Strongly connected components (#2114)

* Implement strongly connected components for graph algorithms

* fixup! Format Python code with psf/black push

* Delete trailing whitespace

* updating DIRECTORY.md

* Add doctests and typehints

* Remove unnecessary comments, change variable names

* fixup! Format Python code with psf/black push

* Change undefined variable's name

* Apply suggestions from code review

Co-authored-by: Christian Clauss <cclauss@me.com>

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

DIRECTORY.md

@@ -261,6 +261,7 @@
   * [Page Rank](https://github.com/TheAlgorithms/Python/blob/master/graphs/page_rank.py)
   * [Prim](https://github.com/TheAlgorithms/Python/blob/master/graphs/prim.py)
   * [Scc Kosaraju](https://github.com/TheAlgorithms/Python/blob/master/graphs/scc_kosaraju.py)
+  * [Strongly Connected Components](https://github.com/TheAlgorithms/Python/blob/master/graphs/strongly_connected_components.py)
   * [Tarjans Scc](https://github.com/TheAlgorithms/Python/blob/master/graphs/tarjans_scc.py)
 
 ## Greedy Method

graphs/strongly_connected_components.py

@@ -0,0 +1,105 @@
+"""
+https://en.wikipedia.org/wiki/Strongly_connected_component
+
+Finding strongly connected components in directed graph
+
+"""
+
+test_graph_1 = {
+    0: [2, 3],
+    1: [0],
+    2: [1],
+    3: [4],
+    4: [],
+}
+
+test_graph_2 = {
+    0: [1, 2, 3],
+    1: [2],
+    2: [0],
+    3: [4],
+    4: [5],
+    5: [3],
+}
+
+
+def topology_sort(graph: dict, vert: int, visited: list) -> list:
+    """
+    Use depth first search to sort graph
+    At this time graph is the same as input
+    >>> topology_sort(test_graph_1, 0, 5 * [False])
+    [1, 2, 4, 3, 0]
+    >>> topology_sort(test_graph_2, 0, 6 * [False])
+    [2, 1, 5, 4, 3, 0]
+    """
+
+    visited[vert] = True
+    order = []
+
+    for neighbour in graph[vert]:
+        if not visited[neighbour]:
+            order += topology_sort(graph, neighbour, visited)
+
+    order.append(vert)
+
+    return order
+
+
+def find_components(reversed_graph: dict, vert: int, visited: list) -> list:
+    """
+    Use depth first search to find strongliy connected
+    vertices. Now graph is reversed
+    >>> find_components({0: [1], 1: [2], 2: [0]}, 0, 5 * [False])
+    [0, 1, 2]
+    >>> find_components({0: [2], 1: [0], 2: [0, 1]}, 0, 6 * [False])
+    [0, 2, 1]
+    """
+
+    visited[vert] = True
+    component = [vert]
+
+    for neighbour in reversed_graph[vert]:
+        if not visited[neighbour]:
+            component += find_components(reversed_graph, neighbour, visited)
+
+    return component
+
+
+def strongly_connected_components(graph: dict) -> list:
+    """
+    This function takes graph as a parameter
+    and then returns the list of strongly connected components
+    >>> strongly_connected_components(test_graph_1)
+    [[0, 1, 2], [3], [4]]
+    >>> strongly_connected_components(test_graph_2)
+    [[0, 2, 1], [3, 5, 4]]
+    """
+
+    visited = len(graph) * [False]
+    reversed_graph = {vert: [] for vert in range(len(graph))}
+
+    for vert, neighbours in graph.items():
+        for neighbour in neighbours:
+            reversed_graph[neighbour].append(vert)
+
+    order = []
+    for i, was_visited in enumerate(visited):
+        if not was_visited:
+            order += topology_sort(graph, i, visited)
+
+    components_list = []
+    visited = len(graph) * [False]
+
+    for i in range(len(graph)):
+        vert = order[len(graph) - i - 1]
+        if not visited[vert]:
+            component = find_components(reversed_graph, vert, visited)
+            components_list.append(component)
+
+    return components_list
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()