02-greedy

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

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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 +...
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