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CScD-320 Assignment 9 Solution Set, Page 1 Spring 2009
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Recursive depth-first
A(1) B(2) C(3) D(4) E(6) F(7) G(5)
From A recursive call stack shown
A to B AB
B to C AB BC
C to D AB BC CD
D to G AB BC CD DG
G to E AB BC CD DB GE
E to F AB BC CD DB GE EF
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B C
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Breadth-first
A(1) B(2) C(3) D(4) E(5) F(7) G(6)
From A (queue) AB AC AD AE AG
A to B AC AD AE AG BC BE...
A to C AD AE AG BC BE CD CF...
A to D AE AG BC BE CD CF...
A to E AG BC BE CD CF...
A to G BC BE CD CF...
Drop BC BE CD CF...
Drop BE CD CF...
Drop CD CF...
C to F_... (discards)_
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Prim's algorithm — Note that using a sorted list may select a different set of edges.
A(1) B(4) C(6) D(7) E(2) F(5) G(3)
From A: AE(1) | AG(1) AD(2) | AC(2) AB(2)
A to E (1): AG(1) | EB(1) EF(1) | AC(2) AB(2) AD(2) EG(2) |
A to G (1): EB(1) | GF(1) EF(1) | EG(2) AB(2) AD(2) GD(1) | AC(2)
E to B (1): GF(1) | BC(1) EF(1) | AC(2) AB(2) AD(2) GD(1) | EG(2)
G to F (1): BC(1) | FC(1) EF(1) | EG(2) AB(2) AD(2) GD(1) | AC(2)
B to C (1): FC(1) | CD(1) EF(1) | AC(2) AB(2) AD(2) GD(1) | EG(2)
Discard FC: CD(1) | EG(2) EF(1) | AC(2) AB(2) AD(2) GD(1)
C to D (1): GD(1) | EG(2) EF(1) | AC(2) AB(2) AD(2)
Six edges in use; terminate run
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Kruskal's Algorithm for MST:
Accept AE1 AG1 BC1 BE1 CD1 CF1 --- this bring us to 6 edges
Printed 29-Nov-20 16:
CScD-320 Assignment 9 Solution Set, Page 2 Spring 2009
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Prim’s Algorithm --- sorted list priority queue, insertion from the
right, use of distance list.
Enter at A, initial priority queue: AE1 AG1 AB2 AC2 AD
Distance list: A: 0 ; B: -> 2 ; C: -> 2 ; D: -> 2 ; E: -> 1 ; F: -> ;
G: -> 1
Edge AE1: enter EB1 after AG1, enter EF1 after EB1, discard EG2 (worse)
AG1 EB1 EF1 AB2 AC2 AD
Distance list: A: 0 ; B: -> 1 ; C: -> 2 ; D: -> 2 ; E: -> 1 ; F: -> 1 ;
G: -> 1
Edge AG1: enter GD1 after EF1, discard GF1 (same)
EB1 EF1 GD1 AB2 AC2 AD
Distance list: A: 0 ; B: -> 1 ; C: -> 2 ; D: -> 1 ; E: -> 1 ; F: -> 1 ;
G: -> 1
Edge EB1: enter BC1 after GD
EF1 GD1 BC1 AB2 AC2 AD
Distance list: A: 0 ; B: -> 1 ; C: -> 1 ; D: -> 1 ; E: -> 1 ; F: -> 1 ;
G: -> 1 — no more changes
Edge EF1: discard FC1 (same)
Edge GD1: discard DC1 (same)
Edge BC1: final edge
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Dijkstra's algorithm
Using a sorted list may select a different set of edges, depending on the list protocol.
A(1) B(7) C(5) D(6) E(2) F(4) G(3)
From A: AE(1) | AG(1) AD(2) | AC(2) AB(2)
A to E (1): AG(1) | AB(2) AD(2) | AC(2) EF(2) omit EB(2=2)
A to G (1): EF(2) | AB(2) AD(2) | AC(2) omit GD(2=2) GF(2=2)
E to F (2): AC(2) | AB(2) AD(2) |
A to C (2): AD(2) | AB(2) omit CD(3>2)
A to D (2): AB(2) |
A to B (2):
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Dijkstra’s Algorithm --- sorted list priority queue, insert from the right.
Enter at A, initial priority queue: AE1 AG1 AB2 AC2 AD
Distance list: A: 0 ; B: -> 2 ; C: -> 2 ; D: -> 2 ; E: -> 1 ; F: -> ;
G: -> 1
Edge AE1: enter EF2 after AD2, discard EB2 (same), discard EG3 (worse)
AG1 AB2 AC2 AD2 EF
Distance list: A: 0 ; B: -> 2 ; C: -> 2 ; D: -> 2 ; E: -> 1 ; F: -> 2 ;
G: -> 1 — no more changes
Edge AG1: discard GD2 (same), discard GF2 (same)
AB2 AC2 AD2 EF
Edge AB2: discard BC3 (worse)
Edge AC2: discard CD3 (worse), discard CF3 (worse)
Edge AD2: all adjacent have been visited
Edge EF2: final edge
Printed 29-Nov-20 16:
