In 2014 the Arizona book rep of some publishing company had to visit all of NAU\

Question

In 2014 the Arizona book rep of some publishing company had to visit all of NAU's Extended Campus sites there are 38 at that time. Excel this number equals 6,881,876,545,613,170,000,000,000,000,000,000,000,000,000 NAU's computing cluster Monsoon (htt news edulnau-computing Cluster-comin online worksho apri-29IH U3P7ocitPbN) can calculate the lengths of 1,000,000,000,000 Hamilton circuits per second. How Iong will it take to find the shortest Hamilton circuit? Express your answer in whatever units seem reasonable seconds, minutes, hours, days, years, etc. Be sure to show your work. 2. For a slightly simpler problem, let us choose a subset of just 14 Extended campus sites (Bullhead City, Flagstaff, Ganado, Glendale, Kingman, Lake Havasu City, Mesa, Phoenix, Prescott, Show Low, Thatcher, Tuba City, Tucson and Yuma). The distance between each pair of cities is given in the chart below: Bu FI Ga GI Ki LHC M Ph Pr SL Th TC Tu Yu Bu o 183 338 210 37 65 247 232 184 321 393 262 347 210 Fl 183 0 156 141 147 206 160 144 95 139 269 78 260 320 Ga 338 156 0 295 303 361 258 271 249 132 291 127 323 474 Gl 210 141 295 0 175 192 27 10 96 187 172 218 127 184 Ki 37 147 303 175 0 60 212 197 149 286 358 227 312 215 LHC 65 206 361 192 60 0 209 193 207 344 355 285 309 155 M 247 160 258 27 212 209 0 20 115 160 147 238 118 192 Ph 232 144 271 10 197 193 20 0 99 180 162 222 116 184 Pr 184 95 249 96 149 207 115 99 0 186 261 173 216 216 SL 321 139 132 187 286 344 160 180 186 0 159 202 190 352 Th 393 269 291 172 358 355 147 162 261 159 0 327 130 368 TO 262 78 127 218 227 285 238 222 173 202 327 0 338 398 Tu 347 260 323 127 312 309 118 116 216 190 130 338 0 240 Yu 210 320 474 184 215 155 192 184 216 352 368 398 240 0

Explanation / Answer

1. See the calculation below

2.

i) For Phoenix:

Route is : Ph -> (10) Gl -> (27) M -> (115) Pr -> (95) Fl -> (78) TC -> (127) Ga -> (132) SL -> (159) Th -> (130) Tu -> (240) Yu -> (155) LHC -> (60) Ki -> (37) Bu -> (232) Ph

Length: 10+27+115+95+78+127+132+159+130+240+155+60+37+232 = 1502

ii) For Tucson:

Route is : Tu -> (116) Ph -> (10) Gl -> (27) M -> (115) Pr -> (95) Fl -> (78) TC -> (127) Ga -> (132) SL -> (159) Th -> (355) LHC-> (60) -> Ki -> (37) Bu -> (347) Tu
Length: 116+10+27+115+95+78+127+132+159+355+60+37+347 = 1658

iii) For Flagstaff:

Route is: Fl -> (78) TC -> (127) Ga -> (132) SL -> (159) Th -> (130) Tu -> (116) Ph -.> (10) Gl -> (27) M -> (115) Pr -> (149) Ki -> (37) Bu -> (65) LHC -> (155) Yu -> (320) Fl

Length: 78+127+132+159+130+116+10+27+115+149+37+65+155+320 = 1620

From the lengths of these 3 routes, it is clear that route starting from Phoenix is shortest of three and hence preferable.

Total No. of Hamiltonian cycles (A) 6.88E+42 No. of Hamiltonian cycles calculated/second (B) 1E+12 Total time taken to calculate required no. of Hamiltonian cycles (in seconds) (C = A/B) 6.88E+30 Total seconds in a year (D) 31536000 Total time taken to calculate required no. of Hamiltonian cycles (in years) (E= C/D) 2.18E+23

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