Merge K Sorted Lists Using Min Heap in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind using a min heap to merge K sorted lists?

A min heap helps efficiently find the smallest element among the heads of all lists, allowing us to build the merged sorted list by always picking the smallest next element.

beginner

In the context of merging K sorted lists, what does each element in the min heap represent?

Each element in the min heap represents the current node (or value) from one of the K lists that is a candidate to be added next to the merged list.

intermediate

Why is the time complexity of merging K sorted lists using a min heap O(N log K)?

Because we insert and remove each of the N total elements once from a min heap of size at most K, and each heap operation takes O(log K) time.

beginner

What happens after extracting the smallest element from the min heap during the merge process?

After extracting the smallest element, we add it to the merged list and then insert the next element from the same list (if any) into the min heap.

beginner

How does the min heap help maintain the sorted order in the merged list?

The min heap always keeps the smallest current elements at the top, so extracting from it gives the next smallest element to add, preserving sorted order.

What data structure is best suited to efficiently merge K sorted lists?

A Queue

B Stack

C Hash map

D Min heap

A min heap efficiently finds the smallest element among multiple lists, making it ideal for merging sorted lists.

What is the maximum size of the min heap during the merge of K sorted lists?

A N (total elements)

B K (number of lists)

C 1

D N/K

The min heap holds at most one element from each of the K lists at any time.

After extracting the smallest element from the min heap, what is the next step?

A Insert the next element from the same list into the min heap

B Insert the largest element from all lists

C Clear the min heap

D Stop the process

We insert the next element from the same list to continue merging in sorted order.

What is the overall time complexity of merging K sorted lists with total N elements using a min heap?

A O(N log N)

B O(K log N)

C O(N log K)

D O(N + K)

Each of the N elements is pushed and popped from a min heap of size K, costing O(log K) per operation.

Why is a min heap preferred over a simple linear search to find the smallest element among K lists?

A Min heap reduces the search time to O(log K) per operation

B Linear search is faster

C Min heap uses more memory

D Linear search is easier to implement

Min heap allows efficient retrieval of the smallest element in O(log K) time, better than O(K) for linear search.

Explain how a min heap is used to merge K sorted lists step-by-step.

Think about how the min heap always gives the smallest current element.

Describe the time complexity of merging K sorted lists using a min heap and why it is efficient.

Focus on how many times heap operations happen and their cost.