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.
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 could be required to perform 5 operations (2 changes, 2 deletions and 1 insertion).
If we want to minimize the number operations, we should do it like
A G T A A G T A G G C
| | | | | | |
A G T C T G * A C G C
and 4 moves would be required (3 changes and 1 deletion).
In this problem we would always consider strings x and y to be fixed, such that the number ofletters in x is m and the number of letters in y is n where n ≥ m.
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