distance matrix (Manhattan)
      A  B  C  D  E  F
   A  0  4  9 11  8  3
   B  4  0  5  7  8  7
   C  9  5  0  6 11 10
   D 11  7  6  0  5  8
   E  8  8 11  5  0  5
   F  3  7 10  8  5  0

triangle inequality holds: yes
MST edge A-F  w = 3
MST edge A-B  w = 4
MST edge B-C  w = 5
MST edge F-E  w = 5
MST edge E-D  w = 5
MST weight d(T) = 22

full walk W    : A B C B A F E D E F A
  d(W) = 44  (= 2 d(T) = 44)
preorder list L: A B C F E D
  d(L) = 40

optimal tour L*: A B C D E F
  d(L*) = 28

ratio d(L)/d(L*) = 1.4286   (the theorem guarantees at most 2)
check d(T) <= d(L*):    22 <= 28
check d(L) <= 2 d(L*):  40 <= 56
