> 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/2023/10-2023-oct-27/28-bleak-numbers.md).

# 28. Bleak Numbers

The problem can be found at the following link: [Question Link](https://practice.geeksforgeeks.org/problems/bleak-numbers1552/1)

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

## My Approach

To determine if a number is bleak, follow these steps:

* Iterate from 1 to the logarithm base 2 of the given number.
  * For each iteration, find the value `x` for the `i`th set bit by subtracting `i` from the given number.
  * Count the set bits in `x` and check if the sum of set bits and the result is equal to the original number `n`.
  * If such a combination exists, return 0 (indicating it is not bleak).
* If no such combination is found, return 1 (indicating it is bleak).

## Time and Auxiliary Space Complexity

* **Time Complexity**: `O(log2(n))` where 'n' is the input number. We iterate through numbers from `1` to `log2(n)`.
* **Auxiliary Space Complexity**: `O(1)`, as we use only a few variables for calculations.

## Code (C++)

```cpp
class Solution {
public:
    int is_bleak(int n) {
        for(int i = 1; i <= log2(n); ++i) {
            int x = n - i;
            int setBits = __builtin_popcount(x);
            if(setBits + x == n)
                return 0;
        }
        return 1;
    }
};
```

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