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Minimum Spanning Trees (MSTs) Prim's Algorithm For each vertex not in the tree, keep track of the lowest cost edge that would connect it to the tree This.

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Presentation on theme: "Minimum Spanning Trees (MSTs) Prim's Algorithm For each vertex not in the tree, keep track of the lowest cost edge that would connect it to the tree This."— Presentation transcript:

1 Minimum Spanning Trees (MSTs) Prim's Algorithm For each vertex not in the tree, keep track of the lowest cost edge that would connect it to the tree This can be as a heap-based priority queue Each time, join a vertex out of tree T with the edge with the smallest weight This is the Prim algorithm

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3 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 aa bb cc dd ff ee gg

4 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 a0 bb cc dd ff ee gg

5 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 gg bb cc dd ff ee

6 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 gg b3 cc dd ff ee

7 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 b3 gg cc dd ff ee

8 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 b3 g3 cc dd ff ee

9 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 cc g3dd ff ee

10 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 g3 cc dd ff ee

11 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 g3 cc d2 ff ee

12 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 d2 cc g3 ff ee

13 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 ff cc g3 ee

14 Minimum Spanning Trees (MSTs) Prim's Algorithm g e cf 3 1 4 4 53 2 g3 cc ff ee a db 3 2

15 Minimum Spanning Trees (MSTs) Prim's Algorithm g e cf 3 1 4 4 53 2 g1 cc ff ee a db 3 2

16 Minimum Spanning Trees (MSTs) Prim's Algorithm g e cf 3 1 4 4 53 2 g1 cc ff e4 a db 3 2

17 Minimum Spanning Trees (MSTs) Prim's Algorithm g e cf 3 1 4 4 53 2 g1 e4ff cc a db 3 2

18 Minimum Spanning Trees (MSTs) Prim's Algorithm g e cf 3 1 4 4 53 2 g1 e4f5 cc a db 3 2

19 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 cc e4f5

20 Minimum Spanning Trees (MSTs) Prim's Algorithm e cf 4 4 53 2 e4 cc f5 ag db 3 31 2

21 Minimum Spanning Trees (MSTs) Prim's Algorithm e cf 4 4 53 2 f5 cc ag db 3 31 2

22 Minimum Spanning Trees (MSTs) Prim's Algorithm cf 53 2 f5 c3 e 4 4 ag db 3 31 2

23 Minimum Spanning Trees (MSTs) Prim's Algorithm cf 53 2 c3 f5 e 4 4 ag db 3 31 2

24 Minimum Spanning Trees (MSTs) Prim's Algorithm f5 cf 53 2 e 4 4 ag db 3 31 2

25 Minimum Spanning Trees (MSTs) Prim's Algorithm f2 cf 53 2 e 4 4 ag db 3 31 2

26 Minimum Spanning Trees (MSTs) Prim's Algorithm cf 53 2 e 4 4 ag db 3 31 2

27 Minimum Spanning Trees (MSTs) Prim's Algorithm cf 53 2 e 4 4 ag db 3 31 2

28 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 aa bb cc dd ff ee gg

29 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 aa bb cc d0 ff ee gg

30 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 d0 bb cc aa ff ee gg

31 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 gg bb cc aa ff ee

32 Minimum Spanning Trees (MSTs) Prim's Algorithm g b e cf 3 31 2 4 4 53 2 gg b2 cc aa ff ee a d

33 Minimum Spanning Trees (MSTs) Prim's Algorithm g b e cf 3 31 2 4 4 53 2 b2 gg cc aa ff ee a d

34 Minimum Spanning Trees (MSTs) Prim's Algorithm g b e cf 3 31 2 4 4 53 2 b2 g1 cc aa ff ee a d

35 Minimum Spanning Trees (MSTs) Prim's Algorithm g b e cf 3 31 2 4 4 53 2 g1 b2 cc aa ff ee a d

36 Minimum Spanning Trees (MSTs) Prim's Algorithm g b e cf 3 31 2 4 4 53 2 g1 b2 cc aa ff e4 a d

37 Minimum Spanning Trees (MSTs) Prim's Algorithm g b e cf 3 31 2 4 4 53 2 g1 b2 cc aa f5e4 a d

38 Minimum Spanning Trees (MSTs) Prim's Algorithm ag b e cf 3 31 2 4 4 53 2 cc b2aa f5e4 d

39 Minimum Spanning Trees (MSTs) Prim's Algorithm e cf 3 2 4 4 53 2 b2 e4aa f5cc g 1 d a b 3

40 Minimum Spanning Trees (MSTs) Prim's Algorithm e cf 3 2 4 4 53 2 b2 e4a3 f5cc g 1 d a b 3

41 Minimum Spanning Trees (MSTs) Prim's Algorithm e cf 3 2 4 4 53 2 f5 e4a3 cc g 1 d a b 3

42 Minimum Spanning Trees (MSTs) Prim's Algorithm e cf 3 4 4 53 2 a3 e4f5 cc 2 g 1 d a b 3

43 Minimum Spanning Trees (MSTs) Prim's Algorithm ag db e cf 3 31 2 4 4 53 2 cc e4f5

44 Minimum Spanning Trees (MSTs) Prim's Algorithm e cf 4 4 53 2 e4 cc f5 ag db 3 31 2

45 Minimum Spanning Trees (MSTs) Prim's Algorithm e cf 4 4 53 2 f5 cc ag db 3 31 2

46 Minimum Spanning Trees (MSTs) Prim's Algorithm cf 53 2 f5 c3 e 4 4 ag db 3 31 2

47 Minimum Spanning Trees (MSTs) Prim's Algorithm cf 53 2 c3 f5 e 4 4 ag db 3 31 2

48 Minimum Spanning Trees (MSTs) Prim's Algorithm f5 cf 53 2 e 4 4 ag db 3 31 2

49 Minimum Spanning Trees (MSTs) Prim's Algorithm f2 cf 53 2 e 4 4 ag db 3 31 2

50 Minimum Spanning Trees (MSTs) Prim's Algorithm cf 53 2 e 4 4 ag db 3 31 2

51 Minimum Spanning Trees (MSTs) Prim's Algorithm cf 53 2 e 4 4 ag db 3 31 2

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