Added bridge-finding algorithm

docs/source/pydatastructs/graphs/algorithms.rst

@@ -20,3 +20,5 @@ Algorithms
 .. autofunction:: pydatastructs.topological_sort
 
 .. autofunction:: pydatastructs.topological_sort_parallel
+
+.. autofunction:: pydatastructs.find_bridges

pydatastructs/graphs/__init__.py

@@ -21,7 +21,8 @@
     all_pair_shortest_paths,
     topological_sort,
     topological_sort_parallel,
-    max_flow
+    max_flow,
+    find_bridges
 )
 
 __all__.extend(algorithms.__all__)

pydatastructs/graphs/algorithms.py

@@ -23,7 +23,8 @@
     'all_pair_shortest_paths',
     'topological_sort',
     'topological_sort_parallel',
-    'max_flow'
+    'max_flow',
+    'find_bridges'
 ]
 
 Stack = Queue = deque
@@ -1216,3 +1217,106 @@ def max_flow(graph, source, sink, algorithm='edmonds_karp', **kwargs):
         f"Currently {algorithm} algorithm isn't implemented for "
         "performing max flow on graphs.")
     return getattr(algorithms, func)(graph, source, sink)
+
+
+def find_bridges(graph):
+    """
+    Finds all bridges in an undirected graph using Tarjan's Algorithm.
+
+    Parameters
+    ==========
+    graph : Graph
+        An undirected graph instance.
+
+    Returns
+    ==========
+    List[tuple]
+        A list of bridges, where each bridge is represented as a tuple (u, v)
+        with u <= v.
+
+    Example
+    ========
+    >>> from pydatastructs import Graph, AdjacencyListGraphNode, find_bridges
+    >>> v0 = AdjacencyListGraphNode(0)
+    >>> v1 = AdjacencyListGraphNode(1)
+    >>> v2 = AdjacencyListGraphNode(2)
+    >>> v3 = AdjacencyListGraphNode(3)
+    >>> v4 = AdjacencyListGraphNode(4)
+    >>> graph = Graph(v0, v1, v2, v3, v4, implementation='adjacency_list')
+    >>> graph.add_edge(v0.name, v1.name)
+    >>> graph.add_edge(v1.name, v2.name)
+    >>> graph.add_edge(v2.name, v3.name)
+    >>> graph.add_edge(v3.name, v4.name)
+    >>> find_bridges(graph)
+    [('0', '1'), ('1', '2'), ('2', '3'), ('3', '4')]
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Bridge_(graph_theory)
+    """
+
+    vertices = list(graph.vertices)
+    processed_vertices = []
+    for v in vertices:
+        if hasattr(v, "name"):
+            processed_vertices.append(v.name)
+        else:
+            processed_vertices.append(v)
+
+    n = len(processed_vertices)
+    adj = {v: [] for v in processed_vertices}
+    for v in processed_vertices:
+        for neighbor in graph.neighbors(v):
+            if hasattr(neighbor, "name"):
+                nbr = neighbor.name
+            else:
+                nbr = neighbor
+            adj[v].append(nbr)
+
+    mapping = {v: idx for idx, v in enumerate(processed_vertices)}
+    inv_mapping = {idx: v for v, idx in mapping.items()}
+
+    n_adj = [[] for _ in range(n)]
+    for v in processed_vertices:
+        idx_v = mapping[v]
+        for u in adj[v]:
+            idx_u = mapping[u]
+            n_adj[idx_v].append(idx_u)
+
+    visited = [False] * n
+    disc = [0] * n
+    low = [0] * n
+    parent = [-1] * n
+    bridges_idx = []
+    time = 0
+
+    def dfs(u):
+        nonlocal time
+        visited[u] = True
+        disc[u] = low[u] = time
+        time += 1
+        for v in n_adj[u]:
+            if not visited[v]:
+                parent[v] = u
+                dfs(v)
+                low[u] = min(low[u], low[v])
+                if low[v] > disc[u]:
+                    bridges_idx.append((u, v))
+            elif v != parent[u]:
+                low[u] = min(low[u], disc[v])
+
+    for i in range(n):
+        if not visited[i]:
+            dfs(i)
+
+    bridges = []
+    for u, v in bridges_idx:
+        a = inv_mapping[u]
+        b = inv_mapping[v]
+        if a <= b:
+            bridges.append((a, b))
+        else:
+            bridges.append((b, a))
+    bridges.sort()
+    return bridges

pydatastructs/graphs/tests/test_algorithms.py

@@ -2,7 +2,7 @@
 breadth_first_search_parallel, minimum_spanning_tree,
 minimum_spanning_tree_parallel, strongly_connected_components,
 depth_first_search, shortest_paths,all_pair_shortest_paths, topological_sort,
-topological_sort_parallel, max_flow)
+topological_sort_parallel, max_flow, find_bridges)
 from pydatastructs.utils.raises_util import raises
 
 def test_breadth_first_search():
@@ -448,3 +448,57 @@ def _test_max_flow(ds, algorithm):
     _test_max_flow("Matrix", "edmonds_karp")
     _test_max_flow("List", "dinic")
     _test_max_flow("Matrix", "dinic")
+
+
+def test_find_bridges():
+    def _test_find_bridges(ds):
+        import pydatastructs.utils.misc_util as utils
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+
+        impl = 'adjacency_list' if ds == "List" else 'adjacency_matrix'
+
+        v0 = GraphNode(0)
+        v1 = GraphNode(1)
+        v2 = GraphNode(2)
+        v3 = GraphNode(3)
+        v4 = GraphNode(4)
+
+        G1 = Graph(v0, v1, v2, v3, v4, implementation=impl)
+        G1.add_edge(v0.name, v1.name)
+        G1.add_edge(v1.name, v2.name)
+        G1.add_edge(v2.name, v3.name)
+        G1.add_edge(v3.name, v4.name)
+
+        bridges = find_bridges(G1)
+        expected_bridges = [('0', '1'), ('1', '2'), ('2', '3'), ('3', '4')]
+        assert sorted(bridges) == sorted(expected_bridges)
+
+        u0 = GraphNode(0)
+        u1 = GraphNode(1)
+        u2 = GraphNode(2)
+
+        G2 = Graph(u0, u1, u2, implementation=impl)
+        G2.add_edge(u0.name, u1.name)
+        G2.add_edge(u1.name, u2.name)
+        G2.add_edge(u2.name, u0.name)
+
+        bridges = find_bridges(G2)
+        assert bridges == []
+
+        w0 = GraphNode(0)
+        w1 = GraphNode(1)
+        w2 = GraphNode(2)
+        w3 = GraphNode(3)
+        w4 = GraphNode(4)
+
+        G3 = Graph(w0, w1, w2, w3, w4, implementation=impl)
+        G3.add_edge(w0.name, w1.name)
+        G3.add_edge(w1.name, w2.name)
+        G3.add_edge(w3.name, w4.name)
+
+        bridges = find_bridges(G3)
+        expected_bridges = [('0', '1'), ('1', '2'), ('3', '4')]
+        assert sorted(bridges) == sorted(expected_bridges)
+
+    _test_find_bridges("List")
+    _test_find_bridges("Matrix")