A solution for a sample combo-geo-polyline detour problem (from Sendy's Combined Orders Use Case challenge)

Given two geo-polylines AD and BC, come up with an algorithm to determine the "detour" associated with their combined geo-polyline and further determine if the detour is negligible enough for one to traverse the combined geo-polyline.

The detour can be expressed as the ratio of twice the length of common or overlapping sections to the sum of both the polyline lengths, i.e 2*len(ol)/(len(ad)+len(bc)) where ol is the overlapping segment polyline and ad & bc are the given geo-polylines. The acceptable detour can be specified as a detour ratio threshold.

• There should be only one set of overlapping segments.
• Overlapping segments will have the same points save for the first and last points of the overlapping polyline.

It's "brute force"-ish and it goes a little something like this:-

1. initialize ad polyline from user input
2. initialize bc polyline from user input
3. initialize overlap polyline to empty points list

4. for each segment in ad
      while overlap polyline is empty
          fetch next bc segment
          if ad and bc segments overlap
              add starting overlap point to overlap polyline
          if at end of bc list

      if overlap is not empty
          if ad and bc segment endpoints differ
              add the least
          else
              add ad segment endpoint to overlap
          fetch next bc segment

4. get overlap length
5. get ad length
6. get bc length
7. return => overlap_length x 2 / (ad_length + bc_length )... aka detour ratio as defined above

The algorithm takes worst case O(ad * bc) time.

Implementation resides in py27/couc.py. Run it like so:-

./couc.py -ad "[[1,2],[17,2]]" -bc "[[3,2],[14,2]]" -t 0.8 (or couc.py on Windows)

Where -ad and -bc are your polylines expressed as json arrays of 2 element arrays (or tuples if you like) and -d is your acceptable "detour ratio" threshold with valid i/p from 0-1.

Test cases reside in py27/test.py. Takes no arguments. Run like so:- ./test.py (or test.py on Windows).