Sponsored
Sponsored
This approach utilizes the Union-Find (or Disjoint Set Union, DSU) data structure to detect cycles. The key operations in Union-Find are 'find', which determines the representative of a set, and 'union', which merges two sets. When processing each edge, we attempt to unite the vertices. If both vertices are already in the same set, a cycle is detected, and this edge is the redundant one.
Time Complexity: O(n) where n is the number of edges because we process each edge once.
Space Complexity: O(n) due to the storage of the parent and rank arrays.
The JavaScript solution mirrors the Union-Find method with adjustments for syntax in JavaScript. The findRedundantConnection function iterates over each edge and utilizes union to potentially find the redundant edge creating a cycle.
The DFS approach involves simulating the construction of the graph and utilizing DFS to detect cycles whenever a new edge is being added. If a cycle is detected upon adjacent traversal, that edge is the redundant one.
Time Complexity: O(n^2), potentially examining each pair of nodes connected by added edges in the worst case.
Space Complexity: O(n), dictated by recursive stack depth in the DFS and the graph representation.
1def dfs(graph, source, target, visited):
2 if source == target:
3 return True
4 visited.add(source)
5 for neighbor in graph[source]:
6 if neighbor not in visited:
7 if dfs(graph, neighbor, target, visited):
8 return True
9 return False
10
11class Solution:
12 def findRedundantConnection(self, edges):
13 graph = collections.defaultdict(set)
14 for u, v in edges:
15 visited = set()
16 if u in graph and v in graph and dfs(graph, u, v, visited):
17 return [u, v]
18 graph[u].add(v)
19 graph[v].add(u)This solution constructs the graph incrementally while running DFS to check for paths from vertex u to vertex v before adding each edge. If the path exists, addition of the edge creates a cycle, thereby identifying it as redundant.