From 49a54952870923042d6eda83597f22d4b36199f8 Mon Sep 17 00:00:00 2001
From: NIHIT SAHA <sahanihit@gmail.com>
Date: Fri, 1 Oct 2021 16:39:18 +0530
Subject: [PATCH] Create Closest pair of points - Geometrical Algorithms

---
 ...st pair of points - Geometrical Algorithms | 133 ++++++++++++++++++
 1 file changed, 133 insertions(+)
 create mode 100644 C++/Closest pair of points - Geometrical Algorithms

diff --git a/C++/Closest pair of points - Geometrical Algorithms b/C++/Closest pair of points - Geometrical Algorithms
new file mode 100644
index 00000000..74231ae9
--- /dev/null
+++ b/C++/Closest pair of points - Geometrical Algorithms	
@@ -0,0 +1,133 @@
+#include <iostream>
+#include <float.h>
+#include <stdlib.h>
+#include <math.h>
+using namespace std;
+
+
+struct Point
+{
+	int x, y;
+};
+
+
+
+int compareX(const void* a, const void* b)
+{
+	Point *p1 = (Point *)a, *p2 = (Point *)b;
+	return (p1->x != p2->x) ? (p1->x - p2->x) : (p1->y - p2->y);
+}
+
+int compareY(const void* a, const void* b)
+{
+	Point *p1 = (Point *)a, *p2 = (Point *)b;
+	return (p1->y != p2->y) ? (p1->y - p2->y) : (p1->x - p2->x);
+}
+
+
+float dist(Point p1, Point p2)
+{
+	return sqrt( (p1.x - p2.x)*(p1.x - p2.x) +
+				(p1.y - p2.y)*(p1.y - p2.y)
+			);
+}
+
+
+float bruteForce(Point P[], int n)
+{
+	float min = FLT_MAX;
+	for (int i = 0; i < n; ++i)
+		for (int j = i+1; j < n; ++j)
+			if (dist(P[i], P[j]) < min)
+				min = dist(P[i], P[j]);
+	return min;
+}
+
+
+float min(float x, float y)
+{
+	return (x < y)? x : y;
+}
+
+
+float stripClosest(Point strip[], int size, float d)
+{
+	float min = d; // Initialize the minimum distance as d
+
+
+	for (int i = 0; i < size; ++i)
+		for (int j = i+1; j < size && (strip[j].y - strip[i].y) < min; ++j)
+			if (dist(strip[i],strip[j]) < min)
+				min = dist(strip[i], strip[j]);
+
+	return min;
+}
+
+
+float closestUtil(Point Px[], Point Py[], int n)
+{
+	
+	if (n <= 3)
+		return bruteForce(Px, n);
+
+	
+	int mid = n/2;
+	Point midPoint = Px[mid];
+
+
+
+	Point Pyl[mid]; // y sorted points on left of vertical line
+	Point Pyr[n-mid]; // y sorted points on right of vertical line
+	int li = 0, ri = 0; // indexes of left and right subarrays
+	for (int i = 0; i < n; i++)
+	{
+	if ((Py[i].x < midPoint.x || (Py[i].x == midPoint.x && Py[i].y < midPoint.y)) && li<mid)
+		Pyl[li++] = Py[i];
+	else
+		Pyr[ri++] = Py[i];
+	}
+
+	
+	float dl = closestUtil(Px, Pyl, mid);
+	float dr = closestUtil(Px + mid, Pyr, n-mid);
+
+	
+	float d = min(dl, dr);
+
+	
+	Point strip[n];
+	int j = 0;
+	for (int i = 0; i < n; i++)
+		if (abs(Py[i].x - midPoint.x) < d)
+			strip[j] = Py[i], j++;
+
+	
+	return stripClosest(strip, j, d);
+}
+
+
+float closest(Point P[], int n)
+{
+	Point Px[n];
+	Point Py[n];
+	for (int i = 0; i < n; i++)
+	{
+		Px[i] = P[i];
+		Py[i] = P[i];
+	}
+
+	qsort(Px, n, sizeof(Point), compareX);
+	qsort(Py, n, sizeof(Point), compareY);
+
+	
+	return closestUtil(Px, Py, n);
+}
+
+
+int main()
+{
+	Point P[] = {{2, 3}, {12, 30}, {40, 50}, {5, 1}, {12, 10}, {3, 4}};
+	int n = sizeof(P) / sizeof(P[0]);
+	cout << "The smallest distance is " << closest(P, n);
+	return 0;
+}