Database Reference
In-Depth Information
Essentially,itwasapathindingproblem,liketherearemanyothers(forexample,
the
knight's ride
problem or the
travelling salesman
problem). It does not seem like
averydificultassignmentatallnowdoesit?However,atthetime,peoplereally
struggled with it and were trying toigureitoutforthelongesttime.Itwasnotuntil
Euler got involved and took a very different, mathematical approach to the problem
that it got solved once and for all.
EulerdidthefollowingtwothingsthatIindreallyinteresting:
1.
First and foremost, he decided not to take the traditional brute force method
to solve the problem (that is, in this case, drawing a number of different
routeoptionsonthemapandtryingtoigureout—essentiallybytrialand
error—if there was such a route through the city), but decided to do something
different. He took a step back and took a different look at the problem by
creating what I call an
abstract version
of the problem at hand, which is
essentially a model of the problem domain that he was trying to work with. In
his mind at least, Euler must have realized that the citizens of Königsberg were
focusing their attention on the wrong part of the problem—the streets. Euler
quickly came to the conclusion that the streets of Königsberg really did not
mattertoindasolutiontotheproblem.Theonlythingsthatmatteredforhis
pathindingoperationwerethefollowing:
° The parts of the city
° The bridges connecting the parts of the city
Now, all of a sudden, we seem to have a very different problem at hand,
which can be accurately represented in what is often regarded as "the world's
irstgraph":
2.
Secondly, Euler solved the puzzle at hand by applying a mathematical
algorithm on the model that he created. Euler's logic was simple: if I
want to take a walk in the town of Königsberg, then:
° I will have to start somewhere in any one of the four parts of the city
° I will have to leave that part of the city; in other words, cross one of
the bridges to go to another part of the city
