K-way merge with heaps in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of a K-way merge?

The main goal of a K-way merge is to combine K sorted lists into one single sorted list efficiently.

beginner

How does a heap help in performing a K-way merge?

A heap helps by always providing the smallest (or largest) element among the heads of the K lists quickly, allowing efficient selection of the next element to add to the merged list.

intermediate

What is the time complexity of a K-way merge using a heap?

The time complexity is O(N log K), where N is the total number of elements across all lists and K is the number of lists being merged.

beginner

Why is a min-heap commonly used in K-way merge?

A min-heap is used because it allows quick access to the smallest element among the current heads of the K lists, which is needed to maintain sorted order in the merged output.

intermediate

Describe the process of updating the heap during a K-way merge.

After extracting the smallest element from the heap, the next element from the same list is inserted into the heap. This keeps the heap updated with the current smallest elements from each list.

What data structure is typically used to efficiently perform a K-way merge?

A Heap

B Stack

C Queue

D Linked List

A heap allows quick access to the smallest element among multiple lists, making it ideal for K-way merge.

If you have 5 sorted lists with a total of 100 elements, what is the time complexity of merging them using a heap?

A O(100 * 5)

B O(100 log 5)

C O(5 log 100)

D O(log 100)

The complexity is O(N log K), where N=100 and K=5, so O(100 log 5).

During K-way merge, what happens after the smallest element is removed from the heap?

A The next element from the same list is added to the heap

B The heap is cleared

C All elements are reinserted

D The largest element is added

To maintain the heap with current smallest elements, the next element from the same list is inserted.

Why is K-way merge more efficient than repeatedly merging two lists at a time?

A Because it ignores some elements

B Because it sorts each list individually

C Because it uses recursion

D Because it uses a heap to reduce comparisons

Using a heap reduces the number of comparisons needed to find the next smallest element.

What does 'K' represent in K-way merge?

A Total number of elements

B Size of the heap

C Number of sorted lists to merge

D Number of elements in the largest list

'K' is the number of sorted lists being merged.

Explain how a heap is used to merge K sorted lists into one sorted list.

Think about how the heap keeps track of the smallest candidates from each list.

Describe the time complexity of K-way merge using a heap and why it is efficient.

Focus on how the heap helps reduce the number of comparisons.