Quick Overview

This question evaluates algorithm design skills and complexity analysis for merging multiple sorted sequences, measuring proficiency with appropriate data structures, time-space trade-offs, and correctness reasoning.

Implement and Analyze 'Merge k Sorted Lists' Algorithm

Company: Amazon

Role: Data Scientist

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Onsite

##### Scenario Algorithm coding challenge during the final interview round. ##### Question Implement LeetCode 23 ‘Merge k Sorted Lists’ and explain your complexity analysis. ##### Hints Compare heap vs divide-and-conquer solutions.

Overview: This question evaluates algorithm design skills and complexity analysis for merging multiple sorted sequences, measuring proficiency with appropriate data structures, time-space trade-offs, and correctness reasoning.

You are given k sorted linked lists represented as arrays of integers. Merge all the lists into one sorted array and return it.

Constraints

  • 0 <= k <= 10^4
  • 0 <= length of each list <= 10^5
  • Sum of lengths across all lists N <= 2 * 10^5
  • -10^9 <= value <= 10^9
  • Each input list is sorted in non-decreasing order

Hints

  1. Use a min-heap that stores (value, list_index, index_in_list). Initialize it with the first element of each non-empty list.
  2. Each pop yields the next smallest value; push the next element from the same list.
  3. An alternative is divide-and-conquer pairwise merging, which also achieves O(N log k).

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Approach

Initialize a min-heap with the first element of each non-empty list. Repeatedly pop the smallest element and append it to the result. When popping (v, i, j), push the next element from the same list i (if it exists). This ensures at most one element from each list is in the heap at a time, maintaining a heap size up to k. This approach is optimal for k-way merging.

Time complexity:
O(N log k), where N is the total number of elements across all lists
Space complexity:
O(k) auxiliary space for the heap (excluding the output array)