#include <bits/stdc++.h>
using namespace std;
// Making a class that stores X and Y coordinates of different points
class Coordinate
{
public:
int x, y;
};
Coordinate p1;
Coordinate p2;
// find distance between two points
float distance(Coordinate p1, Coordinate p2)
{
return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
}
// Brute force algorithm and find distance using it
float brute_force(Coordinate P[], int n)
{
float mini = FLT_MAX;
for (int i = 0; i < n; ++i)
for (int j = i + 1; j < n; ++j)
if (distance(P[i], P[j]) < mini)
{
mini = distance(P[i], P[j]);
if (distance(p1, p2) > distance(P[i], P[j]))
{
p1.x = P[i].x;
p1.y = P[i].y;
p2.x = P[j].x;
p2.y = P[j].y;
}
}
return mini;
}
// function to compare X coodinate for quick sort
int X_cmp(const void *a, const void *b)
{
Coordinate *p1 = (Coordinate *)a, *p2 = (Coordinate *)b;
return (p1->x - p2->x);
}
// function to compare Y coodinate for quick sort
int Y_cmp(const void *a, const void *b)
{
Coordinate *p1 = (Coordinate *)a, *p2 = (Coordinate *)b;
return (p1->y - p2->y);
}
// Function to make the strip
float makeverticalstrip(Coordinate v_strip[], int size, float d)
{
float mini = d; // Initialize the minimum distance as d
for (int i = 0; i < size; ++i)
{
for (int j = i + 1; j < size && (v_strip[j].y - v_strip[i].y) < mini; ++j)
{
if (distance(v_strip[i], v_strip[j]) < mini)
{
mini = distance(v_strip[i], v_strip[j]);
p1.x = v_strip[i].x;
p1.y = v_strip[i].y;
p2.x = v_strip[j].x;
p2.y = v_strip[j].y;
}
}
}
return mini;
}
// Recursive function to divide the plane
float Min(Coordinate Px[], Coordinate Py[], int n)
{
if (n <= 3)
{
return brute_force(Px, n); // Divide until there exist 3 or lesser than 3 points in the partition
}
// Make the vertical (partitioning) line
int middle = n / 2;
Coordinate middle_point = Px[middle];
// simple merge sort like algorithm 110-119
Coordinate Pyl[middle];
Coordinate Pyr[n - middle];
int li = 0, ri = 0;
for (int i = 0; i < n; i++)
{
if (Py[i].x <= middle_point.x && li < middle)
Pyl[li++] = Py[i];
else
Pyr[ri++] = Py[i];
}
// Getting the minimum distance for the left and right partition
float dl = Min(Px, Pyl, middle);
float dr = Min(Px + middle, Pyr, n - middle);
float d;
if (dl < dr)
{
d = dl;
}
else
{
d = dr;
}
// Making a strip that stores points on the left and right side of the partition which are at lesser distance than d.
Coordinate v_strip[n];
int j = 0;
for (int i = 0; i < n; i++)
if (abs(Py[i].x - middle_point.x) < d)
{
v_strip[j] = Py[i];
j++;
}
return makeverticalstrip(v_strip, j, d);
}
float closestdistance(Coordinate P[], int n)
{
Coordinate Px[n];
Coordinate Py[n];
for (int i = 0; i < n; i++)
{
Px[i] = P[i];
Py[i] = P[i];
}
// Sorting the points according to their X and Y coordinates.
qsort(Px, n, sizeof(Coordinate), X_cmp);
qsort(Py, n, sizeof(Coordinate), Y_cmp);
return Min(Px, Py, n);
}
int main()
{
int n;
// cout << "Enter the number of point you want to add in plane" << endl;
cin >> n;
Coordinate P[n];
// cout << "Enter the points' x and y coordinates" << endl;
// for example we will give the co-ordinate of the airplane
for (int i = 0; i < n; i++)
{
cin >> P[i].x;
cin >> P[i].y;
}
// storing first 2 points (if exists)
p1.x = P[0].x;
p1.y = P[0].y;
p2.x = P[1].x;
p2.y = P[1].y;
cout << "The Smallest Distance Is " << closestdistance(P, n);
cout << "\n";
cout << "The Co-Ordinates Of The Points With The Minimum Distance Between Them Are\n";
cout << "First Point : (" << p1.x << "," << p1.y << ")\n";
cout << "Second Point : (" << p2.x << "," << p2.y << ")\n";
return 0;
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