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# Minimum Spanning Tree

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### Minimum Spanning Tree

1. 1. MINIMUM spANNING Trees!<br />By: Makenna , Emmely , and Jessica <br />
2. 2. What is a minimun spanning tree?<br />A graph that connects all nodes together.<br />A minimum spanning tree is used to find the shortest route.<br />
3. 3. Basics<br />Graph- a diagram showing<br />MST-minimum spanning tree<br />Shortest route, the shortest path between all the places you need to go<br />
4. 4. MST Basics<br />NO CYCLES ALLOWED!<br />Algorithm- a problem solving procedure following a set of rules.<br />Cycle-the nodes are connected by more than one edge.<br />
5. 5. Muddy City<br />An example would be having to use the least amount of paving stones to pave roads so that every house could be connected to every other house indirectly.<br />
6. 6. What is an MST Algorithm?<br />An MST algorithm is a way to show the shortest distance.<br />There are many different algorithms.<br />Kruskal<br />Prim<br />Reverse delete<br />
7. 7. Kruskal’s Algorithm<br />Pick out the smallest edges<br />Repeat step 1 as long as the edge selected does not create a cycle<br />When all nodes have been connected you are done<br />
8. 8. Kruskal #0<br />
9. 9. Kruskal #1<br />
10. 10. Kruskal #2<br />
11. 11. Kruskal #3<br />
12. 12. Kruskal #4<br />
13. 13. Kruskal #5<br />28 stones<br />
14. 14. Reverse-Delete Algorithm<br />This is the opposite of Kruskal’s algorithm.<br />Start with all edges <br />Delete the longest edge<br />Continue deleting longest edge as long as all nodes are connected and no cycles.<br />
15. 15. Reverse-Delete #1<br />
16. 16. Reverse-Delete #2<br />
17. 17. Reverse-Delete #3<br />
18. 18. Reverse-Delete #4<br />
19. 19. Reverse-Delete #5<br />
20. 20. Reverse-Delete #6<br />
21. 21. Reverse-Delete #7<br />
22. 22. Reverse-Delete #8<br />
23. 23. Reverse-Delete #9<br />
24. 24. Reverse-Delete #10<br />
25. 25. Reverse-Delete #11<br />
26. 26. Prim’s Algorithm<br />Pick out a node.<br />Pick out the shortest edge that is connected to your tree so far as long as it doesn’t create a cycle.<br />Continue this until all nodes are covered.<br />
27. 27. Prim #1<br />
28. 28. Prim #2<br />
29. 29. Prim #3<br />
30. 30. Prim #4<br />
31. 31. Prim #5<br />
32. 32. Prim #6<br />
33. 33. Prim #7<br />
34. 34. Prim #8<br />
35. 35. Prim #9<br />
36. 36. Prim #10<br />
37. 37. MSTs<br />Kruskal (1956) and Prim (1967)<br />MSTs make our life easier and we save money by using short paths.<br />MST’s was first seen in Poland, France , The Czech Republic and Slovokia Czechoslovakia.<br />
38. 38. Importance of MSTs<br />We need it in computer science because it prevents loops in a switched network with redundant paths.<br />It’s one of the oldest and most basic graphs in theoretical computer science. <br />
39. 39. Why We Love MSTs<br />MSTs are very fun to work with <br />It helps you find the shortest route.<br />
40. 40. ANY QUESTIONS?<br />
41. 41. Thanksfor listening!<br />