Angle Between Hour Hand And Minute Hand
Given the time in hours and minutes, you need to calculate the angle between the hour hand and the minute hand.

Note :

There can be two angles between the hour hand and minute hand, you need to print a minimum of two. Also, print the floor value of angle i.e. if the angle is 15.2, you need to print 15.

Input format:

The first line of input contains an integer ‘T’ denoting the number of test cases. The first and only line of each test case contains two integers H and M denoting the time in hours and minutes.

Output format:

For each test case, print the smaller angle between the hour hand and minute hand.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1

Question

Angle Between Hour Hand And Minute Hand

Given the time in hours and minutes, you need to calculate the angle between the hour hand and the minute hand.

Note :

There can be two angles between the hour hand and minute hand, you need to print a minimum of two. Also, print the floor value of angle i.e. if the angle is 15.2, you need to print 15.

Input format:

The first line of input contains an integer ‘T’ denoting the number of test cases.

The first and only line of each test case contains two integers H and M denoting the time in hours and minutes.

Output format:

For each test case, print the smaller angle between the hour hand and minute hand.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 50
1 <= H <= 12
0 <= M <= 59

Time Limit: 1 sec

Accepted Answer

The idea is to take 12:00 (h = 12, m = 0) as a reference.
Steps :
1. Calculate the angle made by hour hand with respect to 12:00 in h hours and m minutes.
2. Calculate the angle made by minute hand with respect to 12:00 in h hours and m minutes.
3. The difference between the two angles is the angle between the two hands

Pseudocode :
calcAngle(h,m)
{
// validate the input
if (h <0 or m < 0 or h >12 or m > 60)
print("Wrong Input")

if (h is equal to 12) h = 0;
if (m is equal to 60)
{
m = 0;
h += 1;
if(h>12)
h = h-12;
}

// Calculate the angles moved by hour and minute hands with reference to 12:00
initialise hour_angle as 0.5 * (h * 60 + m)
initialise minute_angle as 6 * m

// Find the difference between two angles
initialise angle as absolute value of (hour_angle - minute_angle)

// Return the smaller angle of two possible angles
update angle to minimum of (360 - angle, angle)

return angle
}

Accepted Answer

Using reference time

The idea is to take the 12:00 i.e. H = 12 and M = 0 as reference time.
First, calculate the angle made by the hour hand with respect to 12:00 in H hours and M minutes. In 12 hours the hour hand moves by 360 degrees i.e. 30 degrees in 1 hour and 0.5 degrees in 1 minute. So in H hours and M minutes, the angle moved by hour hand is 0.5 * (H * 60 + M).
Then, calculate the angle made by minute hand with respect to 12:00 in H hours and M minutes. In 60 minutes the minute hand moves by 360 degrees i.e. 6 degrees in 1 minute. So in H hours and M minutes, the angle moved by minute hand is 6 * M.
The difference between the two angles is the required angle.

Space Complexity: O(1)Explanation:

O(1) per test case.

In the worst case, we are taking constant space.

Time Complexity: O(1)Explanation: