632. Smallest Range Covering Elements from K Lists

How to solve Smallest Range Covering Elements from K Lists (LeetCode 632): the approach in brief

The problem

You have k lists of sorted integers in non-decreasing order. Find the smallest range that includes at least one number from each of the k lists.

Pattern

Smallest Range Covering Elements from K Lists is a Heap (Priority Queue) Patterns problem, in the K-way Merge subpattern. The pattern covers top K elements, K-way merge, two heaps for median, and scheduling

Master K-way merge pattern using min heap. Merge k sorted lists and find kth smallest in matrix.

Approach outline

1. Consider how to efficiently keep track of the smallest and largest elements among the current candidates from each list to determine potential ranges.
2. Think about using a min-heap (priority queue) to always access the smallest current element across the k lists while keeping track of the maximum element among them.
3. Initialize the heap with the first element of each list and record the current maximum; this will help define the initial range.

Complexity

The reference solution runs in O(N log k) time and O(k) space.

Asked at

Smallest Range Covering Elements from K Lists has been reported in interviews at Amazon.