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main.cpp
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135 lines (114 loc) · 2.95 KB
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// Graham's convex hull
// input:
// list of points
// output:
// indicies of points that make up the convex hull
// Written by Dmitriy Okoneshnikov, 2021
#include <iostream>
#include <fstream>
#include <cmath>
#include <chrono>
#include <vector>
#include <limits>
#include <algorithm>
using namespace std;
typedef numeric_limits<double> dbl;
struct Point
{
double x;
double y;
Point(double x = 0.0, double y = 0.0)
: x(x), y(y)
{
}
Point operator-(Point pnt) { return Point(x - pnt.x, y - pnt.y); }
};
int getIndex(vector<Point> v, Point k)
{
for (int i = 0; i < v.size(); i++)
{
if (abs(v[i].x - k.x) < 10e-8 && abs(v[i].y - k.y) < 10e-8)
return i;
}
return -1;
}
ostream &operator<<(ostream &stream, const Point &p)
{
stream << p.x << " " << p.y;
return stream;
}
double vect_prod(Point A, Point B)
{
return A.x * B.y - A.y * B.x;
}
bool sort_func(Point a, Point b)
{
return vect_prod(a, b) > 0 || vect_prod(a, b) == 0 && (a.x * a.x + a.y * a.y < b.x * b.x + b.y * b.y);
}
vector<Point> convex_hull(vector<Point> points)
{
Point p0 = points[0];
for (Point p : points)
if (p.x < p0.x || (p.x == p0.x && p.y < p0.y))
p0 = p;
// сдвинуть в начало координат
for (Point &p : points)
{
p.x -= p0.x;
p.y -= p0.y;
}
// отсортировать по углу
sort(points.begin(), points.end(), &sort_func);
vector<Point> hull;
for (Point p : points)
{
// убираем последнюю точку минимальной выпуклой оболочки пока она выпуклая
while (hull.size() >= 2 && (vect_prod((p - hull.back()), (hull[hull.size() - 2] - hull.back())) <= 0))
hull.pop_back();
hull.push_back(p);
}
// сдвигаем обратно точки
for (Point &p : hull)
{
p.x += p0.x;
p.y += p0.y;
}
return hull;
}
int main(int argc, char **argv)
{
string input_filename = "input.txt";
string output_filename = "output.txt";
if (argc == 2)
{
input_filename = argv[1];
}
else if (argc >= 3)
{
input_filename = argv[1];
output_filename = argv[2];
}
ifstream inp(input_filename);
int n;
inp >> n;
vector<Point> arr;
for (int i = 0; i < n; i++)
{
Point temp;
inp >> temp.x;
inp >> temp.y;
arr.push_back(temp);
}
inp.close();
auto start = chrono::steady_clock::now();
vector<Point> ch = convex_hull(arr);
auto end = chrono::steady_clock::now();
auto diff = end - start;
ofstream out(output_filename, std::ios::out | std::ios::trunc);
out.precision(dbl::max_digits10);
out << chrono::duration<double, nano>(diff).count() << endl;
out << ch.size() << endl;
for (int i = 0; i < ch.size(); i++)
out << getIndex(arr, ch[i]) + 1 << " ";
out.close();
}