Exercise $6\mathrm{.}5-9($page $166)$ on merging $k$ sorted lists.

Give an $O(nlgk)-$time algorithm to merge $k$ sorted lists into one sorted list, where $n$ is the total

number of elements in all the input lists. $($Hint: Use a min$-$heap for $k-$way merging.$)$

Include a brief explanation of the running time.