Angle Between Hands of a Clock - Practice Coding Problems

Angle Between Hands of a Clock - Problem

Math Medium

Given two integers hour and minutes, return the smaller angle (in degrees) formed between the hour and minute hands on a clock.

The angle should be calculated as a positive floating-point number. Answers within 10^-5 of the actual value will be accepted as correct.

Note: The hour hand moves continuously as minutes pass, not in discrete jumps.

Input & Output

Example 1 — Basic Case

$ Input: hour = 12, minutes = 30

› Output: 165.0

💡 Note: At 12:30, minute hand points to 6 (180°), hour hand is halfway between 12 and 1 (15°). Angle = |180° - 15°| = 165°

Example 2 — Perfect Alignment

$ Input: hour = 3, minutes = 0

› Output: 90.0

💡 Note: At 3:00, minute hand points to 12 (0°), hour hand points to 3 (90°). Angle = |90° - 0°| = 90°

Example 3 — Obtuse Angle Case

$ Input: hour = 3, minutes = 30

› Output: 75.0

💡 Note: At 3:30, minute hand at 180°, hour hand at 105° (3×30° + 30×0.5°). Angle = |180° - 105°| = 75°

Constraints

1 ≤ hour ≤ 12
0 ≤ minutes ≤ 59

Visualization

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Understanding the Visualization

Input

Given hour and minutes (e.g., 3:15)

Calculate

Find each hand's angle from 12 o'clock position

Output

Return the smaller of two possible angles

Key Takeaway

🎯 Key Insight: Clock hands move at constant rates, making this a pure mathematical calculation problem

Asked in

A Amazon 15 M Microsoft 12 🍎 Apple 8

The key insight is that both clock hands move at constant rates: the minute hand moves 6° per minute, while the hour hand moves 30° per hour plus 0.5° per minute. Best approach uses direct mathematical formulas to calculate each hand's position and find the smaller angle. Time: O(1), Space: O(1)

Common Approaches

Approach	Time	Space	Notes
✓ Mathematical Formula	O(1)	O(1)	Calculate each hand's angle from 12 o'clock and find the difference
Direct Formula Optimization	O(1)	O(1)	Same approach but with cleaner mathematical expression

Mathematical Formula — Algorithm Steps

Step 1: Calculate minute hand angle = minutes × 6°
Step 2: Calculate hour hand angle = (hour % 12) × 30° + minutes × 0.5°
Step 3: Find absolute difference and return minimum of diff and 360° - diff

Visualization

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Step-by-Step Walkthrough

Calculate Positions

Minute hand at 6° per minute, hour hand moves continuously

Find Difference

Calculate absolute difference between the two angles

Get Smaller Angle

Return minimum of difference and 360° - difference

Code -

solution.c — C

#include <stdio.h>
#include <math.h>

double solution(int hour, int minutes) {
    // Minute hand: 6 degrees per minute
    double minuteAngle = minutes * 6.0;
    
    // Hour hand: 30 degrees per hour + 0.5 degrees per minute
    double hourAngle = (hour % 12) * 30.0 + minutes * 0.5;
    
    // Find absolute difference
    double diff = fabs(hourAngle - minuteAngle);
    
    // Return the smaller angle
    return fmin(diff, 360.0 - diff);
}

int main() {
    int hour, minutes;
    scanf("%d", &hour);
    scanf("%d", &minutes);
    
    double result = solution(hour, minutes);
    printf("%f\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

All operations are constant time arithmetic calculations

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables to store angles

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Mathematical Formula — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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