10.6 Prim’s Minimal Spanning Tree Algorithm

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10.6 Prim’s Minimal Spanning Tree Algorithm

Greedy algorithm: Add to the tree in each step a branch with a minimal cost.
Optimal outcome.



...

A priority queue can be utilized for the selection of edges.
Candidate nodes in the queue record the cost of adding them to the tree

e
1 7 |2O||
oao ---------boo----------oco || ||
7| ----- 3 ----- |9 || ||
odo --2------eoo-----6--- ofo cO fO
| --8-- | 4 | 7 | oo |
3| 5 ---- 5 |8 | || || |
ogo ---8-----hoo----1---- oio || g | |i
d7O oo O oo hO oo O

f
1 7 |4O|
oao ---------boo----------oco || ||
7| ----- 3 ----- |9 || ||
odo ---2-----eoo-----6--- ofo dO hO
| ---8- | 4 | 7 | 5
3| 5 ---- 5 |8 || || |
ogo ----8----hoo----1---- oio i| g c
oo O oo O 6O

[Prim’s algorithms]

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