# 01. Array Pair Sum Divisibility Problem

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/array-pair-sum-divisibility-problem3257/1)

![](https://badgen.net/badge/Level/Medium/yellow)

## My Approach

I approached this problem by counting the occurrences of each element's remainder when divided by `k`. Then, I checked whether pairs of remainders that should sum up to `k` have the same frequency.

* Check if the size of the input array is even; return false if not.
* Count the occurrences of each remainder when divided by `k`.
* Compare the frequencies of remainders at positions `l` and `r` where `l` starts from 1 and `r` starts from `k-1` and moves towards each other.
  * If frequencies don't match, return false.
* Check the middle element (if `k` is odd) and the remainder `0`.
  * If either of them has an odd frequency, return false.
* If all checks pass, return true.

## Time and Auxiliary Space Complexity

* **Time Complexity** : O(n), where n is the size of the input vector.
* **Auxiliary Space Complexity** : O(k), where k is the input parameter.

## Code (C++)

```cpp
class Solution {
public:
    bool canPair(vector<int> nums, int k) {
        if(nums.size() % 2 != 0)
            return false;
            
        vector<int> cnt(k, 0);
        
        for(auto i: nums)
            ++cnt[i % k];
        
        int l = 1, r = k - 1;
        
        while(l < r){
            if(cnt[l] != cnt[r])
                return false;
            ++l;
            --r;
        }
        
        if((l == r && cnt[l] % 2 != 0) || cnt[0] % 2 != 0)
            return false;
        
        return true;
    }
};
```

## Contribution and Support

For discussions, questions, or doubts related to this solution, please visit our [discussion section](https://github.com/getlost01/gfg-potd/discussions). We welcome your input and aim to foster a collaborative learning environment.

If you find this solution helpful, consider supporting us by giving a `⭐ star` to the [getlost01/gfg-potd](https://github.com/getlost01/gfg-potd) repository.


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://gl01.gitbook.io/gfg-editorials/2024/01-2024-jan/01-array-pair-sum-divisibility-problem.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.