Add Eulers path problem

Author: TeogopK

Seminars/sem_15/README.md

@@ -98,6 +98,7 @@
 
 ## Задачи за упражнение
 
+- [The Islander](https://www.hackerrank.com/contests/sda-hw-13-2022/challenges/islander/problem)
 - [Permutations](https://leetcode.com/problems/permutations)
 - [All Paths From Source to Target](https://leetcode.com/problems/all-paths-from-source-to-target)
 - [Reconstruct Itinerary](https://leetcode.com/problems/reconstruct-itinerary)

Tasks/tasks_15/README.md

@@ -1,5 +1,6 @@
 ## Условия:
 
+- [The Islander](https://www.hackerrank.com/contests/sda-hw-13-2022/challenges/islander/problem)
 - [Permutations](https://leetcode.com/problems/permutations)
 - [All Paths From Source to Target](https://leetcode.com/problems/all-paths-from-source-to-target)
 - [Reconstruct Itinerary](https://leetcode.com/problems/reconstruct-itinerary)

Tasks/tasks_15/the_islander/solution_euler_dfs.py

@@ -0,0 +1,52 @@
+def dfs(current, visited, graph):
+    for neighbor in graph[current]:
+        if neighbor not in visited:
+            visited.add(neighbor) 
+            dfs(neighbor, visited, graph)
+            
+            
+def is_connected(V, graph):
+    start_vertex = 1
+    visited = set([start_vertex])
+    
+    dfs(start_vertex, visited, graph)
+    
+    return len(visited) >= V
+
+
+def check_euler(V, graph):
+    degrees = [0] * (V + 1)
+    
+    for v in graph:
+        degrees[v] = len(graph[v])
+        
+    count_odd = sum(1 if degree % 2 == 1 else 0 for degree in degrees)
+    
+    if not is_connected(V, graph):
+        return 'none'
+    
+    if count_odd == 0:
+        return 'ecycle'
+    
+    if count_odd == 2:
+        return 'epath'
+    
+    return 'none'
+    
+
+def solve():
+    N, M = map(int, input().split())
+    graph = {v: [] for v in range(N + 1)}
+    
+    for _ in range(M):
+        x, y = map(int, input().split())
+        graph[x].append(y)
+        graph[y].append(x)
+        
+    result = check_euler(N, graph)
+    
+    return result
+
+Q = int(input())
+for _ in range(Q):
+    print(solve())