Separate convex hull algorithm in a header

Author: AbdeltwabMF

.gitignore

@@ -30,3 +30,4 @@
 *.exe
 *.out
 *.app
+build/

CMakeLists.txt

@@ -0,0 +1,11 @@
+cmake_minimum_required(VERSION 3.16)
+
+project(DSA)
+
+set(CMAKE_CXX_STANDARD 17)
+
+set(CMAKE_ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin/$<CONFIG>")
+set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin/$<CONFIG>")
+set(CMAKE_RUNTIME_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin/$<CONFIG>")
+
+add_subdirectory(geometry)

README.md

@@ -126,7 +126,8 @@
 
 ## 6. [geometry](geometry)
 
-- [convex hull](geometry/convex_hull.cpp)
+- [types](geometry/types.h)
+- [convex hull](geometry/convex_hull.h)
 
 ---
 

geometry/CMakeLists.txt

@@ -0,0 +1,5 @@
+cmake_minimum_required(VERSION 3.16)
+
+project(Geometry)
+
+add_executable(main main.cpp)

geometry/convex_hull.cpp

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+#pragma once
+
+#include "types.h"
+
+#include <vector>
+#include <algorithm>
+#include <cmath>
+
+namespace geometry
+{
+	[[nodiscard]] static inline std::vector<ivec2>
+	convex_hull_construct(std::vector<ivec2> points)
+	{
+		// lowest y-coordinate and leftmost point
+		ivec2 pivot = *std::min_element(points.begin(), points.end());
+
+		std::sort(
+			points.begin(),
+			points.end(),
+			[&pivot](const ivec2& a, const ivec2& b)
+			{
+				auto area = (a - pivot) * (b - pivot);
+				auto a_smaller = ::abs(pivot.x - a.x) + ::abs(pivot.y - a.y) < ::abs(pivot.x - b.x) + ::abs(pivot.y - b.y);
+				return (area != 0) * (area > 0) + (area == 0) * a_smaller;
+			}
+		);
+
+		std::vector<ivec2> polygon;
+		polygon.reserve(points.size());
+
+		for (size_t i = 0; i < points.size(); ++i)
+		{
+			while (polygon.size() >= 2)
+			{
+				auto a = polygon.end()[-2];
+				auto b = polygon.end()[-1];
+				auto& c = points[i];
+
+				if ((b - a) * (c - a) > 0)
+					break;
+
+				// remove last point if it results in a clockwise orientation or if the points are collinear
+				polygon.pop_back();
+			}
+			polygon.push_back(points[i]);
+		}
+
+		polygon.shrink_to_fit();
+		return polygon;
+	}
+}

geometry/convex_hull.h

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+#include "convex_hull.h"
+
+// Problem statement: https://open.kattis.com/problems/convexhull
+int main()
+{
+	std::ios_base::sync_with_stdio(false);
+	std::cin.tie(nullptr);
+
+	std::vector<ivec2> points;
+	points.reserve(10'000 + 9);
+
+	int n{};
+	while (std::cin >> n && n)
+	{
+		points.resize(n);
+		for (size_t i = 0; i < n; ++i)
+			std::cin >> points[i];
+
+		auto polygon = geometry::convex_hull_construct(points);
+		if (polygon.size() == 2 && polygon[0] == polygon[1])
+			polygon.pop_back();
+
+		std::cout << polygon.size() << '\n';
+		for (size_t i = 0; i < polygon.size(); ++i)
+			std::cout << polygon[i] << '\n';
+	}
+}

geometry/main.cpp

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+#pragma once
+
+#include <iostream>
+
+struct ivec2
+{
+	int64_t x, y;
+
+	inline bool operator<(const ivec2& other) const
+	{
+		return (y != other.y) ? (y < other.y) : (x < other.x);
+	}
+
+	inline bool operator==(const ivec2& other) const
+	{
+		return (x == other.x) && (y == other.y);
+	}
+
+	inline ivec2 operator-(const ivec2& other) const
+	{
+		return ivec2{x - other.x, y - other.y};
+	}
+
+	inline ivec2& operator-=(const ivec2& other)
+	{
+		x -= other.x;
+		y -= other.y;
+		return *this;
+	}
+
+	inline int64_t operator*(const ivec2& other) const
+	{
+		return x * other.y - y * other.x;
+	}
+};
+
+std::ostream& operator<<(std::ostream& out, const ivec2& vec)
+{
+	out << vec.x << " " << vec.y;
+	return out;
+}
+
+std::istream& operator>>(std::istream& in, ivec2& vec)
+{
+	in >> vec.x >> vec.y;
+	return in;
+}