Algorithm 3 Merge Sorted Lists

Input: $k$ sorted lists with $n$ elements in total

Output: A sorted list of size $n$

1:extract the first element from each sorted list to form $A[1..k]$

2: $A.\text{heap-size} = k$

3:BuildMinHeap( $A$ )

4:let $L$ be the result list

5:while $A.\text{heap-size} \ne 0$ do

6: $x =$ HeapExtractMin( $A$ )

7:let $l$ be the list which $x$ came from

8:if $l$ is not empty then

9:extrace the first element $y$ from $l$

10:MinHeapInsert( $A, y$ )

11:end if

12:append $x$ to $L$

13:end while

14:return $L$