Q: Suppose we want to convert one string S1 to another string S2 using only 3 types of operations:
-Insert(pos,char) (costs 8)
-Delete(pos) (costs 6)
-Replace(pos,char) (costs 8)
Find the sequence of steps to convert S1 to S2 such that the cost to convert S1 to S2 is minimum.
Eg. 'calculate' to 'late' - the possible operations are
Delete(0)
Delete(1)
Delete(2)
Delete(3)
Delete(4)
and the above sequence of operations costs 30.
A: some ideas
1) using levenshtein algorithm
2) Is this the minimum edit distance algorithm. You can look it up at various sources, some of them listed below (AKA "Levenshtein distance"):
w_ww.stanford.edu/class/cs124/lec/med.pdf
w_ww.csse.monash.edu.au/~lloyd/tildeAlgDS/Dynamic/Edit/
e_n.wikipedia.org/wiki/Levenshtein_distance
3) find longest common subseuqence, and use the avail operations on the rest of the characters.