CEditDist Abstract Template Class for Edit Distance Calculation on Generic Data Types

Environment: Any modern C++ compiler

Purpose

The CEditDist class performs edit distance calculations on abstract data types.  The edit distance is defined as the minimum cost required to convert one string into another, where the conversion can include changing one character to another, deleting characters and inserting characters, with user-defined costs for each basic operation.  The algorithm is O(nm) where n and m are the lengths of the two strings compared (this is the fastest known algorithm).  Edit distance calculations are useful for finding the degree of similarity between strings, e.g. in non-exact database queries.

The package is implemented as an abstract template base class.  The programmer derives from this base class in order to define the data types used and the cost functions.  The package includes complete documentation and an example of a simple implementation.

Example

Overview:
This example will create a class that can be used to calculate the edit distance between two arrays of integers, according to the following cost function: Deleting or inserting an integer will have a cost of 5; Changing from one integer value to a different value will have a cost of 3.

Step 1: Instantiate the Base Class.
The instantiation must be explicitly performed because of the special treatment of abstract template classes in C++.  In our case, we want a base class of integers, so we will use the following statement:

template class CEditDist<int>;

Step 2: Derive from CEditDist.
We must now create a derivation from the base class.  This derivation will define the cost functions, which are virtual functions called from the base class during the edit distance calculation.

class CIntEditClass : public CEditDist<int>
{
public:
   int DeleteCost(const int& deleted, int x, int y) { return 5; };
   int InsertCost(const int& inserted,int x, int y) { return 5; };
   int ChangeCost(const int& from, const int& to, int x, int y)
         { return (from==to ? 0 : 3); };
};

Step 3: Using the Class.
To use the class, construct an object from the base class and call its EditDistance function, like so:

CIntEditDist ed;
int a[7] = {1,1,2,3,1,2,2};
int b[6] = {1,2,2,3,1,1};
int c = ed.EditDistance(a,7,b,6);

In the above example, the edit distance stored in variable c should be 11.  This is because the least expensive edit replaces the second character in a from 1 to 2, replaces the sixth character from 2 to 1, and deletes the last character in a, for a total of two changes and one deletion, with a cost of 3+3+5=11.

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