> For the complete documentation index, see [llms.txt](https://programming.arora-aditya.com/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://programming.arora-aditya.com/leetcode/backtracking/401.-binary-watch.md).

# 401. Binary Watch

### Approach 1: Brute Force

```python
class Solution(object):
    def readBinaryWatch(self, num):
        """
        https://leetcode.com/problems/binary-watch/description/
        :type num: int
        :rtype: List[str]
        """
        return ['%d:%02d' % (h, m)
            for h in range(12) for m in range(60)
            if (bin(h) + bin(m)).count('1') == num]
```

Iterating through each of the hours and each of the minutes and checking for the number of ones in them to populate the list. There are 720 iterations for every input.

This solution although not the best comes in at 82.72% percentile

> **Time Complexity:** *O(1)*
>
> **Space Complexity:** *O(1)*

### Approach 2: A very very very bad solution

```python
class Solution(object):
    def readBinaryWatch(self, num):
        """
        :type num: int
        :rtype: List[str]
        """
        if num > 8:
            return []
    	return [["0:00"], ["0:01","0:02","0:04","0:08","0:16","0:32","1:00","2:00","4:00","8:00"],	["0:03","0:05","0:06","0:09","0:10","0:12","0:17","0:18","0:20","0:24","0:33","0:34","0:36","0:40","0:48","1:01","1:02","1:04","1:08","1:16","1:32","2:01","2:02","2:04","2:08","2:16","2:32","3:00","4:01","4:02","4:04","4:08","4:16","4:32","5:00","6:00","8:01","8:02","8:04","8:08","8:16","8:32","9:00","10:00"],	["0:07","0:11","0:13","0:14","0:19","0:21","0:22","0:25","0:26","0:28","0:35","0:37","0:38","0:41","0:42","0:44","0:49","0:50","0:52","0:56","1:03","1:05","1:06","1:09","1:10","1:12","1:17","1:18","1:20","1:24","1:33","1:34","1:36","1:40","1:48","2:03","2:05","2:06","2:09","2:10","2:12","2:17","2:18","2:20","2:24","2:33","2:34","2:36","2:40","2:48","3:01","3:02","3:04","3:08","3:16","3:32","4:03","4:05","4:06","4:09","4:10","4:12","4:17","4:18","4:20","4:24","4:33","4:34","4:36","4:40","4:48","5:01","5:02","5:04","5:08","5:16","5:32","6:01","6:02","6:04","6:08","6:16","6:32","7:00","8:03","8:05","8:06","8:09","8:10","8:12","8:17","8:18","8:20","8:24","8:33","8:34","8:36","8:40","8:48","9:01","9:02","9:04","9:08","9:16","9:32","10:01","10:02","10:04","10:08","10:16","10:32","11:00"],["0:15","0:23","0:27","0:29","0:30","0:39","0:43","0:45","0:46","0:51","0:53","0:54","0:57","0:58","1:07","1:11","1:13","1:14","1:19","1:21","1:22","1:25","1:26","1:28","1:35","1:37","1:38","1:41","1:42","1:44","1:49","1:50","1:52","1:56","2:07","2:11","2:13","2:14","2:19","2:21","2:22","2:25","2:26","2:28","2:35","2:37","2:38","2:41","2:42","2:44","2:49","2:50","2:52","2:56","3:03","3:05","3:06","3:09","3:10","3:12","3:17","3:18","3:20","3:24","3:33","3:34","3:36","3:40","3:48","4:07","4:11","4:13","4:14","4:19","4:21","4:22","4:25","4:26","4:28","4:35","4:37","4:38","4:41","4:42","4:44","4:49","4:50","4:52","4:56","5:03","5:05","5:06","5:09","5:10","5:12","5:17","5:18","5:20","5:24","5:33","5:34","5:36","5:40","5:48","6:03","6:05","6:06","6:09","6:10","6:12","6:17","6:18","6:20","6:24","6:33","6:34","6:36","6:40","6:48","7:01","7:02","7:04","7:08","7:16","7:32","8:07","8:11","8:13","8:14","8:19","8:21","8:22","8:25