Added Kosaraju's algorithm for SCC (#233)

Author: czgdp1807

pydatastructs/graphs/__init__.py

@@ -11,7 +11,8 @@
     breadth_first_search,
     breadth_first_search_parallel,
     minimum_spanning_tree,
-    minimum_spanning_tree_parallel
+    minimum_spanning_tree_parallel,
+    strongly_connected_components
 )
 
 __all__.extend(algorithms.__all__)

pydatastructs/graphs/algorithms.py

@@ -15,7 +15,8 @@
     'breadth_first_search',
     'breadth_first_search_parallel',
     'minimum_spanning_tree',
-    'minimum_spanning_tree_parallel'
+    'minimum_spanning_tree_parallel',
+    'strongly_connected_components'
 ]
 
 def breadth_first_search(
@@ -445,3 +446,105 @@ def minimum_spanning_tree_parallel(graph, algorithm, num_threads):
         "isn't implemented for finding minimum spanning trees."
         %(algorithm, graph._impl))
     return getattr(algorithms, func)(graph, num_threads)
+
+def _visit(graph, vertex, visited, incoming, L):
+    stack = [vertex]
+    while stack:
+        top = stack[-1]
+        if not visited.get(top, False):
+            visited[top] = True
+            for node in graph.neighbors(top):
+                if incoming.get(node.name, None) is None:
+                    incoming[node.name] = []
+                incoming[node.name].append(top)
+                if not visited.get(node.name, False):
+                    stack.append(node.name)
+        if top is stack[-1]:
+            L.append(stack.pop())
+
+def _assign(graph, u, incoming, assigned, component):
+    stack = [u]
+    while stack:
+        top = stack[-1]
+        if not assigned.get(top, False):
+            assigned[top] = True
+            component.add(top)
+            for u in incoming[top]:
+                if not assigned.get(u, False):
+                    stack.append(u)
+        if top is stack[-1]:
+            stack.pop()
+
+def _strongly_connected_components_kosaraju_adjacency_list(graph):
+    visited, incoming, L = dict(), dict(), []
+    for u in graph.vertices:
+        if not visited.get(u, False):
+            _visit(graph, u, visited, incoming, L)
+
+    assigned = dict()
+    components = []
+    for i in range(-1, -len(L) - 1, -1):
+        comp = set()
+        if not assigned.get(L[i], False):
+            _assign(graph, L[i], incoming, assigned, comp)
+        if comp:
+            components.append(comp)
+
+    return components
+
+_strongly_connected_components_kosaraju_adjacency_matrix = \
+    _strongly_connected_components_kosaraju_adjacency_list
+
+def strongly_connected_components(graph, algorithm):
+    """
+    Computes strongly connected components for the given
+    graph and algorithm.
+
+    Parameters
+    ==========
+
+    graph: Graph
+        The graph whose minimum spanning tree
+        has to be computed.
+    algorithm: str
+        The algorithm which should be used for
+        computing strongly connected components.
+        Currently the following algorithms are
+        supported,
+        'kosaraju' -> Kosaraju's algorithm as given in
+                     [1].
+
+    Returns
+    =======
+
+    components: list
+        Python list with each element as set of vertices.
+
+    Examples
+    ========
+
+    >>> from pydatastructs import Graph, AdjacencyListGraphNode
+    >>> from pydatastructs import strongly_connected_components
+    >>> v1, v2, v3 = [AdjacencyListGraphNode(i) for i in range(3)]
+    >>> g = Graph(v1, v2, v3)
+    >>> g.add_edge(v1.name, v2.name)
+    >>> g.add_edge(v2.name, v3.name)
+    >>> g.add_edge(v3.name, v1.name)
+    >>> scc = strongly_connected_components(g, 'kosaraju')
+    >>> scc == [{'2', '0', '1'}]
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm
+
+    """
+    import pydatastructs.graphs.algorithms as algorithms
+    func = "_strongly_connected_components_" + algorithm + "_" + graph._impl
+    if not hasattr(algorithms, func):
+        raise NotImplementedError(
+        "Currently %s algoithm for %s implementation of graphs "
+        "isn't implemented for finding strongly connected components."
+        %(algorithm, graph._impl))
+    return getattr(algorithms, func)(graph)

pydatastructs/graphs/tests/test_algorithms.py

@@ -1,6 +1,6 @@
 from pydatastructs import (breadth_first_search, Graph,
 breadth_first_search_parallel, minimum_spanning_tree,
-minimum_spanning_tree_parallel)
+minimum_spanning_tree_parallel, strongly_connected_components)
 
 
 def test_breadth_first_search():
@@ -155,3 +155,33 @@ def _test_minimum_spanning_tree(func, ds, algorithm, *args):
     _test_minimum_spanning_tree(fmstp, "List", "kruskal", 3)
     _test_minimum_spanning_tree(fmstp, "Matrix", "kruskal", 3)
     _test_minimum_spanning_tree(fmstp, "List", "prim", 3)
+
+def test_strongly_connected_components():
+
+    def _test_strongly_connected_components(func, ds, algorithm, *args):
+        import pydatastructs.utils.misc_util as utils
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+        a, b, c, d, e, f, g, h = \
+        [GraphNode(chr(x)) for x in range(ord('a'), ord('h') + 1)]
+        graph = Graph(a, b, c, d, e, f, g, h)
+        graph.add_edge(a.name, b.name)
+        graph.add_edge(b.name, c.name)
+        graph.add_edge(b.name, f.name)
+        graph.add_edge(b.name, e.name)
+        graph.add_edge(c.name, d.name)
+        graph.add_edge(c.name, g.name)
+        graph.add_edge(d.name, h.name)
+        graph.add_edge(d.name, c.name)
+        graph.add_edge(e.name, f.name)
+        graph.add_edge(e.name, a.name)
+        graph.add_edge(f.name, g.name)
+        graph.add_edge(g.name, f.name)
+        graph.add_edge(h.name, d.name)
+        graph.add_edge(h.name, g.name)
+        comps = func(graph, algorithm)
+        expected_comps = [{'e', 'a', 'b'}, {'d', 'c', 'h'}, {'g', 'f'}]
+        assert comps == expected_comps
+
+    scc = strongly_connected_components
+    _test_strongly_connected_components(scc, "List", "kosaraju")
+    _test_strongly_connected_components(scc, "Matrix", "kosaraju")