prob8.rb

# 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

# ==================================  Utils ===================================
def input_string
  result = "73167176531330624919225119674426574742355349194934"
  result += "96983520312774506326239578318016984801869478851843"
  result += "85861560789112949495459501737958331952853208805511"
  result += "12540698747158523863050715693290963295227443043557"
  result += "66896648950445244523161731856403098711121722383113"
  result += "62229893423380308135336276614282806444486645238749"
  result += "30358907296290491560440772390713810515859307960866"
  result += "70172427121883998797908792274921901699720888093776"
  result += "65727333001053367881220235421809751254540594752243"
  result += "52584907711670556013604839586446706324415722155397"
  result += "53697817977846174064955149290862569321978468622482"
  result += "83972241375657056057490261407972968652414535100474"
  result += "82166370484403199890008895243450658541227588666881"
  result += "16427171479924442928230863465674813919123162824586"
  result += "17866458359124566529476545682848912883142607690042"
  result += "24219022671055626321111109370544217506941658960408"
  result += "07198403850962455444362981230987879927244284909188"
  result += "84580156166097919133875499200524063689912560717606"
  result += "05886116467109405077541002256983155200055935729725"
  result += "71636269561882670428252483600823257530420752963450"

  result
end

def convert_to_fixnum_array num_string
  num_string.split('').map(&:to_i)
end

def compute_product_of_five_tuples num_array
  result = []

  iterations = num_array.length - 4

  return result if iterations < 1

  iterations.times do |index|
    last_index = index + 4
    product = num_array[index..last_index].inject &:*

    result.push(product)
  end


  result
end

# =================================  Solution ==================================
# First pass: build the naive implementation: step through each grouping of 5
# digits, starting with the first 5.  This would give 996
# multiplication-of-five-numbers to perform (my first estimate was 200)

target = input_string

input_digit_array = convert_to_fixnum_array(target)

input_products = compute_product_of_five_tuples input_digit_array

puts input_products.length

result = input_products.max

puts "The largest product of 5 consecutive digits of the input string is: #{result}"


# ==========================  Potential improvements ===========================
# Since a grouping including a zero automatically results in the least possible
# product, this large number can be split up, using the zeroes as delimiters.
# At first glance, this looks like a huge reduction in the number of
# multiplications needed.

# A better implementation might memoize multiplications, since any 3
# consecutive digits will be used in 3 separate calculations, but perhaps YAGNI