Erect the Fence - Solution & Explanation

The Monotone Chain Algorithm is an efficient algorithm for finding the convex hull of a set of 2D points. It constructs the hull in O(n log n) time. The idea is to sort the points, then construct the lower and upper hulls in O(n) time each. Points are rejected if they don't form a 'left turn', which can be determined using cross product.

This C code implements the Monotone Chain Algorithm for finding the convex hull. First, it sorts the points, then constructs the lower and upper hulls. Sorting ensures all points are processed in order, while stack logic applies to maintaining valid hull points by checking the turn direction using cross product.

The Gift Wrapping Algorithm, also known as Jarvis March, is another method to find the convex hull. It builds the hull one vertex at a time, looking for the line tangent to the current edge and a point in the set of all remaining points. It's less efficient than Monotone Chain, operating in O(nh) time complexity, where h is the number of hull vertices.

This C implementation of the Gift Wrapping Algorithm iteratively chooses the most counterclockwise point until it returns to the start point. It determines orientation by calculating the cross product and compares relative angles.