//! @time O(n + m)
+//! @space O(n + m)
+vector<pii> euler_path(auto& adj, int m, int s) {
+  vi vis(m);
+  vector<pii> path;
+  auto dfs = [&](auto&& self, int u, int eu) -> void {
+    while (!empty(adj[u])) {
+      auto [v, ev] = adj[u].back();
+      adj[u].pop_back();
+      if (!vis[ev]) vis[ev] = 1, self(self, v, ev);
+    }
+    path.emplace_back(u, eu);
+  };
+  dfs(dfs, s, -1);
+  ranges::reverse(path);
+  return path;
+}

tests/library_checker_aizu_tests/graphs/euler_walk_directed.test.cpp

@@ -0,0 +1,46 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/eulerian_trail_directed"
+#include "../template.hpp"
+#include "../../../library/graphs/euler_path.hpp"
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int t;
+  cin >> t;
+  while (t--) {
+    int n, m;
+    cin >> n >> m;
+    vector<vector<pii>> adj(n);
+    vi deg(n);
+    int s = -1;
+    rep(i, 0, m) {
+      int u, v;
+      cin >> u >> v;
+      s = u;
+      adj[u].emplace_back(v, i);
+      deg[u]++;
+      deg[v]--;
+    }
+    if (*max_element(all(deg)) >= 2) {
+      cout << "No" << '\n';
+      continue;
+    }
+    if (ranges::count(deg, 1) >= 2) {
+      cout << "No" << '\n';
+      continue;
+    }
+    auto it = ranges::find(deg, 1);
+    if (it != end(deg)) s = it - begin(deg);
+    else if (s == -1) s = 0;
+    vector<pii> res = euler_path(adj, m, s);
+    if (ssize(res) != m + 1) {
+      cout << "No" << '\n';
+      continue;
+    }
+    cout << "Yes" << '\n';
+    rep(i, 0, sz(res)) cout << res[i].first << ' ';
+    cout << '\n';
+    rep(i, 1, sz(res)) cout << res[i].second << ' ';
+    cout << '\n';
+  }
+  return 0;
+}

tests/library_checker_aizu_tests/graphs/euler_walk_undirected.test.cpp

@@ -0,0 +1,43 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/eulerian_trail_undirected"
+#include "../template.hpp"
+#include "../../../library/graphs/euler_path.hpp"
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int t;
+  cin >> t;
+  while (t--) {
+    int n, m;
+    cin >> n >> m;
+    vector<vector<pii>> adj(n);
+    vi deg(n);
+    int s = -1;
+    rep(i, 0, m) {
+      int u, v;
+      cin >> u >> v;
+      s = u;
+      adj[u].emplace_back(v, i);
+      adj[v].emplace_back(u, i);
+      deg[u] ^= 1;
+      deg[v] ^= 1;
+    }
+    if (ranges::count(deg, 1) > 2) {
+      cout << "No" << '\n';
+      continue;
+    }
+    auto it = ranges::find(deg, 1);
+    if (it != end(deg)) s = it - begin(deg);
+    else if (s == -1) s = 0;
+    vector<pii> res = euler_path(adj, m, s);
+    if (ssize(res) != m + 1) {
+      cout << "No" << '\n';
+      continue;
+    }
+    cout << "Yes" << '\n';
+    rep(i, 0, sz(res)) cout << res[i].first << ' ';
+    cout << '\n';
+    rep(i, 1, sz(res)) cout << res[i].second << ' ';
+    cout << '\n';
+  }
+  return 0;
+}