演示截图：

//蛮力法求凸包问题
#include<iostream>
#include<vector>
#include<algorithm>
#include<conio.h>
#include<map>
#include<graphics.h>
using namespace std;
const int maxn = 1e4 + 15;
const double eps = 1e-8;
struct Point {
	double x;
	double y;
};
vector<pair<double, double> > convexHull(vector<pair<double, double> >& point, int n) {
	vector<pair<double, double> > pointPairVec;
	if (n <= 2)
		return	point;
	//扫描每个点
	for (int i = 0; i < n - 1; i++) {
		for (int j = i + 1; j < n; j++) {
			double a = point[j].second - point[i].second;
			double b = point[i].first - point[j].first;
			double c = point[i].first * point[j].second - point[i].second * point[j].first;
			vector<pair<double, double> >  signEqualVec;
			signEqualVec.push_back(point[i]);
			signEqualVec.push_back(point[j]);
			int sign1 = 0, sign2 = 0;  //记录直线两边的点
			//扫描直线外的所有的点
			for (int k = 0; k < n; k++) {
				if (k == i || k == j)
					continue;
				else {
					double sign = a * point[k].first + b * point[k].second - c;
					if (sign == 0)
						signEqualVec.push_back(point[k]);
					else if (sign > 0)
						sign1++;
					else if (sign < 0)
						sign2++;
				}
			}
			if (sign1 > 0 && sign2 > 0)
				continue;
			else {
				for (int l = 0; l < signEqualVec.size(); l++)
					pointPairVec.push_back(signEqualVec[l]);
			}
		}
	}
	return pointPairVec;
}
//点点，将所有点画在坐标轴上
void drow_graph(vector<pair<double, double> >& point, int n) {
	initgraph(800, 800); //画布大小
	setbkcolor(WHITE);
	cleardevice();
	setlinecolor(BLUE);
	line(400, 0, 400, 800); //制作横纵坐标轴
	line(0, 400, 800, 400); //此时理论原点为画布中（400, 400）
	for (int i = 0; i < n; i++) {
		setfillcolor(RED);
		double x = point[i].first + 400;
		double y = 400 - point[i].second;
		fillcircle(x, y, 5);
	}
}
//连线，将点对连接起来
void connect_end(Point* point, int n) {
	setlinecolor(RED);
	setlinestyle(10);
	for (int i = 0; i < n - 1; i++) {
		double x1 = point[i].x + 400;
		double y1 = 400 - point[i].y;
		double x2 = point[i + 1].x + 400;
		double y2 = 400 - point[i + 1].y;
		line(x1, y1, x2, y2);
	}
	double x = point[0].x + 400;
	double y = 400 - point[0].y;
	double x1 = point[n - 1].x + 400;
	double y1 = 400 - point[n - 1].y;
	line(x, y, x1, y1);
	_getch();
	closegraph();
}
Point p[maxn];
int dblcmp(double k) {
	if (fabs(k) < eps) return 0;
	return k > 0 ? 1 : -1;
}
double multi(Point p0, Point p1, Point p2) {
	return (p1.x - p0.x) * (p2.y - p0.y) - (p1.y - p0.y) * (p2.x - p0.x);
}
bool cmp(const Point& a, const Point& b) {
	return dblcmp(multi(p[0], a, b)) > 0;
}
int main()
{
	vector<pair<double, double> > pointsArray(maxn);
	cout << "请输入点的个数：";
	int n; cin >> n;
	cout << "请输入点的坐标：" << endl;
	for (int i = 0; i < n; i++) {
		double x, y; cin >> x >> y;
		pointsArray[i] = make_pair(x, y);
	}
	drow_graph(pointsArray, n);
	vector<pair<double, double> > convex = convexHull(pointsArray, n);
	map<pair<double, double>, int>mp;
	int t = 0;
	//打标记，取消重复点
	for (int i = 0; i < convex.size(); i++) {
		pair<double, double> pa = make_pair(convex[i].first, convex[i].second);
		if (mp[pa] == 0) {
			p[t].x = convex[i].first;
			p[t++].y = convex[i].second;
			mp[pa]++;
		}
	}
	sort(p + 1, p + t, cmp);
	connect_end(p, t);
	return 0;
}