Problem K
Jumbled Compass
The compass gives the current direction the phone is pointing and Jonas’ task is to animate the needle taking the shortest path from the current needle direction to the correct direction. Many ifs, moduli, and even an arctan later, he is still not convinced his minimumDistance function is correct; he calls you on the phone.
Input
The first line of input contains an integer $n_1$ ($0 \le n_1 \le 359$), the current direction of the needle. The second line of input contains an integer $n_2$ ($0 \le n_2 \le 359$), the correct direction of the needle.
Output
Output the change in direction that would make the needle spin the shortest distance from $n_1$ to $n_2$. A positive change indicates spinning the needle clockwise, and a negative change indicates spinning the needle counter-clockwise. If the two input numbers are diametrically opposed, the needle should travel clockwise. I.e., in this case, output $180$ rather than $-180$.
| Sample Input 1 | Sample Output 1 |
|---|---|
315 45 |
90 |
| Sample Input 2 | Sample Output 2 |
|---|---|
180 270 |
90 |
| Sample Input 3 | Sample Output 3 |
|---|---|
45 270 |
-135 |
