How do you solve Angle Between Hands of a Clock on LeetCode?

Angle Between Hands of a Clock (LeetCode #1344) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: The minute hand moves 6 degrees per minute, while the hour hand moves 30 degrees per hour plus an additional 0.5 degrees for each minute.

What is the time complexity of Angle Between Hands of a Clock?

The optimal solution for Angle Between Hands of a Clock runs in O(1) time and uses O(1) space. The optimal solution also runs in O(1) time and space because it performs a constant number of calculations.

What is the brute force solution for Angle Between Hands of a Clock?

The brute force approach for Angle Between Hands of a Clock is Brute Force, with O(1) time complexity and O(1) space complexity. The brute force approach calculates the positions of the hour and minute hands separately and then finds the angle between them. This method is straightforward but involves unnecessary calculations. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Angle Between Hands of a Clock?

Angle Between Hands of a Clock uses the following concepts: Math. The recommended patterns to study are: Mathematical calculations, Geometry.

What are the interview tips for Angle Between Hands of a Clock?

Always clarify the problem statement and constraints before diving into coding. Think out loud to show your thought process and reasoning. Test your solution with edge cases, such as 12:00 or 1:00.

What are common mistakes when solving Angle Between Hands of a Clock?

Not accounting for the minute hand's effect on the hour hand's position. Confusing the angles and calculating them in the wrong order.

#1344

Angle Between Hands of a Clock

Medium

MathMathematical calculationsGeometry

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(1)Space O(1)

The optimal solution is essentially the same as the brute force approach but emphasizes the efficiency of direct calculations without unnecessary steps. It leverages the properties of angles on a circle.

⚙️

Algorithm

4 steps

1Step 1: Calculate the angle of the minute hand: angle_minute = minutes * 6.
2Step 2: Calculate the angle of the hour hand, considering both the hour and the contribution from the minutes: angle_hour = (hour % 12) * 30 + (minutes / 60) * 30.
3Step 3: Calculate the absolute difference between the two angles: angle_difference = abs(angle_hour - angle_minute).
4Step 4: Return the smaller angle: return min(angle_difference, 360 - angle_difference).

solution.py5 lines

1def angleClock(hour, minutes):
2    angle_minute = minutes * 6
3    angle_hour = (hour % 12) * 30 + (minutes / 60) * 30
4    angle_difference = abs(angle_hour - angle_minute)
5    return min(angle_difference, 360 - angle_difference)

ℹ

Complexity note: The optimal solution also runs in O(1) time and space because it performs a constant number of calculations.

1The minute hand moves 6 degrees per minute, while the hour hand moves 30 degrees per hour plus an additional 0.5 degrees for each minute.
2Understanding how both hands move relative to each other is crucial for calculating the angle.

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