Sum Squared Values at Special Array Positions
Company: Bloomberg
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
# Sum Squared Values at Special Array Positions
You are given an integer array `nums` of length `n`, described using 1-based positions. Position `i` is special when `i` divides `n`, meaning `n % i == 0`.
Return the sum of the squares of the elements at all special positions.
### Examples
**Example 1**
```text
Input: nums = [3,4,2,7,6]
Output: 45
```
The length is `5`, so the special positions are `1` and `5`. Their values are `3` and `6`, giving `3 * 3 + 6 * 6 = 45`.
**Example 2**
```text
Input: nums = [4,3,5,8,9,2]
Output: 54
```
The special positions for length `6` are `1`, `2`, `3`, and `6`. Their values are `4`, `3`, `5`, and `2`, so the required sum is `16 + 9 + 25 + 4 = 54`.
### Constraints
- `1 <= nums.length == n <= 50`.
- `1 <= nums[i] <= 50`.
### Clarifying Questions
- Does divisibility apply to the value or its position? It applies to the 1-based position `i`.
- Does a special element contribute its value or its square? Its square.
- How does the problem's indexing map to the C++ vector? Logical position `i` is stored at `nums[i - 1]`.
- Are the first and last positions special? Yes; both `1` and `n` divide `n`. If `n == 1`, they are the same single position, counted once.
### C++ Interface
```cpp
class Solution {
public:
int sumOfSquares(vector<int>& nums) {
}
};
```
### Reasoning Checkpoints
- Keep the mathematical positions separate from C++ storage indices.
- Apply the special-position definition rather than a test on the element value.
- Count each qualifying position once, including the length-one case.
```hint Position versus value
Write down the C++ vector index corresponding to each logical position before deciding which value to square.
```
Overview: Add the squared values at array positions that divide the array length, using the problem’s one-based position convention.