Eleven Fire Crackers
| OK, plugging in my iPod now to drown out the friggin jingle bells playing in the background. It's barely November, I'm in Singapore ... so who invited Bing Crosby and a troop of reindeer godammit?? Spinning thru albums at random I crank up the volume on Eleven Fire Crackers  , and instantly remember why this was a 2 second buy decision back at some music store in Shinjuku. I picked it up while working in Tokyo a few years back. I was going crazy over the local bands, and this album by ELLEGARDEN was kind of lost in all the great music at the time. |
Having just rediscovered ELLEGARDEN, it's sad to now discover I am just a month late - they officially suspend their activities indefinitely in September 2008 and go onto other things.
So no chance to see them live anymore (at least as ELLEGARDEN), only go back and checkout their other albums. I can't imagine anything better than Eleven Fire Crackers
. But maybe I have some treasures to discover yet...read more and comment..
Get Motivated
| I hate motivation books; all that sickly rah-rah and exultations that you too can be like Donald Trump if you just repeat to yourself three times: "I am a success. I am a genius. People love me." Justin Herald's book Get Motivated  is refreshingly different, and a thought-provoking read. You may find it in the bookstore in the "Management Self-help Guru" section, but it is probably better classified under sociology.This is about common sense philosophy for real people. Justin Herald tells it like it is, and sometimes you might not like it (ethics are important? you gotta actually work hard? Jeez!). Here's a selection of chapter headings
|
If you don't stand for something, you will fall for anything.
This reminded me of another great quote from Anthony Bourdain on Chef's Story:
My best advice if you are starting out and want to be a success: set yourself high standards and stick to them.(or words to that effect ...)
A refreshing read, and highly recommended. It may be just what you need to get a fresh perspective and work towards being a more positive life. Or not. I'll leave you with The Bitter Stick Girl's brilliant observation:
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Synchronising two directory trees - tree-sync 2.4
tree-sync.pl has had a little update thanks to a contribution from Dave Stafford.
- Added option 'diff' to view only changes
- Added option 'ignore' to exclude certain extensions
- Added option 'brief' to remove src/dest directories in report view to make cleaner output
In the 2.4 release I've also added the 'force' option to control read-only file handling.
tree-sync.pl is a bit of a geeky tool, suitable for cases where you want detailed control over a file-based copy/mirror/backup process from the command-line. There are many flashier solutions available these days, but if tree-sync scratches your itch - go for it!
tree-sync.pl continues to be available on CPAN, but from the 2.4 release I have moved the source to github. If you have changes to suggest or bugs to fix, please go ahead and join this project.
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Rolling Project Euler on Ruby
I first heard about Project Euler last week on the stackoverflow podcast. Michael Pryor (fogcreek co-founder) makes a quick side reference in discussion with Joel Spolsky, Jeff Atwood and the rest of the SO team.
Well I checked it out last week, got hooked and spent most of the weekend earning my "level 1" badge;-)
Aside from dusting off some long-forgotten and arcane knowledge from my youth, I found it a fantastic opportunity to stretch my fundamental ruby chops. In fact, I'd recommend a few questions at Project Euler as a right-of-passage whenever you are learning a new programming language.
I've only been using ruby for a year or so, and in that time thought I had picked up a fair bit. But I was still able to amaze myself at just how many of the problems were knocked over in just 1 or 2 lines with a bit of duck punching and liberal use of blocks with Enumerables.
I'm late to the Project Euler craze, so you will already find many people posting hints for specific questions if you just google. I thought I'd share some of the "common code" I've been building up as I go through the questions.
I put a recent copy of the source up on github for anyone who is interested (MyMath.rb), but what follows a sampling of some of the more interesting pieces.
First thing you will note is that I have written all these "common" routines as extensions to some of the fundamental classes in the ruby library: Integer, Array, String.
It doesn't have to be this way, and for less trivial activities you might be right to be concerned about messing with the behaviour of the standard classes. Maybe I'm still enjoying my ruby honeymoon period, but I do get a thrill out of being able to write things like
1551.palindrome?
