algoadvance

You are given a 1-indexed integer array nums of length n.

An element nums[i] of nums is called special if i divides n, i.e. n % i == 0.

Return the sum of the squares of all special elements of nums.

Example:

Input: nums = [1, 2, 3, 4]
Output: 17

Explanation:
- nums[1] is special as 4 % 1 == 0 -> 1^2
- nums[2] is special as 4 % 2 == 0 -> 2^2
- nums[4] is special as 4 % 4 == 0 -> 4^2
- Sum of squares = 1^2 + 2^2 + 4^2 = 17

Clarifying Questions

1. Can nums contain negative integers?
   • Yes, nums can contain negative integers.
2. What is the minimum and maximum value of n?
   • Minimum n is 1. There’s no specific maximum value given, but you can assume typical constraints for such problems on LeetCode.
3. Are the elements of nums always integers?
   • Yes, nums contains integers as per the problem description.
4. Do we need to handle invalid input cases?
   • It is typically safe to assume that the input will be valid as per the problem constraints in a competitive programming context.

Strategy

1. Identify Special Elements:
   • Traverse the array and check the indices i (1-indexed). If n % i == 0, the element nums[i-1] (since the array is 0-indexed in Python) is a special element.
2. Calculate Sum of Squares:
   • For each special element, compute its square and maintain a running sum.
3. Return the Result:
   • After processing all the elements, return the final computed sum.

Code

Here’s the implementation based on the strategy:

def sum_of_squares(nums):
    n = len(nums)
    sum_of_squares = 0
    for i in range(1, n + 1):
        if n % i == 0:
            sum_of_squares += nums[i - 1] ** 2
    return sum_of_squares

# Example Usage
print(sum_of_squares([1, 2, 3, 4]))  # Output: 17

Time Complexity

• Time Complexity: (O(n))
  • The algorithm traverses the array once, and for each element, performs a constant time operation (checking divisibility and computing the square).
• Space Complexity: (O(1))
  • Only a few extra variables are used to maintain the running sum, making the space complexity constant.

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