3 6 0 , 0 5 3 , 2 5 2 ▁( K n uth ). ▁The ▁paths ▁can ▁be ▁illustrated ▁with ▁ 3 3 5 8 0 ▁nodes ▁using ▁a ▁Z DD . ▁ ▁A ▁real ▁world ▁example ▁for ▁simple ▁paths ▁was ▁proposed ▁by ▁Rand al ▁Bry ant , ▁“ Supp ose ▁I ▁wanted ▁to ▁take ▁a ▁driving ▁tour ▁of ▁the ▁Cont inental ▁U . S ., ▁visit ing ▁all ▁of ▁the ▁state ▁capit ols , ▁and ▁passing ▁through ▁each ▁state ▁only ▁once . ▁What ▁route ▁should ▁I ▁take ▁to ▁minim ize ▁the ▁total ▁distance ?” ▁Figure ▁ 1 4 ▁shows ▁an ▁und irect ed ▁graph ▁for ▁this ▁road map , ▁the ▁numbers ▁indicating ▁the ▁short est ▁distances ▁between ▁neighbor ing ▁capital ▁cities . ▁The ▁problem ▁is ▁to ▁choose ▁a ▁subset ▁of ▁these ▁edges ▁that ▁form ▁a ▁Hamiltonian ▁path ▁of ▁smallest ▁total ▁length . ▁Every ▁Hamiltonian ▁path ▁in ▁this ▁graph ▁must ▁either ▁start ▁or ▁end ▁at ▁August a , ▁Maine ( ME ). ▁Suppose ▁one ▁starts ▁in ▁CA . ▁One ▁can ▁find ▁a ▁Z DD ▁that ▁character izes ▁all ▁paths ▁from ▁CA ▁to ▁ME . ▁According ▁to ▁Kn uth , ▁this ▁Z DD ▁turns ▁out ▁to ▁have ▁only ▁ 7 8 5 0 ▁nodes , ▁and ▁it ▁effectively ▁shows ▁that ▁exactly ▁ 4 3 7 , 5 2 5 , 7 7 2 , 5 8 4 ▁simple ▁paths ▁from ▁CA ▁to ▁ME ▁are ▁possible . ▁By ▁number ▁of ▁edges , ▁the ▁generating ▁function ▁is ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁▁▁▁▁▁▁▁ ▁; ▁so ▁the ▁longest ▁such