Applications of the Algorithm
Some of the popular use cases of the Union-Find algorithm include:
The Union-Find algorithm proves useful in numerous scenarios:
- Network Connectivity: It can detect if two nodes in a network are connected.
- Cyclicality in Graphs: It can ascertain the presence of cycles in an undirected graph. If, while adding an edge, both vertices belong to the same subset, a cycle exists.
PYTHON
1def isCycle(graph):
2 parent = [-1] * len(graph)
3
4 def find(x):
5 if parent[x] == -1:
6 return x
7 return find(parent[x])
8
9 def union(x, y):
10 xset = find(x)
11 yset = find(y)
12 if xset != yset:
13 parent[xset] = yset
14
15 for i in range(len(graph)):
16 for j in graph[i]:
17 x = find(i)
18 y = find(j)
19 if x == y:
20 return True
21 union(i, j)
22
23 return False- Kruskal’s Minimum Spanning Tree Algorithm: It's employed to detect the shortest possible tree that connects all nodes in a graph.
- Image Segmentation: In computer vision, it helps in segmenting an image into multiple regions or objects.
- Grid percolation
- Network Connectivity
- Least common ancestor in trees
