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:

1. Network Connectivity: It can detect if two nodes in a network are connected.
2. 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.

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

3. Kruskal’s Minimum Spanning Tree Algorithm: It's employed to detect the shortest possible tree that connects all nodes in a graph.
4. Image Segmentation: In computer vision, it helps in segmenting an image into multiple regions or objects.
5. Grid percolation
6. Network Connectivity
7. Least common ancestor in trees