verify/geometry/centroid.test.cpp

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• Last update: 2026-10-06 02:48:54+09:00
• Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A

Depends on

• DSU (Disjoint Set Union) (ds/dsu/dsu.hpp)
• Fenwick Tree (Binary Indexed Tree) (ds/range_query/fenwick_tree.hpp)
• Geometry Bundle (geometry/all.hpp)
• Angle Sort (geometry/angle_sort.hpp)
• Circles (geometry/circle.hpp)
• Circle Coverage Areas (geometry/circle_coverage_areas.hpp)
• Area of Union of Circles (geometry/circle_union_area.hpp)
• Closest Pair of Points (geometry/closest_pair.hpp)
• Convex Decomposition (geometry/convex_decomposition.hpp)
• Convex Hull (geometry/convex_hull.hpp)
• Convex Layers (geometry/convex_layers.hpp)
• Convex Polygons (geometry/convex_polygon.hpp)
• Count Points in Triangle (geometry/count_points_in_triangle.hpp)
• Delaunay Triangulation (geometry/delaunay_triangulation.hpp)
• geometry/detail/convex_polygon_normalize.hpp
• geometry/detail/floating_predicate.hpp
• Euclidean Minimum Spanning Tree (geometry/euclidean_mst.hpp)
• Farthest Pair of Points (geometry/farthest_pair.hpp)
• Half-Plane Intersection (geometry/half_plane_intersection.hpp)
• Lattice-Point Count (geometry/lattice_point_count.hpp)
• Linear Objects (geometry/linear.hpp)
• Manhattan Minimum Spanning Tree (geometry/manhattan_mst.hpp)
• Manhattan Segment Intersections (geometry/manhattan_segment_intersections.hpp)
• Minimum Enclosing Circle (geometry/minimum_enclosing_circle.hpp)
• Minkowski Sum (geometry/minkowski_sum.hpp)
• Perpendicular Bisector (geometry/perpendicular_bisector.hpp)
• 2D Point and Predicates (geometry/point.hpp)
• 2D Point and Predicates (geometry/point.hpp)
• Polygons (geometry/polygon.hpp)
• Area of Union of Rectangles (geometry/rectangle_union_area.hpp)
• Steiner Convex Decomposition (geometry/steiner_convex_decomposition.hpp)
• Voronoi Diagram (geometry/voronoi_diagram.hpp)
• Convolution (math/fps/convolution.hpp)
• math/fps/internal/ntt998_faster.hpp
• ModInt (math/modint.hpp)
• BigInt (utilities/bigint.hpp)
• utilities/detail/fixed_int.hpp
• Fast IO (utilities/fast_io.hpp)
• Int256 (utilities/int256.hpp)
• Int512 (utilities/int512.hpp)

Code

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A"

#include "../../geometry/all.hpp"

#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <cstdint>
#include "../../utilities/fast_io.hpp"
#include <vector>

namespace {

using namespace m1une::geometry;
using P = Point<long long>;

bool close(long double first, long double second) {
    return std::fabs(first - second) <= 1e-10L;
}

void test_fixed() {
    const Point<long double> point_center = centroid(P(3, -5));
    assert(close(point_center.x, 3));
    assert(close(point_center.y, -5));

    const Segment<long long> segment{P(0, 2), P(6, 8)};
    const Point<long double> segment_center = centroid(segment);
    assert(close(segment_center.x, 3));
    assert(close(segment_center.y, 5));
    const Segment<long long> degenerate{P(4, 7), P(4, 7)};
    assert(centroid(degenerate) == Point<long double>(4, 7));

    std::array<P, 3> triangle;
    triangle[0] = P(0, 0);
    triangle[1] = P(6, 0);
    triangle[2] = P(0, 3);
    const Point<long double> triangle_center = centroid(triangle);
    assert(close(triangle_center.x, 2));
    assert(close(triangle_center.y, 1));

    const Circle<long long> circle{P(-3, 9), 5};
    assert(centroid(circle) == Point<long double>(-3, 9));
    const Circle<long long> boundary{P(7, -4), 3, false};
    assert(centroid(boundary) == Point<long double>(7, -4));

