Angle Between Hands of a Clock

LeetCode 1446 | Difficulty: Medium

Medium

Problem Description

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`

Topics: Math

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Approach

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

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Solutions

Solution 1: C# (Best: 47 ms)

Metric	Value
Runtime	47 ms
Memory	25.5 MB
Date	2022-01-17

Solution

public class Solution {
    public double AngleClock(int hour, int minutes) {
        
    hour = (hour==12) ? 0 : hour;
    double hourAngle = hour*30 + (minutes*0.5);
    double minutesAngle = minutes * 6;
    double result = Math.Abs(hourAngle-minutesAngle);
    return Math.Min(result, 360.0-result);
    }
}

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Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.
• LeetCode provides 2 hint(s) for this problem — try solving without them first.

💡 Hints

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.