added Critical Routers

Author: minhyeong-joe

Graph/CriticalRouters/README.md

@@ -0,0 +1,26 @@
+# Critical Routers
+
+[Leetcode Link](https://leetcode.com/discuss/interview-question/436073/)
+
+## Problem:
+
+You are given an undirected **connected** graph. An articulation point (or cut vertex) is defined as a vertex which, when removed along with associated edges, makes the graph disconnected (or more precisely, increases the number of connected components in the graph). The task is to find all articulation points in the given graph.
+
+**Input:**
+The input to the function/method consists of three arguments:
+
+- `numNodes`, an integer representing the number of nodes in the graph.
+- `numEdges`, an integer representing the number of edges in the graph.
+- `edges`, the list of pair of integers - A, B representing an edge between the nodes A and B.
+
+**Output:**
+Return a list of integers representing the critical nodes.
+
+## Example:
+
+```
+Input: numNodes = 7, numEdges = 7, edges = [[0, 1], [0, 2], [1, 3], [2, 3], [2, 5], [5, 6], [3, 4]]
+Output: [2, 3, 5]
+```
+
+![example](./example.png)

Graph/CriticalRouters/example.png

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+from collections import defaultdict
+
+
+def criticalRouters(numNodes, numEdges, edges):
+    criticalVertices = list()
+    adjList = defaultdict(list)
+    # convert edges array form into adjacency list
+    for edge in edges:
+        adjList[edge[0]].append(edge[1])
+        adjList[edge[1]].append(edge[0])
+    # print(adjList)
+    for source, destinations in adjList.items():
+        if len(destinations) <= 1:
+            continue
+        firstDest = destinations[0]
+        for dest in destinations[1:]:
+            if not reachable(adjList, firstDest, dest, source):
+                criticalVertices.append(source)
+                break
+
+    return criticalVertices
+
+# use BFS to see if 'src' can reach 'dest' without going through 'blockedVertex'
+# if false, that means 'blockedVertex' is a critical vertex
+
+
+def reachable(adjList, src, dest, blockedVertex):
+    queue = list()
+    visited = set()
+    visited.add(blockedVertex)
+    queue.append(src)
+    while queue:
+        current = queue.pop(0)
+        if current == dest:
+            return True
+        visited.add(current)
+        for neighbor in adjList[current]:
+            if neighbor not in visited:
+                queue.append(neighbor)
+    return False
+
+
+numNodes = 7
+numEdges = 7
+edges = [[0, 1], [0, 2], [1, 3], [2, 3], [2, 5], [5, 6], [3, 4]]
+print(criticalRouters(numNodes, numEdges, edges))

Graph/CriticalRouters/solution.py

@@ -78,6 +78,7 @@ Languages used: Java and Python
 
 - [All Paths From Src To Target](Graph/AllPathsFromSrcToTarget)
 - [Course Schedule II](Graph/CourseSchedule2)
+- [Critical Routers](Graph/CriticalRouters)
 - [Escape Large Maze](Graph/EscapeLargeMaze)
 - [Minimum Cost to Repair Edges](Graph/MinCostToRepairEdges)
 - [Number to Make Network Connected](Graph/NumToMakeNetworkConnected)