How do I implement Kruskal's algorithm?

How do I implement Kruskal's algorithm?

Kruskal's algorithm is used to find the minimum spanning tree of a graph. Would you like a step-by-step guide?

Yes, please provide the steps.

1. Sort all edges in non-decreasing order of their weight. 2. Pick the smallest edge. 3. Check if it forms a cycle with the spanning tree formed so far. 4. If it doesn't, include it in the tree. 5. Repeat until there are V-1 edges in the tree.

What data structures should I use?

You can use a disjoint-set (union-find) data structure to efficiently manage and merge sets of vertices.

Can you show me a code example?

Sure! Here's a simple Python implementation:

class DisjointSet:
    def __init__(self, n):
        self.parent = list(range(n))
        self.rank = [0] * n

    def find(self, u):
        if self.parent[u] != u:
            self.parent[u] = self.find(self.parent[u])
        return self.parent[u]

    def union(self, u, v):
        root_u = self.find(u)
        root_v = self.find(v)
        if root_u != root_v:
            if self.rank[root_u] > self.rank[root_v]:
                self.parent[root_v] = root_u
            else:
                self.parent[root_u] = root_v
                if self.rank[root_u] == self.rank[root_v]:
                    self.rank[root_v] += 1

# Example usage
edges = [(1, 2, 10), (1, 3, 6), (2, 3, 15)]  # (u, v, weight)
# Sort edges and apply Kruskal's algorithm here

Let me know if you need further details!