Speech recognition systems need to match audio streams that represent the same words spoken at different speeds. Suppose, therefore, that you are given two sequences of numbers, X-(X1, X2 , . . . , Xn), and Y-(y?, y2' . . . , ym), repre- senting two different audio streams that need to be matched. A mapping between X and Y is a list, M, of distinct pairs, (i,j), that is ordered lexicographically. such that, for each ? [1, nl, there is at least one pair, (i,j), in M, and for each j ? [1, m), there is at least one pair, (j), in M. Such a mapping is monotonic if, for any (i,j) and (k, l) in M, with (i,j)) coming before (k, l) in M, we have i3 k and jS 1. For example, given X (3,9, 9,5) and Y - (3,3, 9,5,5), one possible monotonic mapping between X and Y would be The dynamic time warping problem is to find a monotonic mapping, M, between X and Y, that minimizes the distance, D(X, Y), between X and Y, subject to M, which is defined as (i,j)EM where this minimization is taken over all possible monotonic mappings betweern X and Y. For instance, in the example X, Y, and M, given above, we have D(X,Y)0. Describe an efficient algorithm for solving the dynamic time warping problem. What is the running time of your algorithm