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Challenge 1: "The numbers formed by adding one to the products of the
smallest primes are called the Euclid Numbers. Write a script that finds
the smallest Euclid Number that is not prime."
My notes:
From the wiki:
primes are 2, 3, 5, 7, 11, 13..
products are 2, 6, 30, 210, 2310, 30030...
and Euclid numbers are 3, 7, 31, 211, 2301, 30031...
btw, the Wiki page gives the answer:
E(6)=30031 is first composite Euclid number (59x509)
Euclid numbers will grow like factorials, being products, will we need
to use bigint? 30031 being the answer suggests not:-). I already have a
"mkprimes.c" program to generate first N primes, so let's use that, hence
our Perl code will simply use an of primes (rather than generating the primes
ourselves). Just need isprime(n) type function checking i=2..sqrt(n). Simple!
Challenge 2: "Write a script that finds the common directory path,
given a collection of paths and directory separator. For example, if
the following paths are supplied.
/a/b/c/d
/a/b/cd
/a/b/cc
/a/b/c/d/e
and the path separator is /. Your script should return /a/b as common
directory path."
My notes:
The obvious approach is: split each path on pathsep into an array of segments,
eg. /a/b/c/d == (a,b,c,d) note no '' before first element a
then compare do all paths have "a" in their segment 0? if so, prefix += "/a"
etc. make sure we return "/" if the initial segments are not all identical.
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