C/C++ Program to Compute the Angle Between Hands of a Clock

Given two numbers, hour and minutes. Return the smaller angle (in sexagesimal units) formed between the hour and the minute hand.

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

Example 4:
Input: hour = 4, minutes = 50
Output: 155

Example 5:
Input: hour = 12, minutes = 0
Output: 0

Constraints:
1 <= hour <= 12
0 <= minutes <= 59
Answers within 10^-5 of the actual value will be accepted as correct.

Hints:
The tricky part is determining how the minute hand affects the position of the hour hand.
Calculate the angles separately then find the difference.

Algorithm to Compute the Angle of the Hour and Minute Hand on the Clock

We can compute the angle between the Hour to the North (clock-wise) in degrees. And the angle between Minute and the North (clock-wise) can be computed in the same way. The answer is minimum of the absolute difference between these two values.

One minute is 6 degrees (there are 60 minutes on the clock). When minute moves, the hour moves proportional. One hour is 30 degrees (there are 12 hours on the clock).

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class Solution {
public:
    double angleClock(int hour, int minutes) {
        double hourAngle = ((hour % 12) + minutes * 1.0/60) * 30;
        double minutesAngle = minutes * 6;
        double a = abs(hourAngle - minutesAngle);
        double b = 360 - a;
        return a < b ? a : b;
    }
};

class Solution {
public:
    double angleClock(int hour, int minutes) {
        double hourAngle = ((hour % 12) + minutes * 1.0/60) * 30;
        double minutesAngle = minutes * 6;
        double a = abs(hourAngle - minutesAngle);
        double b = 360 - a;
        return a < b ? a : b;
    }
};

The Python solution (slightly different) is here: Compute the Angle of the Hour and Minute Hand on a Clock

See also: Teaching Kids Programming – Hour and Minute Angle on a Clock

–EOF (The Ultimate Computing & Technology Blog) —