euler walk first draft

Author: lrvideckis

library/graphs/euler_walk.hpp

@@ -0,0 +1,18 @@
+#pragma once
+vector<pii> euler_walk(auto& adj, int m, int s) {
+  vi vis(m);
+  vector<pii> path;
+  auto dfs = [&](auto&& self, int u, int e) -> void {
+    while (!empty(adj[u])) {
+      auto [v, e_id] = adj[u].back();
+      adj[u].pop_back();
+      if (vis[e_id]) continue;
+      vis[e_id] = 1;
+      self(self, v, e_id);
+    }
+    path.push_back({u, e});
+  };
+  dfs(dfs, s, -1);
+  ranges::reverse(path);
+  return path;
+}

tests/library_checker_aizu_tests/graphs/euler_walk_directed.test.cpp

@@ -0,0 +1,48 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/eulerian_trail_directed"
+#include "../template.hpp"
+#include "../../../library/graphs/euler_walk.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);
+    vector<int> deg(n);
+    int s = -1;
+    for (int i = 0; i < m; i++) {
+      int u, v;
+      cin >> u >> v;
+      s = u;
+      adj[u].push_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_walk(adj, m, s);
+    if (ssize(res) != m + 1) {
+      cout << "No" << '\n';
+      continue;
+    }
+    cout << "Yes" << '\n';
+    for (int i = 0; i < ssize(res); i++)
+      cout << res[i].first << ' ';
+    cout << '\n';
+    for (int i = 1; i < ssize(res); i++)
+      cout << res[i].second << ' ';
+    cout << '\n';
+  }
+  return 0;
+}

tests/library_checker_aizu_tests/graphs/euler_walk_undirected.test.cpp

@@ -0,0 +1,45 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/eulerian_trail_undirected"
+#include "../template.hpp"
+#include "../../../library/graphs/euler_walk.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);
+    vector<int> deg(n);
+    int s = -1;
+    for (int i = 0; i < m; i++) {
+      int u, v;
+      cin >> u >> v;
+      s = u;
+      adj[u].push_back({v, i});
+      adj[v].push_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_walk(adj, m, s);
+    if (ssize(res) != m + 1) {
+      cout << "No" << '\n';
+      continue;
+    }
+    cout << "Yes" << '\n';
+    for (int i = 0; i < ssize(res); i++)
+      cout << res[i].first << ' ';
+    cout << '\n';
+    for (int i = 1; i < ssize(res); i++)
+      cout << res[i].second << ' ';
+    cout << '\n';
+  }
+  return 0;
+}