15.082 and 6.855J

1
15.082 and 6.855J

• Spanning Tree Algorithms

2
The Greedy Algorithm in Action
4
2
6
1
5
3
7
3
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
4
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
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11
40
40
3
5
7
5
3
7
15
15
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5
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
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11
40
40
3
5
7
5
3
7
15
15
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6
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
7
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
8
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
9
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
10
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
11
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
12
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
13
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
14
The Greedy Algorithm in Action
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
3
7
15
15
11
15
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 2 3 4 5
4 7
10
8
10
8
2
4
6
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
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11
40
40
3
5
7
5
3
7
15
15
11
15
16
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 4 3 4 5
4 7
10
8
10
8
2
4
6
2
4
2
6
35
35
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15
1
1
25
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20
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30
30
17
17
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11
40
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3
5
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5
3
7
15
15
11
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17
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 4 3 4 5
4 5
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
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7
5
3
7
15
15
11
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18
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 4 5 4 5
4 5
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
7
3
5
3
7
15
15
11
18
19
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 1 4 4 4 4
4 4
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
5
7
3
5
3
7
15
15
11
19
20
The Greedy Algorithm in Action
Node 1 2 3 4 5 6
7 First 4 4 4 4 4
4 4
10
8
10
8
2
4
6
4
2
6
35
35
15
15
1
1
1
25
25
20
20
30
30
17
17
21
21
11
40
40
3
5
7
3
5
3
7
15
15
11
20
21
Prims Algorithm in Action
10
8
4
4
6
2
2
6
35
15
1
1
25
20
30
17
21
11
40
5
7
3
5
3
7
15
The minimum cost arc from yellow nodes to green
nodes can be found by placing arc values in a
priority queue.
22
Prims Algorithm in Action
8
10
4
4
6
2
2
2
6
35
35
15
1
25
1
30
20
17
21
11
40
5
7
3
5
3
7
15
23
Prims Algorithm in Action
8
10
10
10
4
2
2
4
6
4
2
6
35
35
15
1
25
25
1
30
17
20
21
11
40
5
7
3
5
3
7
15
24
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
1
25
25
1
17
30
30
20
20
21
21
11
40
5
7
3
5
3
7
15
25
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
40
5
7
3
5
5
3
7
15
26
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
40
5
7
3
5
5
3
7
15
27
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
11
11
40
5
3
7
5
7
5
3
7
15
15
28
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
11
11
40
5
7
7
3
5
3
5
3
7
15
15
15
29
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
11
11
40
5
7
7
3
5
3
5
3
7
15
15
15
30
Prims Algorithm in Action
8
8
8
10
10
10
4
2
2
4
6
6
4
2
6
35
35
15
15
15
1
25
25
1
17
30
30
17
20
20
21
21
11
11
11
40
5
7
7
3
5
3
5
3
7
15
15
15
31
Sollins Algorithm in Action
10
8
4
4
6
2
4
6
2
2
6
35
15
1
1
1
25
20
30
17
21
40
5
7
3
5
7
3
5
3
7
11
15
Treat all nodes as singleton components, and then
select the min cost arc leaving the component.
32
Sollins Algorithm in Action
10
8
4
4
6
2
6
2
6
35
15
1
1
25
20
30
17
21
40
5
7
3
7
3
5
5
3
7
11
15
Find the min cost edge out of each component