▁▁ <0x09> … ▁S 8 : ▁Re pres ents ▁all ▁choices ▁of ▁putting ▁a ▁queen ▁at ▁the ▁e ighth ▁row ▁so ▁that ▁it ▁does ▁not ▁viol ate ▁the ▁previous ▁que ens . ▁ <0x09> ▁ <0x09> The ▁Z DD ▁for ▁S 8 ▁consists ▁of ▁all ▁potential ▁solutions ▁of ▁the ▁ 8 - Que ens ▁problem . ▁▁ <0x09> For ▁this ▁particular ▁problem , ▁caching ▁can ▁significantly ▁improve ▁the ▁performance ▁of ▁the ▁algorithm . ▁Using ▁cache ▁to ▁avoid ▁duplicates ▁can ▁improve ▁the ▁N - Que ens ▁problems ▁up ▁to ▁ 4 . 5 ▁times ▁faster ▁than ▁using ▁only ▁the ▁basic ▁operations ▁( as ▁defined ▁above ), ▁shown ▁in ▁Figure ▁ 1 0 . ▁ ▁The ▁Knight ’ s ▁tour ▁problem ▁▁ <0x09> The ▁Knight ’ s ▁tour ▁problem ▁has ▁a ▁historical ▁significance . ▁The ▁kn ight ’ s ▁graph ▁contains ▁n 2 ▁vertices ▁to ▁dep ict ▁the ▁squares ▁of ▁the ▁ch ess board . ▁The ▁edges ▁illustrate ▁the ▁legal ▁moves ▁of ▁a ▁kn ight . ▁The ▁kn ight ▁can ▁visit ▁each ▁square ▁of ▁the ▁board ▁exactly ▁once . ▁O la f ▁Sch r ö er , ▁M . ▁Lö bb ing , ▁and ▁In go ▁Weg ener ▁approached ▁this ▁problem , ▁namely ▁on ▁a ▁board , ▁by ▁assigning ▁Boolean ▁variables ▁for ▁each ▁edge ▁on ▁the ▁graph , ▁with ▁a ▁total ▁of ▁ 1 5 6 ▁variables ▁to ▁design ate ▁all ▁the ▁edges . ▁A ▁solution ▁of ▁the ▁problem ▁can ▁be ▁expressed ▁by ▁a ▁ 1 5 6 - bit ▁combination ▁vector . ▁According ▁to