Source is S (left-most node):
Next To Do Certain Pathlength Pathpred
S
S
 Of:   A   Is:   15  
Of:   B   Is:   2  		 Of:   A   Is:   S  
Of:   B   Is:   S  
A,B
B
 Of:   A   Is:   12  
Of:   D   Is:   27  		 Of:   A   Is:   B  
Of:   D   Is:   B  
A, D
A
 Of:   D   Is:   32 - keep 27  
Of:   E   Is:   27  		 Of:   D   Is:   same as above (B)  
Of:   E   Is:   A  
D, E
both 27 - pick D
 Of:   T   Is:   42   Of:   T   Is:   D  
E, T
E
 Of:   D   Is:   37 - keep 27
Of:   T   Is:   52 - keep 42 		Of:   D   Is: still B
Of:   T   Is: still D
T
T
 no neighbors Of:   T   Is: still D

All vertices are Certain

Backtrack on Pathpred (path predecessor) to get path
Pathpred of T is D
Pathpred of D is B
Pathpred of B is S

Hence Single source shortest path from S to T is S to B to D to T and its length is 42