Merge K Sorted Lists Using Min Heap in DSA Javascript - 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 current element among all lists by always keeping the smallest element at the top, allowing us to build the merged list in sorted order.

beginner

How do you initialize the min heap when merging K sorted lists?

Insert the first element of each of the K sorted lists into the min heap to start the merging process.

intermediate

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

After extracting the smallest element, insert the next element from the same list (where the extracted element came from) into the min heap, if it exists.

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, and the heap size is at most K, each operation takes O(log K), resulting in O(N log K) overall.

beginner

What data structure is commonly used to represent the min heap in JavaScript for this problem?

A priority queue or a custom binary heap implemented as an array is commonly used to represent the min heap in JavaScript.

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

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

B Merge all lists into one big list and sort it

C Extract the largest element from each list

D Reverse all lists

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

After extracting the smallest element from the min heap, what do you do next?

A Insert the largest element from another list

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

C Remove all elements from 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 maximum size of the min heap during the merge of K sorted lists?

A N (total elements)

B N/K

C 1

D K

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

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

A O(N log K)

B O(N^2)

C O(K log N)

D O(N)

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

Which data structure property is essential for the min heap in this problem?

A Elements are stored in reverse order

B The largest element is always at the top

C The smallest element is always at the top

D Elements are stored in insertion order

The min heap always keeps the smallest element at the top to efficiently find the next smallest element.

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 each time.

Describe why using a min heap is more efficient than merging all lists and sorting them at once.

Compare sorting all elements at once vs. incremental merging.