From 21b8c089e249c2bba3327e323b13d8229f012455 Mon Sep 17 00:00:00 2001
From: yenru0 <yenru0604@gmail.com>
Date: Tue, 25 Mar 2025 10:42:37 +0900
Subject: [PATCH] complete 33650.py

---
 zeta_python/completed/33650.py | 64 ++++++++++++++++++++++++++++++++++
 1 file changed, 64 insertions(+)
 create mode 100644 zeta_python/completed/33650.py

diff --git a/zeta_python/completed/33650.py b/zeta_python/completed/33650.py
new file mode 100644
index 0000000..fd9bb97
--- /dev/null
+++ b/zeta_python/completed/33650.py
@@ -0,0 +1,64 @@
+import sys
+
+input = sys.stdin.readline
+
+
+class TriangleTrees:
+    def __init__(self, n, m, e):
+        """
+        input graph should be triangle-trees
+        """
+        self.n, self.m = n, m
+        self.e: list[int] = e
+        self.e_find: list[list[int]] = [[] for _ in range(self.n)]
+        for u, v in self.e:
+            self.e_find[u - 1].append(v - 1)
+            self.e_find[v - 1].append(u - 1)
+
+    def check_cycle(self) -> bool:
+        D = [(-1, i) for i in range(self.n)]
+        vis = [0] * self.n
+        cycle_flag = False
+        while D:
+            before, now = D.pop()
+            if vis[now]:
+                continue
+            vis[now] = 1
+            for nxt in self.e_find[now]:
+                if nxt == before:
+                    continue
+                elif vis[nxt]:
+                    cycle_flag = True
+                    break
+                else:
+                    D.append((now, nxt))
+            if cycle_flag:
+                break
+        return cycle_flag
+
+    def solve(self) -> list[int]:
+        K_MAX = 3 if self.check_cycle() else 2
+        vis = [0] * self.n
+        colour = [-1] * self.n
+
+        D = [(i, i) for i in range(self.n)]
+        while D:
+            (before, now) = D.pop()
+            if vis[now]:
+                continue
+            else:
+                vis[now] = 1
+
+            now_color = (colour[before] + 1) % K_MAX
+            colour[now] = now_color
+
+            for nxt in self.e_find[now]:
+                if not vis[nxt]:
+                    D.append((now, nxt))
+        return colour
+
+
+if __name__ == "__main__":
+    n, m = map(int, input().split())
+    e = [tuple(map(int, input().split())) for _ in range(m)]
+    print(*map(lambda x: x + 1, TriangleTrees(n, m, e).solve()), sep=" ")