Let m>=1 and n>=1 be integers and consider an m x n matrix A. The rows of this matrix are numbered 1,2,.....,m and its columns are numbered 1,2,...,n. Each entry of A stores one number

Question 8: Let m and n be integers and consider an mx n matrix A. The rows of this ulatrix are numbered 1, 2, . . . ,m, and its columns are numbered 1, 2, . . . ,,I, Each entry of A stores one number and, for each row, all numbers in this row are pairwise distinct. For each1,2....,m define g(i) thep(i.e.. colun mnber) of the sstmber in ro i We say that the matrix A is awesome, it In the matrix below, the smallest number in each row is in boldface. For this example, we have m 4, n 10, ) awesome 3, (2) 13 12 5 8 6 9 15 20 19 7 3 4 1 17 6 13 7 10 2 5 74 17 10 5 14 12 3 20 6 3, 9(3) 5, and g(4) 8. Thus, this matrix is 19 5 12 7 2 4 1 13 6 3 From now on, we assme that the m X nmatrix A is awesome Leti be an integer with 1 i m. Describe, in plain English and a few sentences, an algorithm that computes g(i) in O(n) time Describe, in plain English and a few sentences, an algorithm that computes all values g1). g(2), glm) in O(mn) total time. In the rest of this xercise, you will show that all valucs g(1), g(2).....gm) can be computed in O(m +n log m) total time Assme that m is even and assume that you are given the values Describe, i plain English ad g one or more figures, nn algorithm that computes the values in O(m +n) total time Assume that m2, i.e, a power of two Describe a recusive algorithm FNDMINIMA that has the following specification Algorithm FINDMINIMA(A,): Output: Tlue values y (j-wi/2') Ir j = 1.2.3 For cach i with