JarvisMarch.cpp

Author: lxylxy123456

JarvisMarch.cpp

@@ -0,0 +1,147 @@
+//  
+//  algorithm - some algorithms in "Introduction to Algorithms", third edition
+//  Copyright (C) 2018  lxylxy123456
+//  
+//  This program is free software: you can redistribute it and/or modify
+//  it under the terms of the GNU Affero General Public License as
+//  published by the Free Software Foundation, either version 3 of the
+//  License, or (at your option) any later version.
+//  
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU Affero General Public License for more details.
+//  
+//  You should have received a copy of the GNU Affero General Public License
+//  along with this program.  If not, see <https://www.gnu.org/licenses/>.
+//  
+
+#ifndef MAIN
+#define MAIN
+#define MAIN_JarvisMarch
+#endif
+
+#ifndef FUNC_JarvisMarch
+#define FUNC_JarvisMarch
+
+#include <algorithm>
+#include "utils.h"
+
+#include "SegmentsIntersect.cpp"
+
+template <typename T>
+class Angle: public Vector<T> {
+	public:
+		Angle(): Vector<T>(0, 0) {}
+		Angle(T X, T Y): Vector<T>(X, Y) {}
+		Angle(Vector<T> a, Vector<T> b): Vector<T>(b - a) {}
+		int get_partition() const {	// when x = y = 0, assume inf
+			const T &x = this->x, &y = this->y; 
+			if (y > 0) {			//     2
+				if (x > 0)			//   3 | 1
+					return 1; 		// 4---+---0
+				else if (x == 0)	//   5 | 7
+					return 2; 		//     6
+				else
+					return 3; 
+			} else if (y == 0) {
+				if (x > 0)
+					return 0; 
+				else if (x == 0)
+					return -1; 
+				else
+					return 4; 
+			} else {
+				if (x > 0)
+					return 7; 
+				else if (x == 0)
+					return 6; 
+				else
+					return 5; 
+			}
+		}
+		bool operator<(const Angle<T>& rhs) const {
+			const Angle<T>& lhs = *this; 
+			int lp = lhs.get_partition(), rp = rhs.get_partition(); 
+			if (lp == -1)
+				return false; 
+			else if (rp == -1)
+				return true; 
+			else if (lp != rp)
+				return lp < rp; 
+			else
+				return lhs.Cross(rhs) > 0; 
+		}
+		bool operator==(const Angle<T>& rhs) const {
+			const Angle<T>& lhs = *this; 
+			int lp = lhs.get_partition(), rp = rhs.get_partition(); 
+			if (lp == -1 || rp == -1)
+				return false; 
+			else if (lp != rp)
+				return false; 
+			else
+				return lhs.Cross(rhs) == 0; 
+		}
+}; 
+
+template <typename T>
+void JarvisMarch(std::vector<Vector<T>>& Q, std::vector<Vector<T>>& ans) {
+	Vector<T> p0 = Q[0]; 
+	for (auto i = Q.begin(); i != Q.end(); i++)
+		if (i->y < p0.y || (i->y == p0.y && i->x < p0.x))
+			p0 = *i; 
+	Angle<T> last_angle(1, 0); 
+	Vector<T> last = p0; 
+	while (true) {
+		ans.push_back(last); 
+		Angle<T> candidate_angle; 
+		Vector<T> candidate; 
+		for (auto i = Q.begin(); i != Q.end(); i++) {
+			Angle<T> current(last, *i); 
+			if (!(current < last_angle)) {
+				if (current < candidate_angle || 
+					(current == candidate_angle && 
+					(candidate - last).Length() < (*i - last).Length())) {
+					candidate_angle = current; 
+					candidate = *i; 
+				}
+			}
+		}
+		if (candidate == p0)
+			break; 
+		last = candidate; 
+		last_angle = candidate_angle; 
+	}
+}
+#endif
+
+#ifdef MAIN_JarvisMarch
+int main(int argc, char *argv[]) {
+	const size_t n = get_argv(argc, argv, 1, 200); 
+	const size_t m = get_argv(argc, argv, 2, 10); 
+	std::vector<int> b; 
+	random_integers(b, -n, n, m * 2); 
+	using T = double; 
+	std::vector<Vector<T>> Q, S; 
+	Q.reserve(m); 
+	for (size_t i = 0; i < m; i++)
+		Q.push_back(Vector<T>(b[2 * i + 0], b[2 * i + 1])); 
+	JarvisMarch(Q, S); 
+	std::cout << "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>"
+				 << std::endl; 
+	std::cout << "<svg height=\"" << 2 * n << "\" width=\"" << 2 * n << "\">"
+				 << std::endl; 
+	std::cout << "\t<rect fill=\"#ffffff\" x=\"0\" y=\"0\" width=\"" << 2 * n
+				 << "\" height=\"" << 2 * n << "\"/>" << std::endl; 
+	std::cout << "\t<polygon stroke=\"#000000\" fill=\"#cccccc\" points=\""; 
+	for (auto i = S.begin(); i != S.end(); i++)
+		std::cout << n + i->x + 1 << "," << n + i->y + 1 << " "; 
+	std::cout << "\"/>" << std::endl; 
+	for (auto i = Q.begin(); i != Q.end(); i++)
+		std::cout << "\t<circle cx=\"" << n + i->x + 1 << "\" cy=\""
+				 << n + i->y + 1 << "\" r=\"2\"/>" << std::endl; 
+	std::cout << "</svg>" << std::endl; 
+	return 0; 
+}
+#endif
+

README.md

@@ -220,6 +220,7 @@
 | 33 | AnySegmentsIntersect.cpp		| Below									| 1024 |
 | 33 | AnySegmentsIntersect.cpp		| Any Segments Intersect				| 1025 |
 | 33 | GrahamScan.cpp				| Graham Scan							| 1031 |
+| 33 | JarvisMarch.cpp				| Jarvis March							| 1038 |
 
 # Supplementary Files
 * `utils.h`: Utils