problem11.rb

# http://projecteuler.net/index.php?section=problems&id=11
# Problem 11
# What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 20X20 grid?

m = [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
      [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
      [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
      [ 1, 1, 1, 8, 2,22,97,38,15, 0,40, 0,75, 4, 5, 7,78,52,12,50,77,91, 8, 1, 1, 1],
      [ 1, 1, 1,49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48, 4,56,62, 0, 1, 1, 1],
      [ 1, 1, 1,81,49,31,73,55,79,14,29,93,71,40,67,53,88,30, 3,49,13,36,65, 1, 1, 1],
      [ 1, 1, 1,52,70,95,23, 4,60,11,42,69,24,68,56, 1,32,56,71,37, 2,36,91, 1, 1, 1],
      [ 1, 1, 1,22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80, 1, 1, 1],
      [ 1, 1, 1,24,47,32,60,99, 3,45, 2,44,75,33,53,78,36,84,20,35,17,12,50, 1, 1, 1],
      [ 1, 1, 1,32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70, 1, 1, 1],
      [ 1, 1, 1,67,26,20,68, 2,62,12,20,95,63,94,39,63, 8,40,91,66,49,94,21, 1, 1, 1],
      [ 1, 1, 1,24,55,58, 5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72, 1, 1, 1],
      [ 1, 1, 1,21,36,23, 9,75, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95, 1, 1, 1],
      [ 1, 1, 1,78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92, 1, 1, 1],
      [ 1, 1, 1,16,39, 5,42,96,35,31,47,55,58,88,24, 0,17,54,24,36,29,85,57, 1, 1, 1],
      [ 1, 1, 1,86,56, 0,48,35,71,89, 7, 5,44,44,37,44,60,21,58,51,54,17,58, 1, 1, 1],
      [ 1, 1, 1,19,80,81,68, 5,94,47,69,28,73,92,13,86,52,17,77, 4,89,55,40, 1, 1, 1],
      [ 1, 1, 1, 4,52, 8,83,97,35,99,16, 7,97,57,32,16,26,26,79,33,27,98,66, 1, 1, 1],
      [ 1, 1, 1,88,36,68,87,57,62,20,72, 3,46,33,67,46,55,12,32,63,93,53,69, 1, 1, 1],
      [ 1, 1, 1, 4,42,16,73,38,25,39,11,24,94,72,18, 8,46,29,32,40,62,76,36, 1, 1, 1],
      [ 1, 1, 1,20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74, 4,36,16, 1, 1, 1],
      [ 1, 1, 1,20,73,35,29,78,31,90, 1,74,31,49,71,48,86,81,16,23,57, 5,54, 1, 1, 1],
      [ 1, 1, 1, 1,70,54,71,83,51,54,69,16,92,33,48,61,43,52, 1,89,19,67,48, 1, 1, 1],
      [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
      [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
      [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]
      
vectors = [
  [[0,0], [0,1], [0,2],[0,3]],
  [[0,0], [1,0], [2,0],[3,0]],
  [[0,0], [1,1], [2,2],[3,3]],
  [[0,0], [1,-1], [2,-2],[3,-3]],
  [[0,0], [-1,1], [-2,2],[-3,3]],  
  [[0,0], [-1,-1], [-2,-2],[-3,-3]]
  ]
  

highest = 0  
(0...20).each do |x|
  x += 3
  (0...20).each do |y|
    y += 3

    vectors.each do |v|
      prod = v.inject(1) do |p, i|
        p * m[x + i[0]][y + i[1]]
      end
      highest = prod if prod > highest
    end
  end
end
puts highest

# => 70600674