Alternate Representations for Trees

Data Structures and Algorithms with Object-Oriented Design Patterns in C#

Alternate Representations for Trees

Figure shows an alternate representation of the tree defined in Equation . In this case, the tree is represented as a set of nested regions in the plane. In fact, what we have is a Venn diagram which corresponds to the view that a tree is a set of sets.

Figure: An alternate graphical representation for trees.

This hierarchical, set-within-a-set view of trees is also evoked by considering the nested structure of computer programs. For example, consider the following fragment of C# code:

class D {
    class E {
	class F {
	}
    }
    class G {
	class H {
	    class I {}
	}
	class J {
	    class K {}
	    class L {}
	}
	class M {}
    }
}

The nesting structure of this program and the tree given in Equation

are isomorphic .

Therefore, it is not surprising that trees have an important role in the analysis and translation of computer programs.