Is Angle Between Hands of a Clock easy or hard?

The problem is rated Medium on LeetCode but conceptually closer to an easy math problem once you recognize how the clock hands move. The challenge is remembering that the hour hand moves continuously as minutes pass.

Angle Between Hands of a Clock Python/Java solution

The implementation is identical across languages. Calculate minuteAngle = minutes * 6 and hourAngle = hour * 30 + minutes * 0.5, compute the absolute difference, and return min(diff, 360 - diff). This logic works the same in Python, Java, C++, C#, and JavaScript.

How to solve Angle Between Hands of a Clock in O(n)?

The problem does not require an O(n) algorithm. The angle can be computed directly using constant-time math formulas derived from the rotational movement of the clock hands. The final computation uses only a few arithmetic operations, giving O(1) time complexity.

What is the best approach for Angle Between Hands of a Clock?

The best approach is a direct mathematical calculation. Compute the minute hand angle as minutes × 6 and the hour hand angle as hour × 30 + minutes × 0.5. Take the absolute difference and return the smaller value between diff and 360 − diff. This runs in O(1) time and O(1) space.

Is Angle Between Hands of a Clock asked at Google/Amazon/Meta?

Clock-angle problems appear frequently in technical interviews at companies like Google and Amazon as quick math or reasoning checks. They test whether candidates can model real-world movement with formulas and handle edge cases like partial hour movement.

What data structure is used in Angle Between Hands of a Clock?

No special data structure is required. The problem is purely a mathematical computation involving arithmetic operations and angle normalization.

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

The optimal solution runs in O(1) time because it uses a constant number of arithmetic operations. No loops, recursion, or additional data structures are required. Space complexity is also O(1).

Description Hints 2 Solution Video 8:57

1344. Angle Between Hands of a Clock

Medium69.6% acceptance10 companies

Given two numbers, hour and minutes, return the smaller angle (in degrees) formed between the hour and the minute hand.

Answers within 10^-5 of the actual value will be accepted as correct.

Example 1:

Input: hour = 12, minutes = 30
Output: 165

Example 2:

Input: hour = 3, minutes = 30
Output: 75

Example 3:

Input: hour = 3, minutes = 15
Output: 7.5

Constraints:

1 <= hour <= 12
0 <= minutes <= 59

Asked at 10 companies

Zoho Siemens Epic Systems Bloomberg Salesforce Aurora Amazon

Google Microsoft Meta

Topics

Math

Hints open one at a time

Hint 1

The tricky part is determining how the minute hand affects the position of the hour hand.

Hint 2

Calculate the angles separately then find the difference.

8:57

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

LanguageLoading editor…

1class Solution:
2    def angleClock(self, hour: int, minutes: int) -> float:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

12
30

Input

3
30

Input

3
15

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