Kruskal's Algorithm
External
Internal
Overview
Kruskal's algorithms is a greedy algorithm that computes the minimum cost spanning tree for an undirected connected graph. It has a different approach than Prim's algorithm, in that it does not grow the connected explored territory one node at a time, but it grows the trees in parallel with a lot of simultaneous little pieces, unconnected at first, which eventually merge into the minimum cost spanning tree. It does that by sorting the edges in the ascending order of their cost, and picking edges in that order, one by one, careful not to create cycles. The greediness of the algorithm comes from the fact that at each step, it chooses an edge by attempting to minimize a greedy score, which is the cost of the edge.
Non-Optimized Implementation
Non-Optimized Implementation Running Time
sort edges in the order of increasing cost initialize T = ∅ # the tree we are growing for edge e = (u,v) in the order of increasing cost: if T ⋃ e has no cycles # there is no path in T from u to v add e to T
We could count the edges added to the spanning tree, and once we have n-1 edges, which means the spanning tree is complete, we can abort the loop.