=> true
Integer Extensions
It's just so easy to code up simple calculation and introspection routines..
class Integer
# @see project euler #15,20,34
def factorial
(2..self).inject(1) { |prod, n| prod * n }
end
# sum of digits in the number, expressed as a decimal
# @see project euler #16, 20
def sum_digits
self.to_s.split('').inject(0) { |memo, c| memo + c.to_i }
end
# num of digits in the number, expressed as a decimal
# @see project euler #25
def num_digits
self.to_s.length
end
# tests if all the base10 digits in the number are odd
# @see project euler #35
def all_digits_odd?
self.to_s.split('').inject(0) { |memo, s| memo + ( s.to_i%2==0 ? 1 : 0 ) } == 0
end
# generates triangle number for this integer
# https://en.wikipedia.org/wiki/Triangle_number
# @see project euler #42
def triangle
self * ( self + 1 ) / 2
end
end
Prime numbers feature heavily on Project Euler, and I think calculating a prime series was my first lesson on why you can't brute-force everything;-) Enter the Sieve of Eratosthenes and related goodness..
class Integer
# https://en.wikipedia.org/wiki/Prime_factor
# @see project euler #12
def prime_factors
primes = Array.new
d = 2
n = self
while n > 1
if n%d==0
primes << d
n/=d
else
d+=1
end
end
primes
end
# https://en.wikipedia.org/wiki/Divisor_function
# @see project euler #12
def divisor_count
primes = self.prime_factors
primes.uniq.inject(1) { |memo, p| memo * ( ( primes.find_all {|i| i == p} ).length + 1) }
end
#
# @see project euler #12, 21, 23
def divisors
d = Array.new
(1..self-1).each { |n| d << n if self % n == 0 }
d
end
# @see project euler #
def prime?
divisors.length == 1 # this is a brute force check
end
# prime series up to this limit, using Sieve of Eratosthenes method
# https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
# @see project euler #7, 10, 35
def prime_series
t = self
limit = Math.sqrt(t)
a = (2..t).to_a
n = 2
while (n < limit) do
x = n*2
begin
a[x-2]=2
x+=n
end until (x > t )
begin
n+=1
end until ( a[n-2] != 2 )
end
a.uniq!
end
# @see project euler #23
def perfect?
self == divisors.sum
end
# @see project euler #23
def deficient?
self > divisors.sum
end
# @see project euler #23
def abundant?
self < divisors.sum
end
end
Next we visit the Collatz conjecture and an interesting routine to make numbers "speak english"..
class Integer
# https://en.wikipedia.org/wiki/Collatz_conjecture
# @see project euler #14
def collatz_series
a = Array.new
a << n = self
while n > 1
if n % 2 == 0
n /= 2
else
n = 3*n + 1
end
a << n
end
a
end
# express integer as an english phrase
# @see project euler #17
def speak
case
when self <20
["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten",
"eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen" ][self]
when self > 19 && self < 100
a = ["twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety"][self / 10 - 2]
r = self % 10
if r == 0
a
else
a + "-" + r.speak
end
when self > 99 && self < 1000
a = (self / 100).speak + " hundred"
r = self % 100
if r == 0
a
else
a + " and " + r.speak
end
when self > 999 && self < 10000
a = (self / 1000).speak + " thousand"
r = self % 1000
if r == 0
a
else
a + ( r <100 ? " and " : " " ) + r.speak
end
else
self
end
end
end
Calculating integer partitions is one of my favourites ... a nice, super-fast recursive algorithm. For problems like "how many ways to make $2 in change?"
class Integer
# calculates integer partitions for given number using array of elements
# https://en.wikipedia.org/wiki/Integer_partition
# @see project euler #31
def integer_partitions(pArray, p=0)
if p==pArray.length-1
1
else
self >= 0 ? (self - pArray[p]).integer_partitions(pArray ,p) + self.integer_partitions(pArray,p+1) : 0
end
end
end
Finally, rotations and palindromes (base 2 or 10): methods that rely on some underlying String routines that come later...
class Integer
# returns an array of all the base10 digit rotations of the number
# @see project euler #35
def rotations
self.to_s.rotations.collect { |s| s.to_i }
end
# @see project euler #4, 36, 91
def palindrome?(base = 10)
case base
when 2
sprintf("%0b",self).palindrome?
