rectangle-union-area/main.cpp

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2022-04-16 09:24:00 +02:00
#include <vector>
#include <assert.h>
#include <benchmark/benchmark.h>
#include "geometry.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);
}
// entry i will describe coverage of the interval (x_points[i], x_points[i+1])
std::vector<unsigned> coverage_numbers;
coverage_numbers.reserve(2*rectangles.size() -1);
//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());
// run sweepline
Unit current_cross_section_length = 0;
Unit total_area = 0;
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
for (Index index = y_points[y_index].rect->i_left; index < y_points[y_index].rect->i_right; ++index) {
++coverage_numbers[index];
if (coverage_numbers[index] == 1) {
current_cross_section_length += (x_points[index + 1].coord - x_points[index].coord);
}
}
} else {
assert(y_points[y_index].rect->top_right.y == y_points[y_index].coord);
// rectangle stopping, remove its cross section
for (Index index = y_points[y_index].rect->i_left; index < y_points[y_index].rect->i_right; ++index) {
--coverage_numbers[index];
if (coverage_numbers[index] == 0) {
current_cross_section_length -= (x_points[index + 1].coord - x_points[index].coord);
}
}
}
//cross section is now up to date
if(y_index + 1 < y_points.size()) {
// add area up to next y point
total_area += current_cross_section_length * (y_points[y_index+1].coord - y_points[y_index].coord);
}
}
// sanity check that nothing is covered when arriving at the end
for(auto coverage : coverage_numbers) {
assert(coverage == 0);
}
return total_area;
}
// some benchmark tests using github.com/google/benchmark
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;
}
static void BM_area_computation(benchmark::State& state) {
std::vector<Rectangle> rects;
for (auto _ : state) {
state.PauseTiming();
rects = get_random_instance(state.range(0), state.range(1));
state.ResumeTiming();
get_area_union(rects);
}
state.SetComplexityN(state.range(0));
}
// add benchmark
BENCHMARK(BM_area_computation)->ArgsProduct({benchmark::CreateRange(1,1<<16,4),{1<<10, 1<<15, 1<<20}})->Complexity(benchmark::oNSquared);
// run benchmark as main()
BENCHMARK_MAIN();