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11.1 EXPANDING THE ALGORYTHMICS COLLECTION 117
The array to be sorted can easily be “transformed” into a binary tree using
the formula: the first element of the array is the root, the child nodes of every
internal node i are located (if they exist) in the array at the [2i] and [2i + 1] po¬
sitions. When programming this method, the translation of the array positions
into binary tree nodes is straightforward with the given formula.
We first tried to represent this algorithm linearly as well. Since we found
the resulted choreography draft to be too complicated, we decided to explicitly
visualize the tree structure and to illustrate the sorting strategy on this 2D scene
(see Figure 11.1). At the beginning of the performance, the dance couples (rep¬
resenting the numbers) are arranged linearly as they are stored in the array. Asa
next step, the array opens into a binary tree representing the heap. The operation
sequence of the algorithm is visualized on this 2D structure. As the numbers
reach their final positions, the corresponding dance couples return to the array.
11.1.2 Including new dance styles
The first six choreographies are based on different folk dance styles, and
the numbers are represented by individual dancers. In the case of heap sort, as
mentioned above, we used a folk dance (“Mezéségi”) choreography, in which
the numbers are represented by couples (see Figure 11.1).
Besides, based on the large number of foreign views (from other regions
than Transylvania), we decided to internationalize the music and the chore¬
ography of the demonstrative dances. This way, a new style was introduced,
where algorithm visualizations make use of the rhythm and style of the well¬
known southern Spanish flamenco (see figures 11.2-3). Flamenco was declared
by UNESCO one of the “masterpieces of the oral and intangible heritage of hu¬
manity” (UNESCO, 2010). This art form fits perfectly into the cultural-artistic
framework of our project since, according to the criteria for inscription into
UNESCO, “it is strongly rooted in its community, strengthening its cultural
identity and continuing to be passed down from one generation to the next”. It
can also be considered that there was a dual change as flamenco is not exactly
a folk dance, and it is from a different region.
To increase the diversity of the AlgoRythmics collection, the last element
we added illustrates the algorithm by a professional ballet choreography (see
Figure 11.4).
11.1.3 Moving on to a new algorithm family
As sorting algorithms were covered by the first seven choreographies, we
decided to move on to another very commonly used algorithm family, the search¬
ing algorithms. These algorithms can be classified based on their mechanism of
searching: linear, binary, and backtracking search.