$2\mathrm{.}19.$ A k$-$way merge operation. Suppose you have $k$ sorted arrays, each with

$n$ elements, and you want to combine them into a single sorted array of

$kn$ elements.

$($a$)$ Here's one strategy: Using the merge procedure from Section $2\mathrm{.}3,$ merge

the first two arrays, then merge in the third, then merge in the fourth,

and so on$.$ What is the time complexity of this algorithm, in terms of $k$

and $n?$

$($b$)$ Give a more efficient solution to this problem, using divide$-$and$-$conquer.