# 06. Techfest and the Queue

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/techfest-and-the-queue1044/1)

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

## My Approach

The `primePowers` function is implemented to count the prime factors of a given number. The `sumOfPowers` function iterates from `a` to `b` and sum the total prime factors using the `primePowers` function.

## Time and Auxiliary Space Complexity

* **Time Complexity:** `O(b * sqrt(max_element))`, where max\_element is the maximum number in the range \[a, b].
* **Auxiliary Space Complexity:** `O(1)`

## Code (C++)

```cpp
class Solution {
public:
    int primePowers(int n)
    {
        int cnt = 0;
        for(int i = 2; i <= sqrt(n); i++)
        {
            while(n % i == 0)
            {
                cnt++;
                n = n / i;
            }
        }
        
        if(n > 1)
            cnt++;
        
        return cnt;
    }
    
    int sumOfPowers(int a, int b)
    {
        int cnt = 0;
        for(int i = a; i <= b; i++)
            cnt += primePowers(i);
        
        return cnt;
    }
};
```

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