> For the complete documentation index, see [llms.txt](https://gl01.gitbook.io/gfg-editorials/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://gl01.gitbook.io/gfg-editorials/2024/04-2024-april-9/12-sum-of-products.md).

# 12. Sum of Products

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/sum-of-products5049/1)

## My Approach

To solve this problem, we iterate through each bit position from 0 to 31.

* For each bit position, we count the number of elements in the array that have that bit set.
* Then, we calculate the number of pairs that can be formed using those elements, and multiply it by 2 raised to the power of the current bit position.
* Finally, we sum these values to get the overall sum of products.

## Time and Auxiliary Space Complexity

* **Time Complexity**: `O(n * 32) => O(n)`
* **Auxiliary Space Complexity**: `O(1)`

## Code (C++)

```cpp
class Solution {
public:
    long long pairAndSum(int n, long long arr[]) {
        long long out = 0;
        for (int i = 0; i < 32; ++i) {
            long long cnt = 0;
            for (int j = 0; j < n; ++j)
                if (arr[j] & (1 << i)) 
                    cnt++;
            long long pairs = (cnt * (cnt - 1) / 2);
            out += pairs * (1 << i);
        }
        return out;
    }
};
```

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