From 1351da1b92e39b894028fba40abe9753c760ef6e Mon Sep 17 00:00:00 2001
From: subcrip <contact@subc.rip>
Date: Fri, 20 Sep 2024 15:41:11 +0800
Subject: [PATCH] Update graph/hierholzer.cc

Signed-off-by: subcrip <contact@subc.rip>
---
 graph/hierholzer.cc | 79 +++++++++++++++++++++++++++++++--------------
 1 file changed, 55 insertions(+), 24 deletions(-)

diff --git a/graph/hierholzer.cc b/graph/hierholzer.cc
index a1d6ab1..2f20a71 100644
--- a/graph/hierholzer.cc
+++ b/graph/hierholzer.cc
@@ -1,32 +1,63 @@
-/**
- * 作者：力扣官方题解
- * 链接：https://leetcode.cn/problems/reconstruct-itinerary/solutions/
- * 来源：力扣（LeetCode）
- * 著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。
- */
+struct hierholzer {
+    struct edge_t {
+        int from, to, rev, stale;
+        edge_t(int from, int to, int rev, int stale) : from(from), to(to), rev(rev), stale(stale) {}
+    };
+    int n;
+    vector<edge_t> edges;
+    vector<vector<int>> ch;
+    quick_union qu;
 
-class Solution {
-public:
-    unordered_map<string, priority_queue<string, vector<string>, std::greater<string>>> vec;
+    hierholzer(int n) : n(n), ch(n + 1), qu(n + 1) {}
 
-    vector<string> stk;
-
-    void dfs(const string& curr) {
-        while (vec.count(curr) && vec[curr].size() > 0) {
-            string tmp = vec[curr].top();
-            vec[curr].pop();
-            dfs(move(tmp));
-        }
-        stk.emplace_back(curr);
+    void add_edge(int u, int v) {
+        int left = edges.size(), right = left + 1;
+        edges.emplace_back(u, v, right, false);
+        edges.emplace_back(v, u, left, false);
+        ch[u].emplace_back(left);
+        ch[v].emplace_back(right);
+        qu.merge(u, v);
     }
 
-    vector<string> findItinerary(vector<vector<string>>& tickets) {
-        for (auto& it : tickets) {
-            vec[it[0]].emplace(it[1]);
+    optional<vector<int>> solve() {
+        if (qu.query_size(1) != n) {
+            return nullopt;
         }
-        dfs("JFK");
 
-        reverse(stk.begin(), stk.end());
-        return stk;
+        int odd = 0;
+        int last_odd;
+        for (int i = 1; i <= n; ++i) {
+            if (ch[i].size() % 2) {
+                odd += 1;
+                last_odd = i;
+            }
+        }
+
+        int start;
+        if (odd == 0) {
+            start = 1;
+        } else if (odd == 2) {
+            start = last_odd;
+        } else {
+            return nullopt;
+        }
+
+        vector<int> res;
+
+        auto dfs = [&] (auto&& dfs, int v) -> void {
+            while (ch[v].size()) {
+                int i = ch[v].back();
+                ch[v].pop_back();
+                if (not edges[i].stale) {
+                    edges[i].stale = true;
+                    edges[edges[i].rev].stale = true;
+                    dfs(dfs, edges[i].to);
+                }
+            }
+            res.emplace_back(v);
+        };
+        dfs(dfs, start);
+
+        return res;
     }
 };