added graphs

generics/graphen/graphs.py

@@ -0,0 +1,60 @@
+type Graph[T] = dict[T, list[T]]
+
+
+def is_bidirected[T](graph: Graph[T]) -> bool:
+    for a, vertecies in graph.items():
+        for b in vertecies:
+            if a not in graph[b]:
+                return False
+    return True
+
+
+def depth_first_search[T](graph: Graph[T], node: T,
+                          _visited: set[T] = None) -> set[T]:
+    if _visited is None:
+        _visited = set()
+    if node in _visited:
+        return set()
+    _visited.add(node)
+    for neighbours in graph[node]:
+        depth_first_search(graph, neighbours, _visited)
+    return _visited
+
+
+def all_edges[T](graph: Graph[T]) -> set[tuple[T, T]]:
+    all_vertecies = set()
+    for a, vertecies in graph.items():
+        for b in vertecies:
+            all_vertecies.add((a, b))
+    return all_vertecies
+
+
+def alt_all_edges[T](graph: Graph[T]) -> set[tuple[T, T]]:
+    return {(a, b)
+            for a, vertecies in graph.items()
+            for b in vertecies}
+
+
+if __name__ == '__main__':
+    my_graph: Graph[str] = {
+        'A': ['B', 'D'],
+        'B': ['A', 'C'],
+        'C': ['B', 'D'],
+        'D': ['C', 'A'],
+    }
+    assert all_edges(my_graph) == {('A', 'B'), ('A', 'D'), ('B', 'A'),
+                                   ('B', 'C'), ('C', 'B'), ('C', 'D'),
+                                   ('D', 'C'), ('D', 'A')}
+    assert all_edges(my_graph) == alt_all_edges(my_graph)
+    assert is_bidirected(my_graph)
+    assert not is_bidirected({'A': ['B', 'C'], 'B': [
+        'C'], 'C': ['A', 'B']})
+    my_graph = {
+        0: [1, 2, 3],
+        1: [0],
+        2: [3, 4, 0],
+        3: [0, 2],
+        4: [2],
+        5: [],
+    }
+    print(depth_first_search(my_graph, 5))