cereal2take2

contests/silver/2022/january/prob3/cereal2take2.cpp

@@ -0,0 +1,109 @@
+// I forgot how to solve this, so I decided to re-try it after competition.
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define MAX 1e5
+
+vector<pair<int, int>> cereal(MAX);
+vector<vector<pair<int, int>>> adj(MAX);
+vector<bool> globalVis(MAX, false), vis(MAX);
+
+int main()
+{
+  int N, M;
+  cin >> N >> M;
+
+  int a, b;
+  for (int i = 0; i < N; ++i)
+  {
+    cin >> a >> b;
+    --a, --b;
+    cereal[i] = {a, b};
+    adj[a].push_back({b, i});
+    adj[b].push_back({a, i});
+  }
+
+  vector<int> ans;
+  for (int c = 0;;)
+  {
+
+    // step 1. find an extra edge in the tree
+    int extraEdge = -1;
+    const std::function<void(int, int)> findExtraEdge = [&](int from, int v)
+    {
+      vis[v] = true;
+      globalVis[v] = true;
+      for (int i = 0; i < adj[v].size(); ++i)
+      {
+        const int &w = adj[v][i].first;
+        const int &wI = adj[v][i].second;
+
+        if (!vis[w])
+          findExtraEdge(v, w);
+        else if (w != from && extraEdge == -1) // double-count this edge
+          extraEdge = wI;
+      }
+    };
+
+    fill(vis.begin(), vis.begin() + M, false);
+    findExtraEdge(-1, c);
+
+    // step 2. run a depth first search through the tree to get the order
+    const int root = extraEdge == -1 ? c : cereal[extraEdge].first;
+
+    if (extraEdge != -1)
+      ans.push_back(extraEdge);
+
+    const std::function<void(int)> dfs = [&](int v)
+    {
+      vis[v] = true;
+      for (int i = 0; i < adj[v].size(); ++i)
+      {
+        const int &w = adj[v][i].first;
+        const int &wI = adj[v][i].second;
+
+        if (!vis[w] && wI != extraEdge)
+        {
+          ans.push_back(wI); 
+          dfs(w);
+        }
+      }
+    };
+
+    fill(vis.begin(), vis.begin() + M, false);
+    dfs(root);
+
+    // step 3. continue to next connected component
+    bool found = false;
+    for (int i = 0; i < M; ++i)
+      if (!globalVis[i])
+      {
+        c = i;
+        found = true;
+        break;
+      }
+
+    if (!found)
+      break;
+  }
+
+  // step 4. find hungry cows and add them to end of answer
+  set<int> ansSet;
+  for (int i = 0; i < ans.size(); ++i)
+    ansSet.insert(ans[i]);
+
+  int hungryCows = N - ansSet.size();
+
+  for (int i = 0; i < N; ++i)
+    if (ansSet.find(i) == ansSet.end())
+      ans.push_back(i);
+
+  // step 5. output answer
+  cout << hungryCows << '\n';
+
+  for (int i = 0; i < N; ++i)
+    cout << ans[i] + 1 << '\n';
+
+  return 0;
+}