Leetcode #1344: Angle Between Hands of a Clock
In this guide, we solve Leetcode #1344 Angle Between Hands of a Clock in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Math
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
Example
Input: hour = 12, minutes = 30
Output: 165
Python Solution
class Solution:
def angleClock(self, hour: int, minutes: int) -> float:
h = 30 * hour + 0.5 * minutes
m = 6 * minutes
diff = abs(h - m)
return min(diff, 360 - diff)
Complexity
The time complexity is O(n) or O(1). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.