Let x and y be two strings over some finite alphabet A. We would like to transform x into y allowing only operations given below:
Deletion: a letter in x is missing in y at a corresponding position.
Insertion: a letter in y is missing in x at a corresponding position.
Change: letters at corresponding positions are distinct
Certainly, we would like to minimize the number of all possible operations.
Illustration
A G T A A G T * A G G C | | | | | | | A G T * C * T G A C G C
Deletion: * in the bottom line
Insertion: * in the top line
Change: when the letters at the top and bottom are distinct
This tells us that to transform x = AGTCTGACGC into y = AGTAAGTAGGC we would be required to perform at least 5 operations (2 changes, 2 deletions and 1 insertion).
In this problem we would always consider strings x and y to be fixed, such that the number of letters in x is m and the number of letters in y is n where nm.
Assign 1 as the cost of an operation performed. Otherwise, assign 0 if there is no operation performed.
Write a program that would minimize the number of possible operations to transform any string x into a string y.
Input contains several datasets. Each dataset consists of the strings x and y prefixed by their respective lengths, one in each line.
For each dataset, an integer representing the minimum number of possible operations to transform any string x into a string y.
10 AGTCTGACGC 11 AGTAAGTAGGC
5