Implemented Bellman-Ford algorithm (#283)

Author: czgdp1807

pydatastructs/graphs/__init__.py

@@ -13,7 +13,8 @@
     minimum_spanning_tree,
     minimum_spanning_tree_parallel,
     strongly_connected_components,
-    depth_first_search
+    depth_first_search,
+    shortest_paths
 )
 
 __all__.extend(algorithms.__all__)

pydatastructs/graphs/algorithms.py

@@ -17,7 +17,8 @@
     'minimum_spanning_tree',
     'minimum_spanning_tree_parallel',
     'strongly_connected_components',
-    'depth_first_search'
+    'depth_first_search',
+    'shortest_paths'
 ]
 
 Stack = Queue = deque
@@ -637,3 +638,90 @@ def _depth_first_search_adjacency_list(
                 return None
 
 _depth_first_search_adjacency_matrix = _depth_first_search_adjacency_list
+
+def shortest_paths(graph: Graph, algorithm: str,
+                   source: str, target: str="") -> tuple:
+    """
+    Finds shortest paths in the given graph from a given source.
+
+    Parameters
+    ==========
+
+    graph: Graph
+        The graph under consideration.
+    algorithm: str
+        The algorithm to be used. Currently, the following algorithms
+        are implemented,
+        'bellman_ford' -> Bellman-Ford algorithm as given in [1].
+    source: str
+        The name of the source the node.
+    target: str
+        The name of the target node.
+        Optional, by default, all pair shortest paths
+        are returned.
+
+    Returns
+    =======
+
+    (distances, predecessors): (dict, dict)
+        If target is not provided and algorithm used
+        is 'bellman_ford'.
+    (distances[target], predecessors): (float, dict)
+        If target is provided and algorithm used is
+        'bellman_ford'.
+
+    Examples
+    ========
+
+    >>> from pydatastructs import Graph, AdjacencyListGraphNode
+    >>> from pydatastructs import 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)
+    >>> shortest_paths(G, 'bellman_ford', 'V1')
+    ({'V1': 0, 'V2': 11, 'V3': 21}, {'V1': None, 'V2': 'V1', 'V3': 'V2'})
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_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, source, target)
+
+def _bellman_ford_adjacency_list(graph: Graph, source: str, target: str) -> tuple:
+    distances, predecessor = dict(), dict()
+
+    for v in graph.vertices:
+        distances[v] = float('inf')
+        predecessor[v] = None
+    distances[source] = 0
+
+    edges = graph.edge_weights.values()
+    for _ in range(len(graph.vertices) - 1):
+        for edge in edges:
+            u, v = edge.source.name, edge.target.name
+            w = edge.value
+            if distances[u] + edge.value < distances[v]:
+                distances[v] = distances[u] + w
+                predecessor[v] = u
+
+    for edge in edges:
+        u, v = edge.source.name, edge.target.name
+        w = edge.value
+        if distances[u] + w < distances[v]:
+            raise ValueError("Graph contains a negative weight cycle.")
+
+    if target != "":
+        return (distances[target], predecessor)
+    return (distances, predecessor)
+
+_bellman_ford_adjacency_matrix = _bellman_ford_adjacency_list

pydatastructs/graphs/tests/test_algorithms.py

@@ -1,8 +1,8 @@
 from pydatastructs import (breadth_first_search, Graph,
 breadth_first_search_parallel, minimum_spanning_tree,
 minimum_spanning_tree_parallel, strongly_connected_components,
-depth_first_search)
-
+depth_first_search, shortest_paths)
+from pydatastructs.utils.raises_util import raises
 
 def test_breadth_first_search():
 
@@ -258,3 +258,34 @@ def path_finder(curr_node, next_node, dest_node, parent, path):
 
     _test_depth_first_search("List")
     _test_depth_first_search("Matrix")
+
+def test_shortest_paths():
+
+    def _test_shortest_paths(ds, algorithm):
+        import pydatastructs.utils.misc_util as utils
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+        vertices = [GraphNode('S'), GraphNode('C'),
+                    GraphNode('SLC'), GraphNode('SF'),
+                    GraphNode('D')]
+
+        graph = Graph(*vertices)
+        graph.add_edge('S', 'SLC', 2)
+        graph.add_edge('C', 'S', 4)
+        graph.add_edge('C', 'D', 2)
+        graph.add_edge('SLC', 'C', 2)
+        graph.add_edge('SLC', 'D', 3)
+        graph.add_edge('SF', 'SLC', 2)
+        graph.add_edge('SF', 'S', 2)
+        graph.add_edge('D', 'SF', 3)
+        dist, pred = shortest_paths(graph, algorithm, 'SLC')
+        assert dist == {'S': 6, 'C': 2, 'SLC': 0, 'SF': 6, 'D': 3}
+        assert pred == {'S': 'C', 'C': 'SLC', 'SLC': None, 'SF': 'D', 'D': 'SLC'}
+        dist, pred = shortest_paths(graph, algorithm, 'SLC', 'SF')
+        assert dist == 6
+        assert pred == {'S': 'C', 'C': 'SLC', 'SLC': None, 'SF': 'D', 'D': 'SLC'}
+        graph.remove_edge('SLC', 'D')
+        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')