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Algorithm-a-Day : Day 10 : Binary Search
Got your copy of Programming Pearls at hand?
You have a phone book, and are particularly violent about looking for
numbers. You best friend, Mr. Ericson, has a number that you've forgotten.
You open the phone book up right into the middle: McLean. Ericson comes
earlier in the phone book than McLean, so you tear it in half, toss the
unneeded portion over your shoulder and repeat the process. Firth? Garbage!
Carlson? Garbage! You keep searching the middle name and tearing off
the unneeded half until your find Mr. Ericson's number. If it's in there,
hurray. If it isn't... well you've just wasted a phone book.
Welcome to binary search!
Binary search is a very fast way to search for elements in a sorted list.
If the list is even one element off of being perfectly sorted, you cannot
guarantee the results of the search. Given a big enough list, however,
it can be a bother checking for sortedness before every search. There are
ways around this, but for us, we'll just assume the lists we're given
are sorted.
Since the boolean data type doesn't exist in C, a failure to find the
desired item with result in a -1. Usually we use 0 to represent False,
but in this case 0 is a legitimate array index.
Target less than mid? Go left. Target greater than mid? Go right.
Found it? Save and break. Using 'break' makes some people uncomfortable,
but I find it clearer than say, altering 'lower' or 'upper' manually
so that the loop will break on the next pass.
Make sure to run that **unit test**!
Sexier to look at than the C version. The only Python bonus we gain here
is (less lines and) the ability to infer the length of the list we're given,
instead of it being passed explicitely as in the C version.
Watch out for line 7, that's Python3 only.
Nice and short. Notice a theme here? Guards and 'where' are our friends.
Since Haskell doesn't have loop structures, this is of course done via
recursion. It's safe to say that this will never blow the stack,
as with a default stack depth limit of 1000, that allows us 1000 (give or
take a few) layers, or 2 ^ 999 values. That number is over 3.5 lines long
on my 80 column terminal window. So no overflows :)
'take' and 'drop' also make things easy for tearing our proverbial
phone book in half. Overall, just really short and clean!
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