    std::vector<P> concave;
    concave.emplace_back(0, 0);
    concave.emplace_back(5, 0);
    concave.emplace_back(5, 1);
    concave.emplace_back(1, 1);
    concave.emplace_back(1, 5);
    concave.emplace_back(0, 5);
    const auto concave_center = centroid(concave);
    assert(concave_center.has_value());
    assert(close(concave_center->x, 14.5L / 9));
    assert(close(concave_center->y, 14.5L / 9));
    std::reverse(concave.begin(), concave.end());
    const auto clockwise_center = centroid(concave);
    assert(clockwise_center.has_value());
    assert(close(clockwise_center->x, concave_center->x));
    assert(close(clockwise_center->y, concave_center->y));

    std::vector<P> square;
    square.emplace_back(0, 0);
    square.emplace_back(4, 0);
    square.emplace_back(4, 2);
    square.emplace_back(0, 2);
    const ConvexPolygon<long long> convex(square);
    const auto convex_center = centroid(convex);
    assert(convex_center.has_value());
    assert(close(convex_center->x, 2));
    assert(close(convex_center->y, 1));

    std::vector<P> collinear;
    collinear.emplace_back(0, 0);
    collinear.emplace_back(2, 0);
    collinear.emplace_back(7, 0);
    assert(!centroid(collinear).has_value());
}

void test_randomized_concave_polygons() {
    std::uint64_t state = 0x243f6a8885a308d3ULL;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 3000; ++trial) {
        const long long width = 2 + static_cast<long long>(random() % 100);
        const long long height = 2 + static_cast<long long>(random() % 100);
        const long long inner_x =
            1 + static_cast<long long>(random() % (width - 1));
        const long long inner_y =
            1 + static_cast<long long>(random() % (height - 1));
        const long long translate_x =
            static_cast<long long>(random() % 201) - 100;
        const long long translate_y =
            static_cast<long long>(random() % 201) - 100;

        std::vector<P> polygon;
        polygon.emplace_back(translate_x, translate_y);
        polygon.emplace_back(translate_x + width, translate_y);
        polygon.emplace_back(
            translate_x + width,
            translate_y + inner_y
        );
        polygon.emplace_back(
            translate_x + inner_x,
            translate_y + inner_y
        );
        polygon.emplace_back(
            translate_x + inner_x,
            translate_y + height
        );
        polygon.emplace_back(translate_x, translate_y + height);
        if (random() % 2 != 0) std::reverse(polygon.begin(), polygon.end());

        const long double w = static_cast<long double>(width);
        const long double h = static_cast<long double>(height);
        const long double x = static_cast<long double>(inner_x);
        const long double y = static_cast<long double>(inner_y);
        const long double tx = static_cast<long double>(translate_x);
        const long double ty = static_cast<long double>(translate_y);
        const long double full_area = w * h;
        const long double removed_area = (w - x) * (h - y);
        const long double area = full_area - removed_area;
        const long double expected_x = tx +
            (
                full_area * w / 2 -
                removed_area * (x + w) / 2
            ) / area;
        const long double expected_y = ty +
            (
                full_area * h / 2 -
                removed_area * (y + h) / 2
            ) / area;

        const auto result = centroid(polygon);
        assert(result.has_value());
        assert(close(result->x, expected_x));
        assert(close(result->y, expected_y));
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    test_fixed();
    test_randomized_concave_polygons();

    int size;
    fast_input >> size;
    std::vector<P> polygon(size);
    for (P& point : polygon) fast_input >> point.x >> point.y;
    fast_output.set_fixed(1);
    fast_output << polygon_area(polygon) << '\n';
}

Traceback (most recent call last):
  File "/home/runner/.local/lib/python3.12/site-packages/onlinejudge_verify/documentation/build.py", line 71, in _render_source_code_stat
    bundled_code = language.bundle(stat.path, basedir=basedir, options={'include_paths': [basedir]}).decode()
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/runner/.local/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus.py", line 187, in bundle
    bundler.update(path)
  File "/home/runner/.local/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 401, in update
    self.update(self._resolve(pathlib.Path(included), included_from=path))
  File "/home/runner/.local/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 401, in update
    self.update(self._resolve(pathlib.Path(included), included_from=path))
  File "/home/runner/.local/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 400, in update
    raise BundleErrorAt(path, i + 1, "unable to process #include in #if / #ifdef / #ifndef other than include guards")
onlinejudge_verify.languages.cplusplus_bundle.BundleErrorAt: geometry/lattice_point_count.hpp: line 28: unable to process #include in #if / #ifdef / #ifndef other than include guards

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