michaellang.rb

# Given a series of times, computes the average time for the series, returning the
# calculated average time as a string.
#
# >> average_time_of_day(["11:51pm", "11:56pm", "12:01am", "12:06am", "12:11am"])
# => "12:01am"
# 
# >> average_time_of_day(["6:41am", "6:51am", "7:01am"])
# => "6:51am"

require 'time'

DEGREES_IN_CIRCLE = 360.0
TWENTY_FOUR_HOUR_MINUTES = 24 * 60
DEGREES_PER_MINUTE = DEGREES_IN_CIRCLE / TWENTY_FOUR_HOUR_MINUTES

class Time

  # Treats hours and minutes as "one hand" on a analog clock for 1440 minute clockface
  def degrees
    (self.hour * 60 + self.min) * DEGREES_PER_MINUTE 
  end
  
  # converts degrees to radians
  def radians 
    self.degrees * Math::PI / 180
  end
  
  # computes point on circumference of the imaginary 1440 minute clockface
  def point
    [Math::sin(self.radians), Math::cos(self.radians)]
  end
  
  # given a point on the imaginary 1440 minute clockface, returns time object
  # corresponding to that point.
  def self.at_point(point)
    degrees = Math::atan2(point[0], point[1]) * 180 / Math::PI
    hr = (degrees / DEGREES_PER_MINUTE / 60).to_i
    m = (degrees / DEGREES_PER_MINUTE).round - hr * 60
    parse("#{hr}:#{m}")
  end
end

def average_time_of_day(times)
  # parse the given time strings into Time objects
  real_times = times.map{|m| Time.parse(m)}
  
  # sum up and then take average of the points in the time series 
  sum_pt = real_times.inject([0, 0]) do |pt, t| 
    pt[0] += t.point[0] 
    pt[1] += t.point[1]
    pt
  end
  avg_pt = [sum_pt[0] / times.size, sum_pt[1] / times.size]
  
  # translate the computed average back into time object and print
  Time.at_point(avg_pt).strftime("%I:%M%p").downcase
end