rectangle-union-area/areas.cpp

//
// Created by maximilian on 16.04.22.
//

#include <vector>
#include <assert.h>

#include "geometry.h"
#include "areas.h"
#include "segment_tree.h"


Unit get_area_union(std::vector<Rectangle> rectangles) {
    // do some input sanity checks
    for(const auto &rect : rectangles) {
        assert(rect.bottom_left.x <= rect.top_right.x);
        assert(rect.bottom_left.y <= rect.top_right.y);
    }

    //sorted vector of all x coordinates of all rectangles
    std::vector<RectCoord> x_points;
    x_points.reserve(2* rectangles.size());
    for(auto &rect : rectangles) {
        x_points.push_back({rect.bottom_left.x, &rect});
        x_points.push_back({rect.top_right.x, &rect});
    }
    std::sort(x_points.begin(), x_points.end());

    // preprocessing for constant rectangle lookup during algorithm
    // technically not necessary to achieve quadratic running time
    for(Index i = 0 ; i < x_points.size() ; ++i) {
        if(x_points[i].rect->bottom_left.x == x_points[i].coord) {
            x_points[i].rect->i_left = i;
        } else {
            assert(x_points[i].rect->top_right.x == x_points[i].coord);
            x_points[i].rect->i_right = i;
        }
    }

    // prepare vector of y-coordinates
    std::vector<RectCoord> y_points;
    y_points.reserve(2*rectangles.size());
    for(auto &rect : rectangles) {
        y_points.push_back({rect.bottom_left.y, &rect});
        y_points.push_back({rect.top_right.y, &rect});
    }
    std::sort(y_points.begin(), y_points.end());

    // init data and run sweepline
    Unit total_area = 0;
    SegmentTree segmentTree(x_points);

    for(Index y_index = 0 ; y_index < y_points.size() ; ++y_index) {
        // first, update cross section
        if (y_points[y_index].rect->bottom_left.y == y_points[y_index].coord) {
            // rectangle is starting now, add its cross section
            segmentTree.add_interval(
                    {x_points[y_points[y_index].rect->i_left].coord,
                     x_points[y_points[y_index].rect->i_right].coord}
                    );
        } else {
            assert(y_points[y_index].rect->top_right.y == y_points[y_index].coord);
            // rectangle stopping, remove its cross section
            segmentTree.remove_interval(
                    {x_points[y_points[y_index].rect->i_left].coord,
                     x_points[y_points[y_index].rect->i_right].coord}
            );
        }
        //cross section is now up to date
        if(y_index + 1 < y_points.size()) {
            // add area up to next y point
            total_area +=
                    (y_points[y_index +1].coord - y_points[y_index].coord) *
                    segmentTree.length_covered_intervals();
        }
    }
    // TODO: sanity check that nothing is covered when arriving at the end
    return total_area;
}

std::vector<Rectangle> get_random_instance(unsigned num_rects, Coordinate range) {
    std::vector<Rectangle> rects;
    rects.reserve(num_rects);
    for(unsigned i = 0 ; i < num_rects; ++i) {
        // technically, this might not be (perfectly) evenly distributed, but it will suffice for our purposes anyways
        Coordinate x1 = rand() % range;
        Coordinate x2 = rand() % range;
        Coordinate y1 = rand() % range;
        Coordinate y2 = rand() % range;
        if (x2 < x1) { int tmp = x1; x1 = x2; x2 = tmp; };
        if (y2 < y1) { int tmp = y1; y1 = y2; y2 = tmp; };
        rects.push_back(
                {{x1,y1},{x2, y2}, 0,0}
        );
    }
    return rects;
}