объясни код подробно, что и как происходит:

#include <iostream>
#include <vector>
#include <stack>
#include <cmath>
#include <algorithm>
#include <iomanip>

const double PI = acosl(-1.0);
const double EPS = 1e-12;

struct Sector {
    double x_coord, y_coord;
    double radius;
    double start_angle;
    double angle;
};

struct Event {
    double x;
    int type;
    int sector_id;
    bool operator<(const Event& other) const {
        if (fabs(x - other.x) > EPS) {
            return x < other.x;
        }
        return type < other.type;
    }
};

inline double normalize_angle(double alpha) {
    alpha = fmod(alpha, 2.0 * PI);
    if (alpha < 0) {
        alpha += 2.0 * PI;
    }
    return alpha;
}

inline bool is_angle_between(double alpha, double start, double extent) {
    alpha = normalize_angle(alpha);
    start = normalize_angle(start);
    double end = normalize_angle(start + extent);

    if (extent >= 2.0 * PI - EPS) {
        return true;
    }
    if (start < end) {
        return (alpha >= start - EPS && alpha < end - EPS);
    } else {
        return (alpha >= start - EPS || alpha < end - EPS);
    }
}

inline std::vector<std::pair<double, double>> get_sector_y_coverage(const Sector& sector, double x) {
    std::vector<std::pair<double, double>> intervals;
    double dx = x - sector.x_coord;

    if (fabs(dx) > sector.radius + EPS) {
        return intervals;
    }

    double dy_sq = sector.radius * sector.radius - dx * dx;
    if (dy_sq < -EPS) {
        return intervals;
    }

    double dy = (dy_sq < 0.0) ? 0.0 : sqrt(dy_sq);
    double y_min = sector.y_coord - dy;
    double y_max = sector.y_coord + dy;

    if (sector.angle >= 2.0 * PI - EPS) {
        intervals.emplace_back(y_min, y_max);
        return intervals;
    }

    double alpha_start = normalize_angle(sector.start_angle);
    double alpha_end = normalize_angle(sector.start_angle + sector.angle);

    std::vector<double> y_intersections;

    auto add_y_intersection = [&](double alpha) {
        if (fabs(cos(alpha)) >= EPS) {
            double y = sector.y_coord + dx * tan(alpha);
            if (y >= y_min - EPS && y <= y_max + EPS) {
                y_intersections.emplace_back(y);
            }
        }
    };

    add_y_intersection(sector.start_angle);
    add_y_intersection(sector.start_angle + sector.angle);

    if (fabs(dx) <= EPS) {
        bool includes_upper = is_angle_between(PI / 2.0, sector.start_angle, sector.angle);
        bool includes_lower = is_angle_between(3.0 * PI / 2.0, sector.start_angle, sector.angle);

        if (includes_upper && includes_lower) {
            intervals.emplace_back(y_min, y_max);
            return intervals;
        }
        else if (includes_upper) {
            intervals.emplace_back(sector.y_coord, y_max);
        } else if (includes_lower) {
            intervals.emplace_back(y_min, sector.y_coord);
        }
        return intervals;
    }

    y_intersections.emplace_back(y_min);
    y_intersections.emplace_back(y_max);

    sort(y_intersections.begin(), y_intersections.end());
    y_intersections.erase(unique(y_intersections.begin(), y_intersections.end(),
        [&](double a, double b) -> bool { return fabs(a - b) < EPS; }),
        y_intersections.end());

    for (size_t i = 0; i + 1 < y_intersections.size(); ++i) {
        double y1 = y_intersections[i];
        double y2 = y_intersections[i + 1];
        double ym = (y1 + y2) / 2.0;

        double alpha = atan2(ym - sector.y_coord, dx);
        if (alpha < 0.0) {
            alpha += 2.0 * PI;
        }
        if (is_angle_between(alpha, alpha_start, sector.angle)) {
            y1 = std::max(y1, y_min);
            y2 = std::min(y2, y_max);
            if (y1 < y2 - EPS) {
                intervals.emplace_back(y1, y2);
            }
        }
    }

    return intervals;
}

inline std::vector<std::pair<double, double>> merge_intervals(std::vector<std::pair<double, double>>& intervals) {
    std::vector<std::pair<double, double>> merged;
    if (intervals.empty())
        return merged;

    sort(intervals.begin(), intervals.end());

    double current_start = intervals[0].first;
    double current_end = intervals[0].second;

    for (size_t i = 1; i < intervals.size(); ++i) {
        if (intervals[i].first <= current_end + EPS) {
            current_end = std::max(current_end, intervals[i].second);
        }
        else {
            merged.emplace_back(current_start, current_end);
            current_start = intervals[i].first;
            current_end = intervals[i].second;
        }
    }
    merged.emplace_back(current_start, current_end);
    return merged;
}

inline double coverage_at_x(const std::vector<Sector>& active_sectors, double x) {
    std::vector<std::pair<double, double>> y_coverage;
    y_coverage.reserve(active_sectors.size() * 2);

    for (const auto& sector : active_sectors) {
        auto intervals = get_sector_y_coverage(sector, x);
        for (const auto& interval : intervals) {
            y_coverage.emplace_back(interval.first, interval.second);
        }
    }

    if (y_coverage.empty()) {
        return 0.0;
    }

    auto merged = merge_intervals(y_coverage);
    double coverage = 0.0;
    for (const auto& interval : merged) {
        coverage += (interval.second - interval.first);
    }

    return coverage;
}

struct SimpsonInterval {
    double a, b;
    double S;
    double fa, fb, fm;
    int depth;
};

inline double adaptive_simpson_iterative(const std::vector<Sector>& active_sectors, double a, double b, double eps, int max_depth) {
    std::stack<SimpsonInterval> intervals;
    double fa = coverage_at_x(active_sectors, a);
    double fb = coverage_at_x(active_sectors, b);
    double m = (a + b) / 2.0;
    double fm = coverage_at_x(active_sectors, m);
    double S = (fa + 4.0 * fm + fb) * (b - a) / 6.0;

    intervals.push(SimpsonInterval{a, b, S, fa, fb, fm, max_depth});
    double total = 0.0;

    while (!intervals.empty()) {
        SimpsonInterval current = intervals.top();
        intervals.pop();

        double a1 = current.a;
        double b1 = current.b;
        double m1 = (a1 + b1) / 2.0;
        double lm = (a1 + m1) / 2.0;
        double rm = (m1 + b1) / 2.0;
        double flm = coverage_at_x(active_sectors, lm);
        double frm = coverage_at_x(active_sectors, rm);
        double S_left = (current.fa + 4.0 * flm + current.fm) * (m1 - a1) / 6.0;
        double S_right = (current.fm + 4.0 * frm + current.fb) * (b1 - m1) / 6.0;
        double S_total = S_left + S_right;

        if (current.depth > 0 && fabs(S_total - current.S) > 15.0 * eps) {
            intervals.push(SimpsonInterval{m1, b1, S_right, current.fm, current.fb, frm, current.depth - 1});
            intervals.push(SimpsonInterval{a1, m1, S_left, current.fa, current.fm, flm, current.depth - 1});
        }
        else {
            total += S_total + (S_total - current.S) / 15.0;
        }
    }

    return total;
}

int main() {
    int n;
    while (std::cin >> n) {
        std::vector<Sector> sectors(n);
        std::vector<Event> events;
        events.reserve(n * 4);

        for (int i = 0; i < n; ++i) {
            std::cin >> sectors[i].x_coord >> sectors[i].y_coord >> sectors[i].radius 
                >> sectors[i].start_angle >> sectors[i].angle;

            double x_min = sectors[i].x_coord - sectors[i].radius;
            double x_max = sectors[i].x_coord + sectors[i].radius;
            events.emplace_back(Event{ x_min, 1, i });
            events.emplace_back(Event{ x_max, -1, i });

            auto add_projection = [&](double angle) {
                if (fabs(cos(angle)) >= EPS) {
                    double x_proj = sectors[i].x_coord + sectors[i].radius * cos(angle);
                    if (x_proj > x_min + EPS && x_proj < x_max - EPS) {
                        events.emplace_back(Event{ x_proj, 0, i });
                    }
                }
            };

            add_projection(sectors[i].start_angle);
            add_projection(sectors[i].start_angle + sectors[i].angle);
        }

        sort(events.begin(), events.end());

        std::vector<int> active_ids;
        active_ids.reserve(n);
        double last_x = -300;
        double total_area = 0.0;

        std::vector<Sector> active_sectors_temp;
        active_sectors_temp.reserve(n);

        for (const auto &event : events) {
            double current_x = event.x;

            if (last_x < current_x - EPS && !active_ids.empty()) {
                active_sectors_temp.clear();
                active_sectors_temp.reserve(active_ids.size());
                for (auto id : active_ids) {
                    active_sectors_temp.emplace_back(sectors[id]);
                }

                total_area += adaptive_simpson_iterative(active_sectors_temp, last_x, current_x, 1e-9, 30);
            }

            if (event.type == 1) {
                active_ids.emplace_back(event.sector_id);
            }
            else if (event.type == -1) {
                int id_to_remove = event.sector_id;
                for (int j = 0; j < active_ids.size(); ++j) {
                    if (active_ids[j] == id_to_remove) {
                        active_ids[j] = active_ids.back();
                        active_ids.pop_back();
                        break;
                    }
                }
            }

            last_x = current_x;
        }

        std::cout << std::fixed << std::setprecision(12) << total_area << "\n";
    }
}