Finding first intersection of a turtle's path (N,E,S,W)

turtle.rb

def solution(instructions)
  position = [0,0]
  directions = [ 
    [0,1], # north
    [1,0], # east
    [0,-1], # south
    [-1,0] # west
  ]
  current_dir = 0;
  history = []

  instructions.each_with_index do |num_steps,index|
    direction = directions[ index % 4 ] # only 4 directions, 0th step is 0th direction
    history << Array.new(position)
    num_steps.times do 
      position[0] += direction[0]
      position[1] += direction[1]
      # check to see if we've passed here before
      for h_pos in 0..index-1 # don't overflow and get up to the current nil step
        if ( (history[h_pos][0]..history[h_pos+1][0]).include?(position[0]) and (history[h_pos][1]..history[h_pos+1][1]).include?(position[1]) )
          return index+1
        end
      end
    end
  end
  return 0 # no intersection
end

require 'rspec'

describe "solution finds first intersection" do
  it "with given example" do
    solution([1, 3, 2, 5, 4, 4, 6, 3, 2]).should == 7
  end
  it "one instruction" do
    solution([1]).should == 0
  end
  it "maximal instructions" do
    solution([1000000,1000000,1000000,1000000,1000000]).should == 4 # square spiral
  end
  it "minimal instructions" do
    solution([1,1,1,1,1]).should == 4 # square spiral
  end
  it "no intersection" do
    solution([1, 2, 3, 4, 5, 6, 7, 8, 9]).should == 0
  end
end

Interesting solution. It's possible to do it in O(n) time. Your solution is not O(n) though as far as I can see.