initial commit: Working version

.gitignore

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+*.out
+mybenchmark
+cmake-build-debug/

CMakeLists.txt

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+cmake_minimum_required(VERSION 3.22)
+project(prog)
+
+set(CMAKE_CXX_STANDARD 20)
+
+find_package(benchmark REQUIRED)
+
+add_executable(prog main.cpp segment_tree.h geometry.h)
+
+target_link_libraries(prog benchmark::benchmark)

geometry.h

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+//
+// Created by maximilian on 16.04.22.
+//
+
+#ifndef PROG_GEOMETRY_H
+#define PROG_GEOMETRY_H
+
+#include <cstdint>
+
+using Coordinate = int;
+using Unit = uint64_t;
+using Index = size_t;
+
+struct Point {
+    Coordinate x;
+    Coordinate y;
+};
+
+struct Interval {
+    Coordinate left;
+    Coordinate right;
+};
+
+#endif //PROG_GEOMETRY_H

main.cpp

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+#include <vector>
+#include <assert.h>
+
+#include <benchmark/benchmark.h>
+
+#include "geometry.h"
+
+struct Rectangle {
+    Point bottom_left;
+    Point top_right;
+
+    // only for algorithm
+    Index i_left;
+    Index i_right;
+};
+
+struct RectCoord {
+    Coordinate coord;
+    Rectangle* rect; // guaranteed to be valid at all times
+    bool operator<(const RectCoord &other) {
+        return coord < other.coord;
+    }
+};
+
+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();

segment_tree.h

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+//
+// Created by maximilian on 16.04.22.
+//
+
+#include<vector>
+#include "geometry.h"
+
+#ifndef PROG_SEGMENT_TREE_H
+#define PROG_SEGMENT_TREE_H
+
+
+class SegmentTree {
+    SegmentTree(const std::vector<Coordinate>);
+
+    Unit length_covered_intervals();
+
+    void add_interval(Interval interval);
+    void remove_interval(Interval interval);
+};
+
+#endif //PROG_SEGMENT_TREE_H