How do you solve Binary Watch on LeetCode?

Binary Watch (LeetCode #401) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(n) space complexity. Key insight: Understanding how to represent time in binary is crucial.

What is the brute force solution for Binary Watch?

The brute force approach for Binary Watch is Brute Force, with O(1) time complexity and O(n) space complexity. The brute force approach involves generating all possible combinations of hours and minutes based on the number of LEDs turned on. We check each combination to see if it matches the criteria of the binary watch. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Binary Watch?

Binary Watch uses the following concepts: Backtracking, Bit Manipulation. The recommended patterns to study are: Backtracking, Bit Manipulation.

What are the interview tips for Binary Watch?

Always clarify the output format before coding. Think about edge cases, like when turnedOn = 0 or 10. Practice writing clean and efficient code.

What are common mistakes when solving Binary Watch?

Not formatting the output correctly (e.g., leading zeros in hours). Overlooking the bounds of hours and minutes.

#401

Binary Watch

Easy

BacktrackingBit ManipulationBacktrackingBit Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(1)	O(1)
Space	O(n)	O(n)

💡

Intuition

Time O(1)Space O(n)

The optimal solution leverages backtracking to generate combinations of hours and minutes based on the number of LEDs turned on. This reduces the number of unnecessary checks and directly builds valid times.

⚙️

Algorithm

4 steps

1Step 1: Use a backtracking function that takes the current hour, minute, and the number of LEDs turned on.
2Step 2: If the number of LEDs used exceeds 'turnedOn', return.
3Step 3: If the hour is valid (0-11) and the minute is valid (0-59), check if the total LEDs used equals 'turnedOn' and add the formatted time to the result.
4Step 4: Recursively try adding LEDs to the hour and minute, incrementing the count of LEDs used.

solution.py17 lines

1# Full working Python code
2from typing import List
3
4def readBinaryWatch(turnedOn: int) -> List[str]:
5    result = []
6    def backtrack(hour, minute, count):
7        if count > turnedOn:
8            return
9        if hour < 12 and minute < 60:
10            if count == turnedOn:
11                result.append(f'{hour}:{minute:02}')
12        if hour < 12:
13            backtrack(hour + 1, minute, count + bin(hour).count('1'))
14        if minute < 60:
15            backtrack(hour, minute + 1, count + bin(minute).count('1'))
16    backtrack(0, 0, 0)
17    return result

ℹ

Complexity note: The time complexity remains O(1) since we are still limited by the fixed number of hours and minutes. The space complexity is O(n) due to the result list.

1Understanding how to represent time in binary is crucial.
2Efficiently counting bits can significantly reduce unnecessary computations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.