This documentation is automatically generated by online-judge-tools/verification-helper
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/courses/library/4/CGL/3/CGL_3_A
#include "src/real-geometry/area/polygon-area.hpp"
#include "src/real-geometry/class/polygon.hpp"
#include "src/real-geometry/utility/io-set.hpp"
#include <iostream>
int main() {
using R = long double;
int n;
std::cin >> n;
geometry::polygon<R> poly(n);
for (auto &p: poly) {
std::cin >> p;
}
geometry::IoSetup(1);
std::cout << geometry::polygon_area(poly) << std::endl;
}
#line 1 "test/aoj/cgl/3_A.test.cpp"
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/courses/library/4/CGL/3/CGL_3_A
#line 2 "src/real-geometry/area/polygon-area.hpp"
#line 2 "src/real-geometry/common/size-alias.hpp"
#include <cstddef>
namespace geometry {
using isize = std::ptrdiff_t;
using usize = std::size_t;
}
#line 2 "src/real-geometry/class/polygon.hpp"
#line 2 "src/real-geometry/class/point.hpp"
#line 2 "src/real-geometry/class/vector.hpp"
#include <complex>
#include <iostream>
namespace geometry {
template< typename R >
class vec2d : public std::complex< R > {
using complex = std::complex< R >;
public:
using complex::complex;
vec2d(const complex &c): complex::complex(c) {}
const R x() const { return this->real(); }
const R y() const { return this->imag(); }
friend vec2d operator*(const vec2d &v, const R &k) {
return vec2d(v.x() * k, v.y() * k);
}
friend vec2d operator*(const R &k, const vec2d &v) {
return vec2d(v.x() * k, v.y() * k);
}
friend std::istream &operator>>(std::istream &is, vec2d &v) {
R x, y;
is >> x >> y;
v = vec2d(x, y);
return is;
}
};
}
#line 4 "src/real-geometry/class/point.hpp"
#include <vector>
namespace geometry {
template< typename R >
using point = vec2d<R>;
template< typename R >
using points = std::vector< point< R > >;
}
#line 4 "src/real-geometry/class/polygon.hpp"
#line 6 "src/real-geometry/class/polygon.hpp"
namespace geometry {
template< typename R >
using polygon = std::vector< point<R> >;
template< typename R >
using polygons = std::vector< polygon<R> >;
}
#line 2 "src/real-geometry/operation/cross-product.hpp"
#line 4 "src/real-geometry/operation/cross-product.hpp"
namespace geometry {
template< typename R >
R cross_product(const vec2d<R> &a, const vec2d<R> &b) {
return a.x() * b.y() - a.y() * b.x();
}
}
#line 2 "src/real-geometry/utility/next-idx.hpp"
#line 4 "src/real-geometry/utility/next-idx.hpp"
namespace geometry {
inline usize next_idx(usize idx, usize size) {
return idx + 1 == size ? 0 : idx + 1;
}
}
#line 7 "src/real-geometry/area/polygon-area.hpp"
namespace geometry {
template< typename R >
R polygon_area(const polygon<R> &poly) {
usize n = poly.size();
R res = 0;
for (usize i = 0; i < n; ++i) {
res += cross_product(poly[i], poly[next_idx(i, n)]);
}
return res / 2;
}
}
#line 2 "src/real-geometry/utility/io-set.hpp"
#include <iomanip>
namespace geometry {
class IoSetup {
using u32 = unsigned int;
void set(std::ostream &os, u32 precision) {
os << std::fixed << std::setprecision(precision);
}
public:
IoSetup(u32 precision = 15) {
std::cin.tie(0);
std::ios::sync_with_stdio(0);
set(std::cout, precision);
set(std::cerr, precision);
}
} iosetup;
}
#line 6 "test/aoj/cgl/3_A.test.cpp"
#line 8 "test/aoj/cgl/3_A.test.cpp"
int main() {
using R = long double;
int n;
std::cin >> n;
geometry::polygon<R> poly(n);
for (auto &p: poly) {
std::cin >> p;
}
geometry::IoSetup(1);
std::cout << geometry::polygon_area(poly) << std::endl;
}