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Decode the Coding Interview in C++: Real-World Examples

Angle Between the Hands of a Clock

Understand how to compute the smaller angle between the hour and minute hands of a clock given any time. Explore angle calculation using modular arithmetic and linear equations to derive efficient code. This lesson helps you implement a solution with O(1) time and space complexity, sharpening your problem-solving skills for coding interviews.

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Description

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

Let’s look at some examples to better understand this:

Coding exercise

C++ 17
double clockAngle(int hour, int minutes){
    // write your code here!
    return 0;
}
Angle between hands of a clock

Solution

The idea is to separately calculate the angles between the 0-minutes vertical line and each hand. The answer will be the difference that is found between the two angles.

Note: Black lines in the clock represent the 0-minutes vertical lines.

Minute hand angle

Let’s start from the minute hand. The minute hand moves with 1 min intervals. At 1 min, the angle of the minute hand is 6°. . Since the whole circle of the clock is equal to 360° degrees and 60 minutes, we estimated that the minute hand moves 1 min = 360° / 60 = 6° degree with each minute.

Now, we can easily find an angle between the 0-minutes vertical line and a minute hand, using minutesAngle = minutes X 6°. ...