Introduction

In this blog post, we will explore how to solve the LeetCode problem "2916" 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

You are given a 0-indexed integer array nums. The distinct count of a subarray of nums is defined as: Let nums[i..j] be a subarray of nums consisting of all the indices from i to j such that 0 <= i <= j < nums.length. Then the number of distinct values in nums[i..j] is called the distinct count of nums[i..j]. Return the sum of the squares of distinct counts of all subarrays of nums. Since the answer may be very large, return it modulo 109 + 7. A subarray is a contiguous non-empty sequence of elements within an array. Example 1: Input: nums = [1,2,1] Output: 15 Explanation: Six possible subarrays are: [1]: 1 distinct value [2]: 1 distinct value [1]: 1 distinct value [1,2]: 2 distinct values [2,1]: 2 distinct values [1,2,1]: 2 distinct values The sum of the squares of the distinct counts in all subarrays is equal to 12 + 12 + 12 + 22 + 22 + 22 = 15. Example 2: Input: nums = [2,2] Output: 3 Explanation: Three possible subarrays are: [2]: 1 distinct value [2]: 1 distinct value [2,2]: 1 distinct value The sum of the squares of the distinct counts in all subarrays is equal to 12 + 12 + 12 = 3. Constraints: 1 <= nums.length <= 105 1 <= nums[i] <= 105

Explanation

Here's an efficient solution to calculate the sum of squares of distinct counts of all subarrays, along with a complexity analysis.

• High-Level Approach: The core idea is to iterate through all possible subarrays of the input array nums. For each subarray, determine the count of distinct elements. Accumulate the square of this count into a running sum, taking the modulo at each step to prevent overflow. The distinct count is calculated efficiently using a set to avoid recounting duplicates within each subarray.

• Complexity:

  • Runtime: O(n²), where n is the length of the input array nums.
  • Storage: O(n) in the worst case, due to the space used by the distinct_elements set.

Code

    def sum_of_squares_of_distinct_counts(nums):
    """
    Calculates the sum of the squares of distinct counts of all subarrays of nums.

    Args:
        nums: A 0-indexed integer array.

    Returns:
        The sum of the squares of distinct counts modulo 10^9 + 7.
    """

    n = len(nums)
    total_sum = 0
    modulo = 10**9 + 7

    for i in range(n):
        for j in range(i, n):
            subarray = nums[i : j+1]
            distinct_elements = set(subarray)
            distinct_count = len(distinct_elements)
            total_sum = (total_sum + (distinct_count * distinct_count)) % modulo

    return total_sum