Solved
Difficulty: D2C

思考题 inspired by Saionji Video Channel

Eastmost Eki

There are n points on a 2D plane. You can select any real point as pivot in the rectangle bounded by (a,b) and (c,d) and rotate the entire plane by d degree clockwise or anticlockwise. This operation can only be done once. What's the minimum d required to make the x coordinate of point 1 no less than any other points' (in other words, the rightmost point) after the rotation or report it is not possible.

n\leq 10^5, |a|,|b|,|c|,|d|\leq 10^9

Solution

By XGN

Hint: The pivot does not matter. Then calculate the angle between P1 and other points and try to find a 180 degree gap.