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Question 4. The strings X[1 ... n] and Y[1 ...m] are given. Our aim is to use the string X[1 ... n] with the least cost. Y[1...m]to the order. Adding a new character costs up to TL, deleting an existing character It costs t dollars and converting an x character to a y character is f (x, y) dollars. Where k and t given positive integers, f (x, y) is a function with positive integers. a) Write down the recurrence required to solve the problem using dynamic programming. b) Pseudo code of the algorithm you designed with dynamic programming method (pseudo code) c) (15 points) Let k = 2, t = 1 and f (x, y) function given by the table below. (In this table the x variable column and y variable is given in the row.) By applying the algorithm you wrote down, it is necessary to convert the word ARABA to BAAR Calculate the cost.

00 A 1 B 1 1 R 1 A B 2 2 2 02 1 2 0 4 1 4 0 4 1 4 R 2 4 1 4 0 1