# 題目: UVa 1206 - Boundary Points

# 題目說明

給數個點 (x, y 平面座標)，求這些點的 凸包(Convex Hull)

INPUT:
每筆測資輸入一行，輸入表示為 (x,y) ，代表一個點的平面座標

OUTPUT:
輸出組成 凸包(Convex Hull) 的點的座標

如果使用 Graham's Scan 演算法需要做極角排序
使用 Andrew's Monotone Chain 演算法則跑兩次半邊，將所有點覆蓋

直接讀入座標後跑 Andrew's Monotone Chain 即可

	#include <iostream>
	#include <string>
	#include <vector>
	#include <sstream>
	#include <algorithm>
	#include <math.h>

	using namespace std;

	static auto fast_io = []
	{
	ios::sync_with_stdio(false);
	cout.tie(nullptr);
	cin.tie(nullptr);
	return 0;
	}();

	struct point
	{
	double x;
	double y;
	double d;
	};
	vector< point > V;
	vector< point > ret;
	string str;

	double dist(point& a, point& b)
	{
	return sqrt(pow(a.x - b.x, 2) + pow(a.y - b.y, 2));
	}

	double cross(point& o, point& a, point& b)
	{
	return (a.x - o.x) * (b.y - o.y) - (a.y - o.y) * (b.x - o.x);
	}

	bool cmp(point& a, point& b)
	{
	auto c = cross(V[0], a, b);
	return c == 0 ? a.d < b.d : c > 0;
	}

	void init()
	{
	V.clear();
	ret.clear();
	}

	void read()
	{
	char _;
	double a, b;
	stringstream ss(str);
	while (ss >> _ >> a >> _ >> b >> _) V.push_back({ a, b });
	}

	void GrahamScan()
	{
	sort(V.begin(), V.end(), [](point& a, point& b)
	{ return a.y < b.y \|\| (a.y == b.y && a.x < b.x); });
	for (int i = 1; i < V.size(); ++i) V[i].d = dist(V[0], V[i]);
	sort(V.begin() + 1, V.end(), cmp);

	V.emplace_back(V[0]);
	for (int i = 0; i < V.size(); ++i)
	{
	int m = ret.size();
	while (m >= 2 && cross(ret[m - 2], ret[m - 1], V[i]) <= 0)
	{
	ret.pop_back();
	--m;
	}
	ret.emplace_back(V[i]);
	}
	}

	void print()
	{
	int S = ret.size();
	for (auto& [x, y, d] : ret)
	{
	cout << '(' << x << ',' << y << ')';
	if (--S) cout << ' ';
	}
	cout << "\n";
	}

	int main()
	{
	while (getline(cin, str))
	{
	init();
	read();
	GrahamScan();
	print();
	}
	}

	#include <iostream>
	#include <string>
	#include <sstream>
	#include <vector>
	#include <algorithm>

	using namespace std;

	struct point
	{
	double x;
	double y;
	};

	string str;
	vector<point> V;
	vector<point> ret;

	void init()
	{
	V.clear();
	ret.clear();
	}

	void read()
	{
	char _;
	double a, b;
	stringstream ss(str);
	while (ss >> _ >> a >> _ >> b >> _) V.push_back({ a, b });
	}

	double cross(point& o, point& a, point& b)
	{
	return (a.x - o.x) * (b.y - o.y) - (a.y - o.y) * (b.x - o.x);
	}

	void Andrews_Monotone_Chain()
	{
	sort(V.begin(), V.end(), [](point& a, point& b)
	{ return a.y < b.y \|\| (a.y == b.y && a.x < b.x); });

	for (int i = 0; i < V.size(); ++i)
	{
	int m = ret.size();
	while (m >= 2 && cross(ret[m - 2], ret[m - 1], V[i]) <= 0)
	{
	ret.pop_back();
	--m;
	}
	ret.emplace_back(V[i]);
	}

	for (int i = V.size() - 2, t = ret.size() + 1; i >= 0; --i)
	{
	int m = ret.size();
	while (m >= t && cross(ret[m - 2], ret[m - 1], V[i]) <= 0)
	{
	ret.pop_back();
	--m;
	}
	ret.emplace_back(V[i]);
	}
	}

	void print()
	{
	int S = ret.size();
	for (auto& [x, y] : ret)
	{
	cout << "(" << x << "," << y << ")";
	if (--S) cout << " ";
	}
	cout << "\n";
	}

	int main()
	{
	while (getline(cin, str))
	{
	init();
	read();
	Andrews_Monotone_Chain();
	print();
	}
	}