Let σ be an alphabet set of size k, and a = a1 · · · am and b = b1 · · · bn be two strings over σ with length m and n, respectively. design a dynamic programming based algorithm to convert a into b with minimum cost using the following rules. for a cost of dk/3e, one can delete any letter from a string. for a cost of dk/2e, one can insert a letter in any position. for a cost of |rank(a)−rank(b)|, one can replace a letter a by another letter b, where rank(a) and rank(b) are the ranks of a and b in σ (i. e., the ranks of 3 and 5 are 2 and 3, respectively, in an alphabet of {1, 3, 5, 7}).