TheAlgorithms-C-Plus-Plus/geometry/graham_scan_algorithm.cpp

/******************************************************************************
* @file
* @brief Implementation of the [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull)
* implementation using [Graham Scan](https://en.wikipedia.org/wiki/Graham_scan)
* @details
* In geometry, the convex hull or convex envelope or convex closure of a shape
* is the smallest convex set that contains it. The convex hull may be defined
* either as the intersection of all convex sets containing a given subset of a
* Euclidean space, or equivalently as the set of all convex combinations of
* points in the subset. For a bounded subset of the plane, the convex hull may
* be visualized as the shape enclosed by a rubber band stretched around the subset.
*
* 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.
*
* ### Implementation
*
* Sort points
* We first find the bottom-most point. The idea is to pre-process
* points be sorting them with respect to the bottom-most point. Once the points
* are sorted, they form a simple closed path.
* The sorting criteria is to use the orientation to compare angles without actually
* computing them (See the compare() function below) because computation of actual
* angles would be inefficient since trigonometric functions are not simple to evaluate.
*
* Accept or Reject Points
* Once we have the closed path, the next step is to traverse the path and
* remove concave points on this path using orientation. The first two points in
* sorted array are always part of Convex Hull. For remaining points, we keep track
* of recent three points, and find the angle formed by them. Let the three points
* be prev(p), curr(c) and next(n). If orientation of these points (considering them
* in same order) is not counterclockwise, we discard c, otherwise we keep it.
*
* @author [Lajat Manekar](https://github.com/Lazeeez)
*
*******************************************************************************/
#include <iostream>                       /// for IO Operations
#include <cassert>                        /// for std::assert
#include <vector>                         /// for std::vector
#include <./graham_scan_functions.h>      /// for all the functions used

/*******************************************************************************
 * @brief Self-test implementations
 * @returns void
 *******************************************************************************/
void test() {
    std::vector<geometry::grahamscan::Point> points = {{0, 3},
                                                       {1, 1},
                                                       {2, 2},
                                                       {4, 4},
                                                       {0, 0},
                                                       {1, 2},
                                                       {3, 1},
                                                       {3, 3}};
    std::vector<geometry::grahamscan::Point> expected_result = {{0, 3},
                                                                {4, 4},
                                                                {3, 1},
                                                                {0, 0}};
    std::vector<geometry::grahamscan::Point> derived_result;
    std::vector<geometry::grahamscan::Point> res;

    derived_result = geometry::grahamscan::convexHull(points, points.size());

    std::cout << "Test#1...";
    for (int i = 0; i < expected_result.size(); i++) {
        assert(derived_result[i].x == expected_result[i].x);
        assert(derived_result[i].y == expected_result[i].y);
    }
    std::cout << "Passed" << std::endl;
}

/*******************************************************************************
 * @brief Main function
 * @returns 0 on exit
 *******************************************************************************/
int main() {
    test();
    return 0;
}