![Kruskal algorithm(E,cost,n,t) //E is set of edges in G .G has n vertices.Cost[u,v] is //cost of edge(u,v).t is the set of edges in minimum-cost //spanning tree.the final cost is returned. { //construct a heap out of the edge costs using heapify For i=:1 to n do parent[i]:=-1; //each vertex is in a different set. i:=0;mincost:=0.0; While((i<n-1) and (heap not empty)) do { //delete a minimum cost edje(u,v) from the heap and reheapify using Adjust; j:=Find(u); k:=Find(v);](https://image.slidesharecdn.com/chaithrams-091219100107-phpapp01/85/KRUSKAL-S-algorithm-from-chaitra-8-320.jpg)
![If (j!=k) then { i:=i+1; t[i,1]:=u; t[i,2]:=v; mincost:=mincost+cost[u,v]; union(j,k); } } if(i!=n-1) then write(“no spanning tree”); else return mincost; }](https://image.slidesharecdn.com/chaithrams-091219100107-phpapp01/85/KRUSKAL-S-algorithm-from-chaitra-9-320.jpg)
KRUSKAL'S algorithm from chaitra
- 1. KUVEMPU UNIVERSITY Department of Computer Science Jnana Sahyadri Shankarghatta Seminar on “ Kruskal’s Algorithm ” Presented by, Chaitra.M.S 3 rd sem , M.Sc, Dept. Of Computer Science, Shankarghatta. Under the guidance of, Suresh.M, Dept. Of Computer Science, Shankarghatta.
- 2. Contents Spanning trees Finding a spanning tree Minimum-cost spanning trees Kruskal’s algorithm And example
- 4. Spanning trees Suppose you have a connected undirected graph Connected: every node is reachable from every other node Undirected: edges do not have an associated direction ...then a spanning tree of the graph is a connected subgraph in which there are no cycles A connected, undirected graph Four of the spanning trees of the graph
- 5. Finding a spanning tree To find a spanning tree of a graph, pick an initial node and call it part of the spanning tree do a search from the initial node: each time you find a node that is not in the spanning tree, add to the spanning tree both the new node and the edge you followed to get to it An undirected graph
- 6. Minimizing costs Suppose you want to supply a set of houses (say, in a new subdivision) with: electric power water sewage lines telephone lines To keep costs down, you could connect these houses with a spanning tree (of, for example, power lines) However, the houses are not all equal distances apart To reduce costs even further, you could connect the houses with a minimum-cost spanning tree
- 7. Minimum-cost spanning trees Suppose you have a connected undirected graph with a weight (or cost ) associated with each edge The cost of a spanning tree would be the sum of the costs of its edges A minimum-cost spanning tree is a spanning tree that has the lowest cost A B E D F C 16 19 21 11 33 14 18 10 6 5 A connected, undirected graph A B E D F C 16 11 18 6 5 A minimum-cost spanning tree A B E D F C 16 19 21 11 33 14 18 10 6 5 A connected, undirected graph
- 8. Kruskal algorithm(E,cost,n,t) //E is set of edges in G .G has n vertices.Cost[u,v] is //cost of edge(u,v).t is the set of edges in minimum-cost //spanning tree.the final cost is returned. { //construct a heap out of the edge costs using heapify For i=:1 to n do parent[i]:=-1; //each vertex is in a different set. i:=0;mincost:=0.0; While((i<n-1) and (heap not empty)) do { //delete a minimum cost edje(u,v) from the heap and reheapify using Adjust; j:=Find(u); k:=Find(v);
- 9. If (j!=k) then { i:=i+1; t[i,1]:=u; t[i,2]:=v; mincost:=mincost+cost[u,v]; union(j,k); } } if(i!=n-1) then write(“no spanning tree”); else return mincost; }
- 10. Example graph
- 19. Minimum cost spanning tree we obtained finally
- 20. Any queries???????????
- 21. Thank U………………