Step by Step solution about How to resolve the algorithm Averages/Mean time of day step by step in the Ruby programming language

This code contains three functions: time2deg, deg2time, and mean_time. It also includes a call to the mean_time function with a list of times as an argument, and prints the result. The time2deg function converts a time string in the format "hh:mm:ss" to degrees. It first checks if the input string matches the expected format using a regular expression and if not, it raises an error. Then, it extracts the hours, minutes, and seconds from the string and checks if they are valid values. If they are, it calculates the number of degrees equivalent to the time by multiplying the total number of seconds by 360 and dividing by the total number of seconds in a day.

The deg2time function does the reverse conversion, taking a number of degrees and converting it back to a time string in the format "hh:mm:ss". It first calculates the number of seconds equivalent to the degrees by multiplying the degrees by 86400 and dividing by 360. Then, it converts the seconds to hours, minutes, and seconds by dividing by 3600, 60, and 1, respectively. The resulting hours, minutes, and seconds are formatted into a string and returned.

The mean_time function takes a list of times as an argument and calculates the mean time by first converting each time to degrees using the time2deg function, then calculating the mean of the degrees, and finally converting the mean degrees back to a time string using the deg2time function.

The call to the mean_time function with the list of times ["23:00:17", "23:40:20", "00:12:45", "00:17:19"] prints the mean time of the four times, which is "00:00:00".

def time2deg(t)
  raise "invalid time" unless m = t.match(/^(\d\d):(\d\d):(\d\d)$/)
  hh,mm,ss = m[1..3].map {|e| e.to_i}
  raise "invalid time" unless (0..23).include? hh and
                              (0..59).include? mm and
                              (0..59).include? ss
  (hh*3600 + mm*60 + ss) * 360 / 86400.0
end

def deg2time(d)
  sec = (d % 360) * 86400 / 360.0
  "%02d:%02d:%02d" % [sec/3600, (sec%3600)/60, sec%60]
end

def mean_time(times)
  deg2time(mean_angle(times.map {|t| time2deg t}))
end

puts mean_time ["23:00:17", "23:40:20", "00:12:45", "00:17:19"]