Recent graduate and world traveler Alastair Bor is planning a European trip. He is influenced by his curiosity about urban culture in the EU and by his study of international relations while he was in school. Accordingly, he has decided to make one stop in each of twelve European capitals in the time he has available. The distances between the capitals are shown below:

a. What sequence achieves a minimum-distance tour of the cities, starting and ending in Brussels? What is the length of the minimum-distance tour?
b. Suppose that Alastair need not return to Brussels but can finish the tour in any of the cities. What sequence achieves a minimum-distance path through all the cities, starting in
Brussels?

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To City Dub Lis From City Lon Ams Ath Par Ber Bru Cop 622 2132 Lux Mad Rom 175 577 1889 339 319 1462 430 712 2817 1273 Amsterdam 2166 1297 1053 1184 1173 1527 1849 1907 1419 2100 878 262 1027 2166 577 175 2377 1905 1806 2899 2313 1836 1293 2046 1452 2092 653 Athens Berlin 1806 2092 2132 2345 1738 2505 912 348 598 190 Brussels Copenhagen Dublin Lisbon London 653 768 732 1203 300 942 440 1616 348 768 732 1203 1738 2505 622 712 1889 797 914 1747 475 2817 1273 2345 912 598 1656 743 1482 1656 440 914 1452 2899 2377 1905 2313 2100 1053 600 1259 1616 1747 331 293 339 319 300 190 942 797 2046 1027 1527 475 Luxembourg 1254 987 1308 Madrid Paris Rome 1462 430 1297 1293 262 1173 1254 1259 331 1419 1836 1033 600 1482 878 293 1033 1108 743 1108 1907 1184 1308 987 1849