Added Floyd Warshall algorithm (#302)

Author: Kiran-Venkatesh

pydatastructs/graphs/__init__.py

@@ -15,6 +15,7 @@
     strongly_connected_components,
     depth_first_search,
     shortest_paths,
+    all_pair_shortest_paths,
     topological_sort,
     topological_sort_parallel
 )

pydatastructs/graphs/algorithms.py

@@ -20,6 +20,7 @@
     'strongly_connected_components',
     'depth_first_search',
     'shortest_paths',
+    'all_pair_shortest_paths',
     'topological_sort',
     'topological_sort_parallel'
 ]
@@ -672,7 +673,7 @@ def shortest_paths(graph: Graph, algorithm: str,
         is 'bellman_ford'/'dijkstra'.
     (distances[target], predecessors): (float, dict)
         If target is provided and algorithm used is
-        'bellman_ford'.
+        'bellman_ford'/'dijkstra'.
 
     Examples
     ========
@@ -762,6 +763,86 @@ def _dijkstra_adjacency_list(graph: Graph, start: str, target: str):
 
 _dijkstra_adjacency_matrix = _dijkstra_adjacency_list
 
+def all_pair_shortest_paths(graph: Graph, algorithm: str) -> tuple:
+    """
+    Finds shortest paths between all pairs of vertices in the given graph.
+
+    Parameters
+    ==========
+
+    graph: Graph
+        The graph under consideration.
+    algorithm: str
+        The algorithm to be used. Currently, the following algorithms
+        are implemented,
+        'floyd_warshall' -> Floyd Warshall algorithm as given in [1].
+
+    Returns
+    =======
+
+    (distances, predecessors): (dict, dict)
+
+    Examples
+    ========
+
+    >>> from pydatastructs import Graph, AdjacencyListGraphNode
+    >>> from pydatastructs import all_pair_shortest_paths
+    >>> V1 = AdjacencyListGraphNode("V1")
+    >>> V2 = AdjacencyListGraphNode("V2")
+    >>> V3 = AdjacencyListGraphNode("V3")
+    >>> G = Graph(V1, V2, V3)
+    >>> G.add_edge('V2', 'V3', 10)
+    >>> G.add_edge('V1', 'V2', 11)
+    >>> G.add_edge('V3', 'V1', 5)
+    >>> dist, _ = all_pair_shortest_paths(G, 'floyd_warshall')
+    >>> dist['V1']['V3']
+    21
+    >>> dist['V3']['V1']
+    5
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm
+    """
+    import pydatastructs.graphs.algorithms as algorithms
+    func = "_" + algorithm + "_" + graph._impl
+    if not hasattr(algorithms, func):
+        raise NotImplementedError(
+        "Currently %s algorithm isn't implemented for "
+        "finding shortest paths in graphs."%(algorithm))
+    return getattr(algorithms, func)(graph)
+
+def _floyd_warshall_adjacency_list(graph: Graph):
+    dist, next_vertex = dict(), dict()
+    V, E = graph.vertices, graph.edge_weights
+
+    for v in V:
+        dist[v] = dict()
+        next_vertex[v] = dict()
+
+    for name, edge in E.items():
+        dist[edge.source.name][edge.target.name] = edge.value
+        next_vertex[edge.source.name][edge.target.name] = edge.source.name
+
+    for v in V:
+        dist[v][v] = 0
+        next_vertex[v][v] = v
+
+    for k in V:
+        for i in V:
+            for j in V:
+                dist_i_j = dist.get(i, dict()).get(j, float('inf'))
+                dist_i_k = dist.get(i, dict()).get(k, float('inf'))
+                dist_k_j = dist.get(k, dict()).get(j, float('inf'))
+                next_i_k = next_vertex.get(i + '_' + k, None)
+                if dist_i_j > dist_i_k + dist_k_j:
+                    dist[i][j] = dist_i_k + dist_k_j
+                    next_vertex[i][j] = next_i_k
+
+    return (dist, next_vertex)
+
+_floyd_warshall_adjacency_matrix = _floyd_warshall_adjacency_list
 
 def topological_sort(graph: Graph, algorithm: str) -> list:
     """

pydatastructs/graphs/tests/test_algorithms.py

@@ -262,7 +262,7 @@ def path_finder(curr_node, next_node, dest_node, parent, path):
 
 def test_shortest_paths():
 
