Tracking Santa

December 24, 2010

Each year since 1955, Norad has tracked Santa Claus on his annual journey to deliver toys to good little girls and boys around the world. Since Santa must file his flight plan in advance, we already know where his journey will take him: the route at is reproduced on the next page.

Your task is to calculate the number of miles that Santa will travel during his journey; you might find Wikipedia’s Great-circle distance page helpful. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.


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8 Responses to “Tracking Santa”

  1. […] today’s Programming Praxis, our task is to calculate the total distance traveled by Santa based on data […]

  2. My Haskell solution (see for a version with comments):

    import Data.List.HT
    import Text.HJson
    import Text.HJson.Query
    dist :: RealFloat a => (a, a) -> (a, a) -> a
    dist (lat1, lng1) (lat2, lng2) =
      let toRad d = d * pi / 180
          haversin x = sin (toRad $ x / 2) ^ 2
          a = haversin (lat2 - lat1) +
              cos (toRad lat1) * cos (toRad lat2) * haversin (lng2 - lng1)
      in 2 * 6371 * atan2 (sqrt a) (sqrt (1 - a))
    coords :: Json -> [(Double, Double)]
    coords = map ((\[JString lat, JString lng] -> (read lat, read lng)) .
                  getFromKeys ["lat", "lng"]) . getFromArr
    totalMiles :: RealFloat a => [(a, a)] -> Int
    totalMiles = round . (* 0.621371192) . sum . mapAdjacent dist
    main :: IO ()
    main = either print (print . totalMiles . coords) . fromString .
           drop 16 =<< readFile "santa.txt"
  3. Hey guys,

    I’m new to Ruby so I did my best to throw this together in about 30 min…

    My solution

    Any help and comments are welcome!

  4. Jebb said

    With the file data.js saved in the same directory, having deleted the ‘var locations = ‘ bit at the beginning:

    def read_locations(file_name):
    	import json
    	f = open(file_name, 'r')
    	locations = json.load(f)
    	return locations
    def distance(pointA, pointB):
    	from math import radians, cos, acos
    	lat1 = radians(float(pointA['lat']))
    	lat2 = radians(float(pointB['lat']))
    	dlat = lat2 - lat1
    	dlong = radians(float(pointB['lng']) - float(pointA['lng']))
    	ang_dist = acos(cos(dlat) - cos(lat1) * cos(lat2) * (1 - cos(dlong)))
    	return 6371 * ang_dist
    def main():
    	locations = read_locations('data.js')
    	journey = 0
    	for i in range(len(locations) - 1):
    		journey += distance(locations[i], locations[i+1])
    	print 'Total distance traveled %.0f km' % journey
    if __name__ == '__main__':

    that’s 320,627 km to the metric-inclined.

  5. Graham said

    A few days late, but here’s my Python
    version. I went with the arctangent formula given by Wikiepdia, which it calls
    “a more complicated formula that is accurate for all distances.” I also followed
    Jebb’s lead of saving “data.js” with the var locations = portion
    removed. This can be run (at least on my system) with ./ data.js.

  6. Actually I screwed up my first solution, this is correct I believe:

  7. Mike said

    Another Python version.

    Download the data.js and save to Edit the first line to remove “var “, so it starts with “location =”.
    Remove the “;” from the last line. This creates a python compatible statement defining ‘locations’ to be a list of dictionaries. Importing ‘santaflightpath’ executes the code in the file, so there are clearly security implications.

    pairwise is from the recipies in the itertools documentation.

    Of interest, the flight plan is 28 hours long; stays within 600 miles of the north pole for the first 4 hours; doesn’t appear to visit Antarctica; and doesn’t return to the starting point.

    from santaflightplan import locations
    from math import asin, sin, cos, radians, sqrt
    from itertools import starmap
    from utils import pairwise

    earth_radius = 3958.76 #average

    def distance(p1, p2):
    lat1, lng1 = map(radians, p1)
    lat2, lng2 = map(radians, p2)
    dlat = lat1 – lat2
    dlng = lng1 – lng2
    ang = 2*asin(sqrt(sin(dlat/2)**2 + cos(lat1)*cos(lat2)*sin(dlng/2)**2))
    return ang * earth_radius

    locs = ((float(p[‘lat’]),float(p[‘lng’])) for p in locations)
    print sum(starmap(distance, pairwise(locs)))

  8. With a little delay, my commented Python version (looks like the one above

    def get_coords():
        from json import load
        f = open("data.js", encoding='utf-8')
        l = load(f)
        return l
    def distance(o1, o2):
        from math import radians, cos, sin, acos
        lat1, lng1 = radians(float(o1['lat'])), float(o1['lng'])
        lat2, lng2 = radians(float(o2['lat'])), float(o2['lng'])
        sins = sin(lat1) * sin(lat2)
        coss = cos(lat1) * cos(lat2)
        da = acos(sins + coss * cos(radians(lng2 - lng1)))
        return 6372.8 * da * 0.621371192
    def track_santa():
        l = get_coords()
        res = 0
        for i in range(len(l) - 1):
            res = res + distance(l[i], l[i+1])
        return res
    if __name__ == "__main__":
        d = track_santa()

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