Wednesday, February 23, 2011

Project Euler–Problem 8

Description

From Project Euler:
Find the greatest product of five consecutive digits in the 1000-digit number.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Solution

This problem is another one that is very easy to brute force, especially since Ruby has some nice built-in methods that make it a no brainer. One thing we will need is an easy way to take a number and break it up into it’s digits. For that a simple method added to the Integer class will do.
class Integer
 def digits
  self.to_s.split('').map { |s| s.to_i }
 end
end
This method doesn’t do much, it converts the number to a string, splits it into individual characters, then converts the characters back into integers. Again, simple, but this method will come in handy for this problem as well as several in the future.
The first thing we need to find is all the combinations of 5 consecutive digits. We can make use of the Enumerable#each_cons method to accomplish this.
class Problem008
 def partition(number)
  number.digits.each_cons(5)
 end
end
This will give us an enumerator that contains arrays of 5 consecutive digits. We can now map each of these arrays to the product of their values.
class Problem008
 def products(number)
  partition(number).map { |a| a.reduce(1, :*) }
 end
end
And the final step, just find the largest product.
THOUSAND_DIGIT_NUM = # number from problem statement
products(THOUSAND_DIGIT_NUM).max

# This could have been written all in one line as
THOUSAND_DIGIT_NUM.digits.each_cons(5).map { |a| a.reduce(1, :*) }.max
The full source and specifications can be seen on github. Next time, finding the only Pythagorean triplet, {a, b, c} for which a + b + c  = 1000.

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