Subarrays with K Different Integers

Problem Description

Given an integer array nums and an integer k, return the number of good subarrays of nums. A good array is an array where the number of different integers in that array is exactly k. A subarray is a contiguous part of an array.

Key Insights

• A subarray is defined as a contiguous sequence of elements within an array.
• The challenge lies in counting subarrays that contain exactly k distinct integers.
• Using a sliding window technique can efficiently track the number of distinct integers in the current window.
• The problem can be reframed using the principle of inclusion-exclusion: the number of subarrays with exactly k distinct integers can be derived from the number of subarrays with at most k distinct integers.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve this problem, we can use a sliding window approach alongside a hash map (or dictionary) to count the frequency of each integer within the current window. We maintain two pointers to represent the start and end of the window.

1. First, implement a helper function atMostK(k) that counts the number of subarrays with at most k distinct integers.
2. The main function can then calculate the number of subarrays with exactly k distinct integers by calling atMostK(k) and atMostK(k-1) and taking the difference.
3. This method ensures that we efficiently count the required subarrays without explicitly generating all subarrays.

Code Solutions