building the ajo-danza link at this point you figure you can send out the construction crew to actually install the cable from ajo to danza how can you be sure the ajo-danza route will eventually be part of the cheapest solution (the minimum spanning tree)so faryou only know the cost of two links in the system don' you need more informationto get feel for this situationtry to imagine some other route linking ajo to danza that would be cheaper than the direct link if it doesn' go directly to danzathis other route must go through bordo and circle back to danzapossibly via one or more other towns but you already know the link to bordo is more expensiveat million dollars,than the link to danzaat so even if the remaining links in this hypothetical circle route are cheapas shown in figure it will still be more expensive to get to danza by going through bordo alsoit will be more expensive to get to towns on the circle routelike xby going through bordo than by going through danza figure hypothetical circle route we conclude that the ajo-danza route will be part of the minimum spanning tree this isn' formal proof (which is beyond the scope of this book)but it does suggest your best bet is to pick the cheapest link so you build the ajo-danza link and install an office in danza why do you need an officedue to magnaguena government regulationyou must install an office in town before you can send out surveyors from that town to adjacent towns in graph termsyou must add vertex to the tree before you can learn the weight of the edges leading away from that vertex all towns with offices are connected by cable with each othertowns with no offices are not yet connected building the ajo-bordo link once you've completed the ajo-danza link and built your office in danzayou can send out surveyors from danza to all the towns reachable from there these are bordocolinaand erizo the surveyors reach their destinations and report back costs of and million dollarsrespectively (of course you don' send surveyor to ajo because you've already surveyed the ajo-danza route and installed its cable now you know the costs of four links from towns with offices to towns with no officesajo-bordo$ million danza-bordo$ million danza-colina$ million danza-erizo$ million