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

Recall & Review

beginner

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

Use a min heap to always extract the smallest element among the heads of all lists, then insert the next element from that list into the heap, repeating until all lists are merged.

beginner

What data structure is typically used to efficiently find the smallest element among multiple sorted lists during merging?

A min heap (priority queue) is used because it allows quick access to the smallest element and efficient insertion of new elements.

intermediate

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 smallest node from one of the K lists, along with information about which list it came from.

intermediate

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

Because each of the N total elements is pushed and popped from the min heap, which has size at most K, and heap operations take O(log K) time.

beginner

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

The next element from the same list as the extracted element is inserted into the min heap if it exists, maintaining the heap property.

What is the initial step when merging K sorted lists using a min heap?

A Insert all elements of all lists into the min heap

B Concatenate all lists and sort them

C Insert the first element of each list into the min heap

D Merge two lists at a time

We start by inserting the first element of each list into the min heap to efficiently find the smallest among them.

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

A K (number of lists)

B N/K

C 1

D N (total number of elements)

The min heap contains at most one element from each list at any time, so its size is at most K.

Which operation is repeated until all elements are merged in the min heap approach?

A Extract min and insert next element from the same list

B Extract max and insert previous element

C Sort the heap after each insertion

D Remove duplicates from the heap

We repeatedly extract the smallest element and insert the next element from the same list to maintain the heap.

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(N log K)

C O(K log N)

D O(N + K)

Each of the N elements is pushed and popped from a heap of size K, so the complexity is O(N log K).

What data is stored in the min heap nodes during the merge?

A The entire list

B Only the element value

C Only the index of the list

D Element value and index of the list it belongs to

We store the element value and the list index to know where to get the next element after extraction.

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

Think about how the min heap helps pick the smallest element at each step.

Describe why a min heap is efficient for merging K sorted lists compared to other methods.

Compare with sorting all elements or merging lists one by one.