unreasonably effective

link For each pair of points we consider one as top-left (A) and the other as bottom-right (C) corner of an axis-aligned rectangle. Then, we try finding B and D. Once we have found all four corners, we check if other points lie on the rectangle, if not, we include it in max area computation.…

link Exclude each point We can find the max distance between pairs of points excluding each point and take the minimum. Time: , space: . Extreme points We want to remove one of the “extreme points” because extreme points are the furthest apart from each other. Say we have a pair of points: . The…

link For a not-convex polygon, the direction of travel changes: say, clockwise to counter-clockwise. If we have three consecutive points , the sign of the cross product between the two consecutive vectors: and gives us the direction of travel. If the direction changes, we declare the polygon to be not-convex. Time: , space: .

link For each pair of points we want to consider one as the top-left and the other as the bottom-right. Then, we want to find the other two corners: top-right and bottom-left. Since left two corners must have smaller x-coordinates than the right two corners, we first sort the points by x-coordinate. This reduces the…

link Like in atoi, we detect if there will be an overflow or an underflow before including the next digit. Time: , space: .

link We check side lengths and perpedicularity like below: Time: , space: .

link Each full cut adds two more regions. So, for even n’s we can use full cuts. For example, when n = 4, we have two full cuts which can be thought of as four aligned half-cuts. To go from n = 4 to n = 5, we need to adjust the angles between these…

link Say the line has slope . If a point’s slope with a point on the line is , the new point is also on the line. For each pair of consecutive points we check if they have the same slope. With points, time: , space: .