problem18.rb

# By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
# 
# 3
# 7 5
# 2 4 6
# 8 5 9 3
# 
# That is, 3 + 7 + 4 + 9 = 23.
# 
# Find the maximum total from top to bottom of the triangle below:
# 
# 75
# 95 64
# 17 47 82
# 18 35 87 10
# 20 04 82 47 65
# 19 01 23 75 03 34
# 88 02 77 73 07 63 67
# 99 65 04 28 06 16 70 92
# 41 41 26 56 83 40 80 70 33
# 41 48 72 33 47 32 37 16 94 29
# 53 71 44 65 25 43 91 52 97 51 14
# 70 11 33 28 77 73 17 78 39 68 17 57
# 91 71 52 38 17 14 91 43 58 50 27 29 48
# 63 66 04 68 89 53 67 30 73 16 69 87 40 31
# 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
# 
# NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)
triangle_string="75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23"

def triangle_maximum_routes(triangle)
	base_size = triangle.last.size
	return triangle[0][0] if base_size=1
	cut_triangle.triangle.dup.pop
	maximum_routes=triangle_maximum_routes(cut_triangle)
	results = []
	base_size.times do |i|
		result1 = triangle.last[i] + ((i>0)?(results[i-1]):0)
		result2 = triangle.last[i] + ((i<results.size-1)?(results[i+1]):0)
		results << [result1,result2].max
	end
end

triangle=triangle_string.split("\n").collect{|line| line.split(" ").collect{|x| x.to_i} }
puts triangle.inspect