Added solution 262

Problems/262.txt

@@ -0,0 +1,3 @@
+PROBLEM 262:
+
+A bridge in a connected (undirected) graph is an edge that, if removed, causes the graph to become disconnected. Find all the bridges in a graph.

Solutions/262.py

@@ -0,0 +1,90 @@
+'''
+Problem:
+
+A bridge in a connected (undirected) graph is an edge that, if removed, causes the
+graph to become disconnected. Find all the bridges in a graph.
+'''
+
+from sys import maxsize
+from typing import Dict, List, Optional, Tuple
+
+# local import from the DataStructure module
+from DataStructures.Graph import GraphUndirectedUnweighted
+
+
+def get_bridges_helper(self, 
+                       node: int,
+                       visited: set,
+                       parent: Dict[int, Optional[int]],
+                       low: Dict[int, int],
+                       disc: Dict[int, int],
+                       bridges: List[Tuple[int, int]]) -> None:
+    # DFS based helper function to find all bridges
+    visited.add(node)
+    disc[node] = self.time 
+    low[node] = self.time 
+    self.time += 1
+    for neighbour in self.connections[node]:
+        if neighbour not in visited:
+            parent[neighbour] = node
+            self.get_bridges_helper(neighbour, visited, parent, low, disc, bridges)
+            # check if the subtree rooted with neighbour has a connection to one of the
+            # ancestors of node
+            low[node] = min(low[node], low[neighbour])
+            # if the lowest vertex reachable from subtree under neighbour is below node
+            # in DFS tree, then node-neighbour is a bridge
+            if low[neighbour] > disc[node]:
+                bridges.append((node, neighbour))
+        elif neighbour != parent[node]:
+            # update low value of node for parent function calls.
+            low[node] = min(low[node], disc[neighbour])
+
+
+def get_bridges(self) -> List[Tuple[int, int]]: 
+    # function to get all the bridges in a graph
+    visited = set()
+    disc = {node: maxsize for node in self.connections}
+    low = {node: maxsize for node in self.connections}
+    parent = {node: None for node in self.connections}
+    bridges = []
+    self.time = 0
+    for node in self.connections:
+        if node not in visited:
+            self.get_bridges_helper(node, visited, parent, low, disc, bridges)
+    return bridges
+
+
+# adding the required methods and attributes to the graph class
+setattr(GraphUndirectedUnweighted, 'get_bridges_helper', get_bridges_helper)
+setattr(GraphUndirectedUnweighted, 'get_bridges', get_bridges)
+setattr(GraphUndirectedUnweighted, 'time', 0)
+
+
+if __name__ == "__main__":
+    g1 = GraphUndirectedUnweighted()
+    g1.add_edge(1, 0) 
+    g1.add_edge(0, 2) 
+    g1.add_edge(2, 1) 
+    g1.add_edge(0, 3) 
+    g1.add_edge(3, 4)
+    print("Bridges in first graph:")
+    print(*g1.get_bridges())
+
+    g2 = GraphUndirectedUnweighted() 
+    g2.add_edge(0, 1) 
+    g2.add_edge(1, 2) 
+    g2.add_edge(2, 3) 
+    print("\nBridges in second graph:")
+    print(*g2.get_bridges())
+
+    g3 = GraphUndirectedUnweighted () 
+    g3.add_edge(0, 1) 
+    g3.add_edge(1, 2) 
+    g3.add_edge(2, 0) 
+    g3.add_edge(1, 3) 
+    g3.add_edge(1, 4) 
+    g3.add_edge(1, 6) 
+    g3.add_edge(3, 5) 
+    g3.add_edge(4, 5) 
+    print("\nBridges in third graph:")
+    print(*g3.get_bridges())