Use the Edge$-$Picking Algorithm to find a Hamiltonian circuit in the weighted graph.

$A-C-D-E-F-B-A$

$A-D-B-F-E-C-A$

$A-B-E-D-F-C-A$

$A-F-D-E-B-C-A$

$A-E-B-C-F-D-A$