Graham Scan Algorithm

We have discussed Jarvis’s Algorithm for Convex Hull. The worst case time complexity of Jarvis’s Algorithm is O(n^2). Using Graham’s scan algorithm, we can find Convex Hull in O(nLogn) time. Following is Graham’s algorithm 
Let points[0..n-1] be the input array.

1) Find the bottom-most point by comparing y coordinate of all points. If there are two points with the same y value, then the point with smaller x coordinate value is considered. Let the bottom-most point be P0. Put P0 at first position in output hull.

2) Consider the remaining n-1 points and sort them by polar angle in counterclockwise order around points[0]. If the polar angle of two points is the same, then put the nearest point first.

3 After sorting, check if two or more points have the same angle. If two more points have the same angle, then remove all same angle points except the point farthest from P0. Let the size of the new array be m.

4) If m is less than 3, return (Convex Hull not possible)

5) Create an empty stack ‘S’ and push points[0], points[1] and points[2] to S.

6) Process remaining m-3 points one by one. Do following for every point ‘points[i]’ 

       4.1) Keep removing points from stack while orientation of following 3 points is not counterclockwise (or they don’t make a left turn). 

           a) Point next to top in stack 
           b) Point at the top of stack 
           c) points[i] 

        4.2) Push points[i] to S

5) Print contents of S

Graham Scan Algorithm : https://www.geeksforgeeks.org/convex-hull-set-2-graham-scan/