Question

I am faced with the problem of representing a Venn diagram as a tree structure in order to process the information as XML.

Do anyone have an elegant way for doing this, or maybe some acute observations?

Please note that I am not able to handle individual elements in the sets. Diagrams would be illustrating situations equivalent to “There are 20 students in all, of which 5 do sports, 8 play chess and 3 do both”.

Answer 1

From your description my understanding is you are talking about dealing with the aggregate data (count for each set) rather than discrete items. So with that assumption, I would first look at how another code base represents Venn Diagrams (Google Chart API)

The Google chart API represents Venn Diagrams using seven values. I have extracted the descripions below from here: http://code.google.com/apis/chart/image/docs/gallery/venn_charts.html

• The first three values specify the sizes of three circles: A, B, and C. For a chart with only two circles, specify zero for the third value.
• The fourth value specifies the size of the intersection of A and B.
• The fifth value specifies the size of the intersection of A and C. For a chart with only two circles, do not specify a value here.
• The sixth value specifies the size of the intersection of B and C. For a chart with only two circles, do not specify a value here.
• The seventh value specifies the size of the common intersection of A, B, and C. For a chart with only two circles, do not specify a value here.

We can apply the same approach to represent your problem domain in XML:

<venn_diagram item_type="Students" item_count="20">
    <set_a name="Play Sports" item_count="5"/>
    <set_b name="Play Chess" item_count="8"/>
    <set_a_and_b name="Play Both" item_count="3"/>
</venn_diagram>

With this information you know enough to draw the diagram.