-    def _test_shortest_paths(ds, algorithm):
+    def _test_shortest_paths_positive_edges(ds, algorithm):
         import pydatastructs.utils.misc_util as utils
         GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
         vertices = [GraphNode('S'), GraphNode('C'),
@@ -288,10 +288,57 @@ def _test_shortest_paths(ds, algorithm):
         graph.add_edge('D', 'SLC', -10)
         assert raises(ValueError, lambda: shortest_paths(graph, 'bellman_ford', 'SLC'))
 
-    _test_shortest_paths("List", 'bellman_ford')
-    _test_shortest_paths("Matrix", 'bellman_ford')
-    _test_shortest_paths("List", 'dijkstra')
-    _test_shortest_paths("Matrix", 'dijkstra')
+    def _test_shortest_paths_negative_edges(ds, algorithm):
+        import pydatastructs.utils.misc_util as utils
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+        vertices = [GraphNode('s'), GraphNode('a'),
+                    GraphNode('b'), GraphNode('c'),
+                    GraphNode('d')]
+
+        graph = Graph(*vertices)
+        graph.add_edge('s', 'a', 3)
+        graph.add_edge('s', 'b', 2)
+        graph.add_edge('a', 'c', 1)
+        graph.add_edge('b', 'd', 1)
+        graph.add_edge('b', 'a', -2)
+        graph.add_edge('c', 'd', 1)
+        dist, pred = shortest_paths(graph, algorithm, 's')
+        assert dist == {'s': 0, 'a': 0, 'b': 2, 'c': 1, 'd': 2}
+        assert pred == {'s': None, 'a': 'b', 'b': 's', 'c': 'a', 'd': 'c'}
+        dist, pred = shortest_paths(graph, algorithm, 's', 'd')
+        assert dist == 2
+        assert pred == {'s': None, 'a': 'b', 'b': 's', 'c': 'a', 'd': 'c'}
+
+    _test_shortest_paths_positive_edges("List", 'bellman_ford')
+    _test_shortest_paths_positive_edges("Matrix", 'bellman_ford')
+    _test_shortest_paths_negative_edges("List", 'bellman_ford')
+    _test_shortest_paths_negative_edges("Matrix", 'bellman_ford')
+    _test_shortest_paths_positive_edges("List", 'dijkstra')
+    _test_shortest_paths_positive_edges("Matrix", 'dijkstra')
+
+def test_all_pair_shortest_paths():
+
+    def _test_shortest_paths_negative_edges(ds, algorithm):
+        import pydatastructs.utils.misc_util as utils
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+        vertices = [GraphNode('1'), GraphNode('2'),
+                    GraphNode('3'), GraphNode('4')]
+
+        graph = Graph(*vertices)
+        graph.add_edge('1', '3', -2)
+        graph.add_edge('2', '1', 4)
+        graph.add_edge('2', '3', 3)
+        graph.add_edge('3', '4', 2)
+        graph.add_edge('4', '2', -1)
+        dist, next_v = shortest_paths(graph, algorithm, 's')
+        assert dist == {'1': {'3': -2, '1': 0, '4': 0, '2': -1},
+                        '2': {'1': 4, '3': 2, '2': 0, '4': 4},
+                        '3': {'4': 2, '3': 0, '1': 5, '2': 1},
+                        '4': {'2': -1, '4': 0, '1': 3, '3': 1}}
+        assert next_v == {'1': {'3': '1', '1': '1', '4': None, '2': None},
+                          '2': {'1': '2', '3': None, '2': '2', '4': None},
+                          '3': {'4': '3', '3': '3', '1': None, '2': None},
+                          '4': {'2': '4', '4': '4', '1': None, '3': None}}
 
 def test_topological_sort():