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My project mates and I figured we'd use the computer to look at all possible
combinations, calculate the distances between points, two at a time - using geometric
formulas - add them and arrive at the solution. It sounds like a murderous job, but we
weren't going to do it - the computer was. We'd start
with one hundred random points on
a graph, using A0 for the home point and A1, A2, A3, etc. up to A100 for the places to
cover. The distance between A0 (x
0
, y
0
) and A1 (x
1
, y
1
) is the square root of the sum of
(x
1
-x
0
)
2
+ (y
1
-y
0
)
2
. If you played hooky the day, we were taught that in math class, trust
me. A similar calculation had to be done for all the remaining combinations.
For the number of combinations, just consider traveling to five places. There are
five choices for the first location, four left for the second, then three, two and of course,
one left. Using the asterisk to indicate multiplication, this becomes 5*4*3*2*1, which
equals 120 possibilities. If we have one hundred places but consider only twenty, we have
one hundred choices for the first location, then ninety-nine, ninety-eight on down, or
100*99*98*97*96*95*94*93*92*91*90*89*88*87*86*85*84*83*82*81. I'm not going
to waste my time calculating that number, but instead use an approximation of 100
20
,
which is larger than the value worked out, but since we still have eighty more locations, it
should suffice, actually being a low estimate. The number, 100
20
equals 10
40
, since 100
equals 10
2
. Don't tell me you cut math again.
According to a 2008 New York Times story, a super computer could perform
1.026 quadrillion calculations per second. This number is approximately 10
15
. In a year,
there are 60*60*24*365, or 31,536,000 seconds. For a thousand years we have
31,536,000,000 seconds. Multiplying these two numbers (approximately 10
15
calculations
per second times about 10
12
) would result in fewer than 10
27
calculations for a thousand
years. Compare this to 10
40
. Since we're only considering a fraction of the one hundred
locations, we're going to come up way short - by a long shot. We'll need a faster
computer - much, much faster.
I think Jerry tricked us.
Indeed, a computer can't do everything. It has limitations. This effects business
applications as well. Assume that a business needs to shut down the online system for a
short time to do some updating of files, say a half hour. If that process takes twenty
minutes, that's cutting it close. In today's crazy, stressed out environment of 24/7, how
can the corporation even afford to shut down for fifteen minutes? Perhaps the solution is
to handle the updates without any shutdown. It will have to be figured out.
Speaking of solutions, specifically the traveling salesman problem, what if I hire
ten go-getters to cover the one hundred locations, ten each. I implore that to really hustle
for mucho dollars. I turn the dough over to my boss and he is overwhelmed and pleased,
completely forgetting about the problem originally assigned.
