Computes the edit distance between two strings.
The edit distance is defined by the series of operations that transforms the second string into the first one. The allowed operations are:
- Insertion of a character
- Deletion of a character
- Substitution of a character for another For example, the string “kitten” can be transformed into “splitting” as follows: substitute “k” with “s”, insert “p” at position 1, insert “l” at position 2, substitute “e” with “I”, and insert “g” at the end. The sequence of operations is not unique; another possibility is to delete the “k” (one operation), then insert “s” “p” and “l”. Each operation incurs a cost. The edit distance is the cost of the minimum-cost series of operations that accomplishes the desired transformation.
For this problem, the strings will be composed only of letters a-zA-Z. The costs of the operations are as follows:
- insertion of a symbol, cost 3
- deletion of a symbol, cost 2
- substitution of a vowel with another vowel, cost 0.5 (vowels are aeiouAEIOU)
- substitution of a symbol with another (where not both are vowels), cost 1
The program should take as arguments the two strings, and write out the edit distance (the cost of the minimum-cost sequence of operations), as well as the operations themselves.
If there are several sequences with the same cost, print them all out.