","8:26","8:28","8:35","8:37","8:38","8:41","8:42","8:44","8:49","8:50","8:52","8:56","9:03","9:05","9:06","9:09","9:10","9:12","9:17","9:18","9:20","9:24","9:33","9:34","9:36","9:40","9:48","10:03","10:05","10:06","10:09","10:10","10:12","10:17","10:18","10:20","10:24","10:33","10:34","10:36","10:40","10:48","11:01","11:02","11:04","11:08","11:16","11:32"],["0:31","0:47","0:55","0:59","1:15","1:23","1:27","1:29","1:30","1:39","1:43","1:45","1:46","1:51","1:53","1:54","1:57","1:58","2:15","2:23","2:27","2:29","2:30","2:39","2:43","2:45","2:46","2:51","2:53","2:54","2:57","2:58","3:07","3:11","3:13","3:14","3:19","3:21","3:22","3:25","3:26","3:28","3:35","3:37","3:38","3:41","3:42","3:44","3:49","3:50","3:52","3:56","4:15","4:23","4:27","4:29","4:30","4:39","4:43","4:45","4:46","4:51","4:53","4:54","4:57","4:58","5:07","5:11","5:13","5:14","5:19","5:21","5:22","5:25","5:26","5:28","5:35","5:37","5:38","5:41","5:42","5:44","5:49","5:50","5:52","5:56","6:07","6:11","6:13","6:14","6:19","6:21","6:22","6:25","6:26","6:28","6:35","6:37","6:38","6:41","6:42","6:44","6:49","6:50","6:52","6:56","7:03","7:05","7:06","7:09","7:10","7:12","7:17","7:18","7:20","7:24","7:33","7:34","7:36","7:40","7:48","8:15","8:23","8:27","8:29","8:30","8:39","8:43","8:45","8:46","8:51","8:53","8:54","8:57","8:58","9:07","9:11","9:13","9:14","9:19","9:21","9:22","9:25","9:26","9:28","9:35","9:37","9:38","9:41","9:42","9:44","9:49","9:50","9:52","9:56","10:07","10:11","10:13","10:14","10:19","10:21","10:22","10:25","10:26","10:28","10:35","10:37","10:38","10:41","10:42","10:44","10:49","10:50","10:52","10:56","11:03","11:05","11:06","11:09","11:10","11:12","11:17","11:18","11:20","11:24","11:33","11:34","11:36","11:40","11:48"],["1:31","1:47","1:55","1:59","2:31","2:47","2:55","2:59","3:15","3:23","3:27","3:29","3:30","3:39","3:43","3:45","3:46","3:51","3:53","3:54","3:57","3:58","4:31","4:47","4:55","4:59","5:15","5:23","5:27","5:29","5:30","5:39","5:43","5:45","5:46","5:51","5:53","5:54","5:57","5:58","6:15","6:23","6:27","6:29","6:30","6:39","6:43","6:45","6:46","6:51","6:53","6:54","6:57","6:58","7:07","7:11","7:13","7:14","7:19","7:21","7:22","7:25","7:26","7:28","7:35","7:37","7:38","7:41","7:42","7:44","7:49","7:50","7:52","7:56","8:31","8:47","8:55","8:59","9:15","9:23","9:27","9:29","9:30","9:39","9:43","9:45","9:46","9:51","9:53","9:54","9:57","9:58","10:15","10:23","10:27","10:29","10:30","10:39","10:43","10:45","10:46","10:51","10:53","10:54","10:57","10:58","11:07","11:11","11:13","11:14","11:19","11:21","11:22","11:25","11:26","11:28","11:35","11:37","11:38","11:41","11:42","11:44","11:49","11:50","11:52","11:56"],  	["3:31","3:47","3:55","3:59","5:31","5:47","5:55","5:59","6:31","6:47","6:55","6:59","7:15","7:23","7:27","7:29","7:30","7:39","7:43","7:45","7:46","7:51","7:53","7:54","7:57","7:58","9:31","9:47","9:55","9:59","10:31","10:47","10:55","10:59","11:15","11:23","11:27","11:29","11:30","11:39","11:43","11:45","11:46","11:51","11:53","11:54","11:57","11:58"],["7:31","7:47","7:55","7:59","11:31","11:47","11:55","11:59"]][num]
        
```

This solution stores all the times in a list and just returns appropriate answer when requested

> **Time Complexity:** *O(1), fixed object size*
>
> **Space Complexity:** *O(1), fixed object size*