Make the one tree bigger and as good as it can be

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ! After adding n-1 edges, you have one tree, the MST 38 connect two trees. Kruskal’s MST Algorithm Idea: Grow a forest out of edges that do not create a cycle. Pick an edge with the smallest weight. G=(V,E) v 39 MST 2 v3 5 v2 v5 v4 v6 v7 10 7 v4 8 v6 v3 3 1 4 v1 v2 2 v1 v5 4 1 6 v7 Kruskal code void Graph::kruskal(){ int edgesAccepted = 0; |E| heap ops DisjSet s(NUM_VERTICES); while (edgesAccepted < NUM_VERTICES – 1){ e = smallest weight edge not deleted yet; // edge e = (u, v) 2|E| finds uset = s.find(u); vset = s.find(v); if (uset != vset){ edgesAccepted++; 41 s.unionSets(uset, vset); |V| unions Strategy for Kruskal’s EL = sorted set of edges ascending by weight Foreach edge e in EL T1 = tree for head(e) T2 = tree for tail(e) If (T1 != T2) add e to the output (the MST) Combine trees T1 and T2 Seems simple, no? 42 But, how do you keep track of what trees a node is in? kruskal(edgelist,n) { sort(edgelist) f or i = 1 to n makeset(i) count = 0 i = 1 while (count < n ­ 1) { if (findset(edgelist[i].v) != findset(edgelist[i].w)) { println(edgelist[i].v +...
View Full Document

Ask a homework question - tutors are online