K-way Merge

anil gurung
2 min readFeb 1, 2021

In this blog post, I will be giving a brief introduction about another data structure that is very important for technical interviews.This data structure is called K-way Merge. This pattern is very useful to solve problems that involve a sets of sorted arrays. Whenever, we are given K sorted arrays, we can use a Heap to efficiently perform a sorted traversal of all elements of all arrays.

We can push the smallest element of each sorted array in a Min Heap to get the overall minimum. While inserting elements to the Min Heap, we keep track of which array the element came from.

The K-way Merge pattern looks like this;

  1. We can push the smallest (first) element of each sorted array in a Min Heap to get the overall minimum.
  2. After this step, we can take out the smallest (top) element from the heap and then add it to the merged list.
  3. After removing the smallest element from the heap, insert the next element of the same list into the heap.
  4. We can repeat steps 2 and 3 to populate the merged list in sorted order.

For this pattern,

Time Complexity = O(N log K) where N is the total number of elements in all the K input arrays.

Space Complexity = O(K)

Ways to identify this pattern:

  • For this kind of pattern, the problem will feature sorted arrays, lists, or a matrix
  • The problem will ask us to merge sorted lists, find the smallest element in a sorted list.

References:

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