feat: new graph problem formatted.

rede-anel-estelar/src/alternative-ac.py

@@ -0,0 +1,60 @@
+from collections import deque
+
+
+def check_connectivity(adj, n):
+    vis = [False for _ in range(n)]
+    def dfs(x):
+        vis[x] = True
+        for v in adj[x]:
+            if not vis[v]:
+                dfs(v)
+    dfs(0)
+    return all(vis)
+
+
+def check_cthulhu(adj, degree, n):
+    marked = [False for _ in range(n)]
+    dq = deque([])
+    for i, d in enumerate(degree):
+        if d == 1:
+            dq.append(i)
+            marked[i] = True
+
+    while len(dq) != 0:
+        i = dq.popleft()
+        for v in adj[i]:
+            if not marked[v]:
+                degree[v] -= 1
+                if degree[v] == 1:
+                    dq.append(v)
+                    marked[v] = True
+
+    # if all are marked it means that there was no cycle
+    if all(marked):
+        return False
+
+    # if some of the non-marked vertices does not have degree 2, it is not a simple cycle    
+    for v in range(n):
+        if not marked[v] and degree[v] != 2:
+            return False
+
+    return True
+
+
+n, m = map(int, input().split())
+adj = [[] for _ in range(n)]
+degree = [0] * n
+
+for i in range(m):
+    u, v = map(int, input().split())
+    u -= 1
+    v -= 1
+    adj[u].append(v)
+    adj[v].append(u)
+    degree[u] += 1
+    degree[v] += 1
+
+if not check_connectivity(adj, n) or not check_cthulhu(adj, degree, n):
+    print("OFFLINE")
+else:
+    print("ONLINE")