Introduction

In this blog post, we will explore how to solve the LeetCode problem "992" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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. For example, [1,2,3,1,2] has 3 different integers: 1, 2, and 3. A subarray is a contiguous part of an array. Example 1: Input: nums = [1,2,1,2,3], k = 2 Output: 7 Explanation: Subarrays formed with exactly 2 different integers: [1,2], [2,1], [1,2], [2,3], [1,2,1], [2,1,2], [1,2,1,2] Example 2: Input: nums = [1,2,1,3,4], k = 3 Output: 3 Explanation: Subarrays formed with exactly 3 different integers: [1,2,1,3], [2,1,3], [1,3,4]. Constraints: 1 <= nums.length <= 2 * 104 1 <= nums[i], k <= nums.length

Explanation

Here's a solution to the problem, focusing on efficiency and clarity:

• Problem Decomposition: The core idea is to transform the "exactly k" problem into a "at most k" problem. We can calculate the number of subarrays with at most k distinct elements and then subtract the number of subarrays with at most (k-1) distinct elements. The difference will be the number of subarrays with exactly k distinct elements.

• Sliding Window: We use a sliding window approach to count the number of subarrays with at most k distinct elements. The window expands to the right, and when the number of distinct elements exceeds k, the window contracts from the left until the condition is met again.

• atMost(k) Helper: A helper function efficiently calculates the number of "at most k" subarrays, avoiding redundant code.

• Time & Space Complexity: O(n) time complexity and O(n) space complexity.

Code

    def subarraysWithKDistinct(nums, k):
    """
    Calculates the number of good subarrays of nums (subarrays with exactly k distinct integers).

    Args:
    nums (List[int]): An integer array.
    k (int): An integer representing the desired number of distinct integers in a good subarray.

    Returns:
    int: The number of good subarrays of nums.
    """

    def atMost(k):
        """
        Calculates the number of subarrays with at most k distinct elements.

        Args:
        k (int): The maximum number of distinct elements allowed in a subarray.

        Returns:
        int: The number of subarrays with at most k distinct elements.
        """
        if k < 0:
            return 0

        count = 0
        left = 0
        distinct_count = 0
        freq = {}  # Store frequency of elements within the sliding window

        for right in range(len(nums)):
            num = nums[right]
            if num not in freq:
                freq[num] = 0
                distinct_count += 1
            freq[num] += 1

            while distinct_count > k:
                left_num = nums[left]
                freq[left_num] -= 1
                if freq[left_num] == 0:
                    del freq[left_num]
                    distinct_count -= 1
                left += 1

            count += right - left + 1

        return count

    return atMost(k) - atMost(k - 1)