Program to determine when the hands of a clock align

Posted by Parveen(Hoven),
Aptitude Trainer and Software Developer

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Program to determine when the hands of a clock meet and align.

Write a program to determine all times of a day when the hands of a clock meet, i.e., are perfectly aligned at an angle of zero degrees.

Step 1: First create a function that takes hours and minutes, and tells a true or false value whether the hands meet at that moment of time.

bool areAligned(int h, float m)
{
    // first calculate angle for hours clock 
    // The angle is measured in degrees 
    // from the mark of number 12 clockwise.
 
    // so far how many minutes have elapsed?
    float totalMinutes = 60 * h + m;
 
    // hours clock travels (360 / 12 ) / 60 =
    // 0.5 degrees in one minute. so total degrees?
    float angleHours = totalMinutes * 0.5f;
 
    // next take the minutes hand
    // it travels 360 degrees in 60 minutes
    // so in one minute it travels = 
    // 360 / 60 = 6 degrees. total angle?
    float angleMinutes = m * 6.0f;
 
    // the difference 
    float angle = angleMinutes - angleHours;
 
    // if it is negative, make absolute
    if(angle < 0)
    {
        angle *= -1;
    }
 
    return angle < 0.1f;
 

}
 

Step 2: Call the above function from your main. We will have to loop for all the moments of the day and check each point.

int main()
{
    for(int h = 0; h < 12; h++)
    {
        for(int m = 0; m < 59; m++)
        {
            // check for each fractional second
            // at this minute
            for(int inc = 0; inc < 100; inc++)
            {
                float minute = m + (float)(inc/100.0);

                if(areAligned(h, minute))
                {
                    cout << "Aligned at: " << h;

                    cout << ":" << minute;

                    cout << endl;

                    break;
                }
            }
        }
    }
    return 0;
}

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