Dancing Algorithms

Yes, it appears that the two can go together. Not in that the algorithms are dancing, but one can do a dance with a choreography such that it demonstrates an algorithm. Zoltan Katai and Laszlo Toth from Romania came up with the idea of this intercultural computer science education [1], with a theoretical motivation traced all the way back to Montessori. It has nothing to do with the scope of my earlier post on folk dancing and cultural heritage preservation, yet at the same time, it contributes to it: watching the videos of the dances immerses you in the folk music, rhythm, the traditional clothes of the region, and some typical steps and and movements used in their dances.

The context, in short: learning to program is not easy for most students—as our almost 900 first-year students are starting to experience from next week onwards—and especially understanding the workings of algorithms. Katai and Toth’s approach is to involve ‘playing out’ the algorithm with people, not by clumsily walking around, but using folk dance and music to make students understand and remember it more easily. They took several sorting algorithms to demonstrate the idea, and tested it on their students, demonstrating that it improved understanding significantly [1].

Perhaps because of my bias toward the dancing, I didn’t take note of the algorithm being danced-out when I watched it the first time, or perhaps it is useful to have read the core steps of the algorithm before watching anyway. You choose: watch the video of the selection sort algorithm—given a list, repeatedly select the smallest remaining element and move that to the ‘sorted’ section of the list—with a Gypsy (Roma) folk dance, or read further below what selection sort is. (note: the video goes on double speed in the middle, for it gets a bit repetitive.)

So, what was happening in the dance? We have one ‘comparer’ (x, for short) and one ‘compared with’ (y). The left-most dancer, with number 3 (our first value of x), starts to dance to the front, calls on the second one in line, being the guy with 0 (our first y), he swirls her back in the line in the spot he came from and stays at the front (0 being the new value of x), and calls on the next, the lady with the 1 (the new value of y), who gets back in the line; and so on till the last one (with number 6). Dancer 0 does a solo act and goes to the first spot: he’s now the first one in the ‘sorted’ part, and we have completed one iteration. Starting with the second main iteration: now number 3 is again at the front of the unsorted, and she dances again to the front (so the value of our x is 3 at this point), calling the second one in the unsorted list, who has number 1, so the lady with number 3 goes back in the unsorted again, and the dancer with 1 continues through the remainder of the list, has her solo, and joins the guy with the 0 in the sorted part, having completed the second main iteration. And so on until about 6:20 minutes into the video clip when the list is sorted and the dancers do a little closing act.

A bit more structured, the following is happening in the choreography of the dance in the video:

  1. Divide the list into a ‘sorted’ part (initially empty) and an ‘unsorted’ part (initially the list you want to sort)

  2. Do for as long as there’s more than one item in the ‘unsorted’ (find the smallest item in that list):

    1. select first element of the unsorted list (with some value, that we refer to with x)

    2. if we’re not at the end of the ‘unsorted’ list, then get the next element of the ‘unsorted’ list (with some value, let’s call that one y)

      1. if x < y, then y is put back in the same spot in the unsorted list, and we return to the start of step (b) to get the next item to test x against (being the one after the one we just tested)

      2. else (i.e., x > y), then the value of x takes y‘s spot in the unsorted list, we assign the value of y to x, and we return to the start of step (b) to get the next element from the unsorted list

    3. else (i.e., we’re at the end of the list and thus x is the lowest value), place (the value of) x in the next available spot in the ‘sorted’ part. Then go back to the start of step 2.

  3. Place the last item from ‘unsorted’ at the end of the ‘sorted’.

  4. Done (i.e., there’s nothing more in ‘unsorted’ to sort)

The algorithm itself is less cumbersome by not having those “let’s pick out one and come to the front” steps, but direct comparisons. I did not plan to include here, but do after all for it makes a nice sequence of artsy → informal analysis → semi-precise structure → specification the computer can work with. (Never mind that that was not the order things came about). Using our CSC1015F course material (2012 samples) that teaches Python, one of the possible sample code snippets is as follows:

def selection_sort ( values ):
   """Sort values using selection sort algorithm."""
   # iterate over outer positions in list
   for outer in range (len (values)):
      # assume first value is minimum
      minimum = outer
      # compare minimum to rest of list and update
      for inner in range (outer+1, len (values)):
         if values[inner] < values[minimum]:
            minimum = inner
      # swap minimum with outer position
      temp = values[minimum]
      values[minimum] = values[outer]
      values[outer] = temp
   return values

This is not the only way of achieving it, btw, and the 1017F lecture and lab lecture files have another version of achieving the same (I just thought that this one may be more readable by non-CS readers of the post).

Other danced sorting algorithms are insertion sort (video) with Romanian dance, and shell-sort (video) and bubble sort (video) on Hungarian dances, and more information is also available from the Algo-rythmics website. This isn’t new, and dances on many other tunes can be viewed on youtube, e.g., various bubble-sort dances. Reconstructing the bubble-sort algorithm from the dance below (5min, no fastforward) is an exercise left to the reader… likewise making dances on other algorithms (the ICPC’14 solution to the baggage problem seems like a fun candidate line dance-like), and the same dances but with other folk dances and music.

References

[1] Zoltan Katai and Laszlo Toth. Technologically and artistically enhanced multi-sensory computer programming education. Teaching and Teacher Education, 2010, 26(2): 244-251.

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