# Tag Archives: Algorithms

## An Alternative to “Hello world!”

There’s an appreciable risk that this post may be considered sacrilegious within the programming world.  If there’s one thing, even  just one tiny, single thing, that every programmer knows about teaching programming, it’s that the first lesson should be how to output the string, “Hello world!”  (There’s some dispute as to whether the ‘w’ should be capitalised but the ‘!’ is entirely necessary.)  How heretical would it be to suggest that, not only is this probably not the best place to start, but that a better alternative can be found by turning around a bottle of shampoo?

## Are There Any Hard Problems?

That looks like a hopelessly vague question, and it is unless we’re prepared to clarify it a bit.  On the other hand, we already know there are some impossible problems so surely there are some that are just hard?  Again, we’ll need to work out what on earth we’re talking about here.  Let’s start with what we actually mean by a problem in a computational sense …

(Be warned: There are one or two simplifications and liberties with precision in what follows; it’s well-intentioned but may upset the purist.)

Well, actually, even that isn’t simple and there’s no absolute agreement on what a good definition would be.  (We’ve seen previously that mathematicians and computer scientists don’t always see eye-to-eye.)  It’s cheating a bit but it’s probably easier to give examples and this should work well enough for us.  At least in the context of computing, these are all valid problems:

1. Calculate    2 x 4 + 9 – 3
2. If   5 – x  =  2   what’s x?
3. Find the largest from    5, 7, 1, 4, 8, 5, 2, 4, 8, 5, 2, 6, 7, 7, 3, 3, 2, 4, 3, 6, 7, 7, 6, 5, 4
4. Sort    25, 44, 66, 72, 12, 45, 56, 90, 45, 69, 11, 10, 12, 42, 88     into ascending order
5. Arrange   1, 2, 3, 4, 5, 6, 7, 8, 9   into a magic square
6. What’s the best way to get to Paris?