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Kruskal's Minimum Spanning Tree

Build an MST by sorting every edge and greedily keeping the cheapest ones — using union-find to skip any edge that would close a cycle. Watch separate forests merge into one tree.

Time: O(E log E)

Space: O(V)

Uses: Union-Find

Greedy: Sorted edges

MST edges:0 / 6Weight:0

Speed: 1100ms

Step 1 of 0100%

In MST

Considering

Skipped (cycle)

· node colour = union-find set

Edges sorted by weight:

0-2(2)3-6(2)2-4(3)0-1(4)1-3(5)5-6(6)4-6(7)2-5(8)1-4(10)

Current Step

Algorithm Details

Time:O(E log E)

Space:O(V)

Data Structure:Union-Find

Strategy:Greedy (sorted)

Kruskal's vs Prim's

Sorts edges globally — great when edges are few (sparse)
Union-Find makes the cycle check near O(1)
Merges a forest of trees; Prim's grows one tree
Sorting cost hurts on very dense graphs — prefer Prim's there

Knowledge Check

Question 1 of 3

How does Kruskal's algorithm decide which edges to keep?