I'm learning C++ as well as algorithms. Here's my implementation of finding the closest pair problem. I tried to minimize memory by using only iterators.
And points are being read from points.txt
file content:
2,1
3,5
8,3
5,8
9,1
5,2
3,3
4,5
6,5
1,9
Output is:
Closest pair are:
3, 5
4, 5
Here's the code:
#include <iostream>
#include <array>
#include <algorithm>
#include <fstream>
#include <cfloat>
#include <cmath>
struct Point {
Point(double x = 0, double y = 0) {
x_coordinate = x;
y_coordinate = y;
}
double x_coordinate;
double y_coordinate;
static bool sortByX(const Point &lhs, const Point &rhs) {
return lhs.x_coordinate < rhs.x_coordinate;
}
static bool sortByY(const Point &lhs, const Point &rhs) {
return lhs.y_coordinate < rhs.y_coordinate;
}
};
template<std::size_t SIZE>
using p_iterator = typename std::array<Point, SIZE>::iterator;
template<std::size_t SIZE>
using p_iterators_array = std::array<typename std::array<Point, SIZE>::iterator, SIZE>;
void initialize_points(std::array<Point, 10> &points) {
double x, y;
int i = 0;
char c;
std::ifstream infile("./points.txt");
while((infile >> x >> c >> y) && (c == ',') && (i < 11)) {
points[i++] = Point(x, y);
}
}
double calculate_distance(Point &p1, Point &p2) {
return std::sqrt(std::pow(p1.x_coordinate - p2.x_coordinate, 2) + std::pow(p1.y_coordinate - p2.y_coordinate , 2));
}
template<typename T>
p_iterators_array<2> eucledian_closest(T &points, int size) {
p_iterators_array<2> closest_arr;
double closest_distance = DBL_MAX, distance = 0.0;
for(int i = 0; i < size - 1; i++){
for(int j = i + 1; j < size; j++) {
distance = calculate_distance(points[i], points[j]);
if(distance < closest_distance && distance != 0) {
closest_distance = distance;
closest_arr[0] = points + i;
closest_arr[1] = points + j;
}
}
}
return closest_arr;
}
template<std::size_t SIZE>
p_iterators_array<2> closest_split_pair(p_iterator<SIZE> points_iterator, p_iterators_array<2> &closest_side_pairs) {
std::vector<p_iterator<SIZE>> split_pairs;
p_iterators_array<2> final_result;
double closest_distance = DBL_MAX, distance = 0.0;
typename std::array<Point, SIZE>::iterator midpoint = points_iterator + (SIZE/2);
//filtering points to only points in sigma-2sigma rectangle
for (size_t i = 0; i < SIZE; i++) {
if(std::abs(points_iterator[i].x_coordinate - midpoint->x_coordinate) < calculate_distance(*(closest_side_pairs[0]), *(closest_side_pairs[1]))){
split_pairs.push_back(points_iterator + i);
}
}
//finding closest pair in split_pairs
for (size_t i = 0; i < split_pairs.size() - 1; i++) {
for (size_t j = i+1; (j < 7) && (j < split_pairs.size()) ; j++) {
distance = calculate_distance(*(split_pairs[i]), *(split_pairs[j]));
if(distance < closest_distance && distance != 0) {
closest_distance = distance;
final_result[0] = split_pairs[i];
final_result[1] = split_pairs[j];
}
}
}
//comparing split paris distance and side pairs distance
if(calculate_distance(*(closest_side_pairs.front()), *(closest_side_pairs.back())) < calculate_distance(*(final_result.front()), *(final_result.back()))) {
final_result = closest_side_pairs;
}
return final_result;
}
template<std::size_t SIZE>
p_iterators_array<2> closest_side_pair(p_iterator<SIZE> points_iterator, p_iterator<SIZE> x_arr_iterator, p_iterator<SIZE> y_arr_iterator) {
std::size_t delimeter = SIZE / 2 ;
if(delimeter <= 3) {
return eucledian_closest(points_iterator, delimeter);
}
p_iterators_array<2> closest_left, closest_right, result;
closest_left = closest_side_pair<SIZE / 2>(points_iterator, x_arr_iterator, y_arr_iterator);
closest_right = closest_side_pair<SIZE / 2>(points_iterator + delimeter, x_arr_iterator + delimeter, y_arr_iterator + delimeter);
if(calculate_distance(*(closest_left.front()), *(closest_left.back())) < calculate_distance(*(closest_right.front()), *(closest_right.back()))) {
result = closest_left;
} else {
result = closest_right;
}
return closest_split_pair<SIZE>(points_iterator, result);
}
int main()
{
std::array<Point, 10> points;
initialize_points(points);
std::array<Point, 10> x_p = points;
std::array<Point, 10> y_p = points;
std::sort(x_p.begin(), x_p.end(), Point::sortByX);
std::sort(y_p.begin(), y_p.end(), Point::sortByY);
p_iterators_array<2> closest_result = closest_side_pair<10>(points.begin(), x_p.begin(), y_p.begin());
closest_result = closest_split_pair<10>(points.begin(), closest_result);
std::cout << "Closest pair are: " << std::endl;
for(auto p: closest_result) {
std::cout << p->x_coordinate << ", " << p->y_coordinate << std::endl;
}
}
closest_side_pair()
doesn't callclosest_split_pair()
. How can you find the closest points in one half by only recursively splitting in half without considering points split across the half? \$\endgroup\$