Shortest subarray with mode K

Shortest subarray with mode K

Shortest subarray with mode K

Problem Description

Given an integer array nums and an integer k, return the length of the shortest non-empty subarray of nums with a mode of at least k. If there is no such subarray, return -1.

A subarray is a contiguous part of an array.

The mode of an array is the frequency of the most frequent element in the array.

Solution Approach

To solve this problem, we can use binary search to find the answer. The idea is to observe that if there exists a subarray of length L with a mode of at least K, then there will also exist subarrays of all lengths greater than or equal to L with a mode of at least K. Hence, we can binary search the answer.

To check if we have a subarray of a given length with a mode of at least K, we can use a sliding window of length L where we add and discard items. To keep track of the frequency, we can use a hashmap. However, to find the mode of every window, we need a data structure that allows operations such as add(item), delete(item), and getMax(item).

All these operations can be performed in O(log N) time complexity using an ordered set. While a Priority Queue can allow add(item) and getMax(item), deleting arbitrary elements is trickier in a Priority Queue. It is possible but requires additional exploration.

By using this approach, we can check if a subarray of a given length with a mode of at least K exists in O(N log N) time complexity. By applying binary search on the length, the overall complexity of this solution is O(N log^2 N).

Here's the solution code to demonstrate this technique, you can access it in this playground link.

Test Cases

Test Case:

Input:
nums = [1, 2, 3, 1, 2, 1, 1]
K = 3

Output:
4

Explanation:
The shortest subarray with a mode of at least 3 is [1, 2, 1, 1], which has a length of 4.

Test Case:

Input:
nums = [1, 2, 3, 4]
K = 2

Output:
-1

Explanation:
There is no subarray with a mode of at least 2, so the output is -1.

Tags

Binary Search, Ordered Set, Hash Table, Sliding Window

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