else
self.to_s.palindrome?
end
end
end
Array Manipulations
Array handling is particularly important. Start with some simple helpers, then move onto greatest common factor and a couple of least-common multiple implementations. My favourite here - lexicographic permutations.
class Array
# sum elements in the array
def sum
self.inject(0) { |sum, n| sum + n }
end
# sum of squares for elements in the array
# @see project euler #6
def sum_of_squares
self.inject(0) { |sos, n| sos + n**2 }
end
# @see project euler #17
def square_of_sum
( self.inject(0) { |sum, n| sum + n } ) ** 2
end
# index of the smallest item in the array
def index_of_smallest
value, index = self.first, 0
self.each_with_index {| obj, i | value, index = obj, i if obj<value }
index
end
# removes numbers from the array that are factors of other elements in the array
# @see project euler #5
def remove_factors
a=Array.new
self.each do | x |
a << x if 0 == ( self.inject(0) { | memo, y | memo + (x!=y && y%x==0 ? 1 : 0) } )
end
a
end
# http://utilitymill.com/edit/GCF_and_LCM_Calculator
# @see project euler #5
def GCF
t_val = self[0]
for cnt in 0...self.length-1
num1 = t_val
num2 = self[cnt+1]
num1,num2=num2,num1 if num1 < num2
while num1 - num2 > 0
num3 = num1 - num2
num1 = [num2,num3].max
num2 = [num2,num3].min
end
t_val = num1
end
t_val
end
# http://utilitymill.com/edit/GCF_and_LCM_Calculator
# @see project euler #5
def LCM
a=self.remove_factors
t_val = a[0]
for cnt in 0...a.length-1
num1 = t_val
num2 = a[cnt+1]
tmp = [num1,num2].GCF
t_val = tmp * num1/tmp * num2/tmp
end
t_val
end
# brute force method:
# http://www.cut-the-knot.org/Curriculum/Arithmetic/LCM.shtml
# @see project euler #5
def lcm2
a=self.remove_factors
c=a.dup
while c.uniq.length>1
index = c.index_of_smallest
c[index]+=a[index]
end
c.first
end
# returns the kth Lexicographical permutation of the elements in the array
# https://en.wikipedia.org/wiki/Permutation#Lexicographical_order_generation
# @see project euler #24
def lexicographic_permutation(k)
k -= 1
s = self.dup
n = s.length
n_less_1_factorial = (n - 1).factorial # compute (n - 1)!
(1..n-1).each do |j|
tempj = (k / n_less_1_factorial) % (n + 1 - j)
s[j-1..j+tempj-1]=s[j+tempj-1,1]+s[j-1..j+tempj-2] unless tempj==0
n_less_1_factorial = n_less_1_factorial / (n- j)
end
s
end
# returns ordered array of all the lexicographic permutations of the elements in the array
# https://en.wikipedia.org/wiki/Permutation#Lexicographical_order_generation
# @see project euler #24
def lexicographic_permutations
a=Array.new
(1..self.length.factorial).each { |i| a << self.lexicographic_permutation(i) }
a
end
end
String Helpers
Last but not least, some String methods that just make things so much easier...
class String
# sum of digits in the number
# @see project euler #16, 20
def sum_digits
self.split('').inject(0) { |memo, c| memo + c.to_i }
end
# product of digits in the number
# @see project euler #8
def product_digits
self.split('').inject(1) { |memo, c| memo * c.to_i }
end
#
# @see project euler #4, 36, 91
def palindrome?
self==self.reverse
end
# returns an array of all the character rotations of the string
# @see project euler #35
def rotations
s = self
rots = Array[s]
(1..s.length-1).each do |i|
s=s[1..s.length-1]+s[0,1]
rots << s
end
rots
end
end
With all the above in place - and with the aid of a few brain cells - some deceptively complicated questions (like "How many different ways can £2 be made using any number of coins?") are essentially one-liners:
require 'benchmark'
require 'MyMath'
Benchmark.bm do |r|
r.report {
answer = 200.integer_partitions([200,100,50,20,10,5,2,1])
}
end
Love it;-)
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