Closest Pair Of Points

c/.gitkeep

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+// A divide and conquer program in C to find the smallest distance from a given set of points.
+
+#include <stdio.h>
+#include <float.h>
+#include <stdlib.h>
+#include <math.h>
+
+// A structure to represent a Point in 2D plane
+struct Point
+{
+	int x, y;
+};
+
+// Needed to sort array of points according to X coordinate
+int compareX(const void* a, const void* b)
+{
+	Point *p1 = (Point *)a, *p2 = (Point *)b;
+	return (p1->x - p2->x);
+}
+// Needed to sort array of points according to Y coordinate
+int compareY(const void* a, const void* b)
+{
+	Point *p1 = (Point *)a, *p2 = (Point *)b;
+	return (p1->y - p2->y);
+}
+
+// A utility function to find the distance between two points
+float dist(Point p1, Point p2)
+{
+	return sqrt( (p1.x - p2.x)*(p1.x - p2.x) +
+				(p1.y - p2.y)*(p1.y - p2.y)
+			);
+}
+
+// A Brute Force method to return the smallest distance between two points in P[] of size n
+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;
+}
+
+// A utility function to find a minimum of two float values
+float min(float x, float y)
+{
+	return (x < y)? x : y;
+}
+
+
+// A utility function to find the distance between the closest points of strip of a given size. All points in strip[] are sorted according to y coordinate. 
+// They all have an upper bound on minimum distance as d.
+
+float stripClosest(Point strip[], int size, float d)
+{
+	float min = d; // Initialize the minimum distance as d
+
+	qsort(strip, size, sizeof(Point), compareY);
+
+	// Pick all points one by one and try the next points till the difference between y coordinates is smaller than d.
+	// This is a proven fact that this loop runs at most 6 times
+	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;
+}
+
+// A recursive function to find the smallest distance. The array P contains all points sorted according to x coordinate
+float closestUtil(Point P[], int n)
+{
+	// If there are 2 or 3 points, then use brute force
+	if (n <= 3)
+		return bruteForce(P, n);
+
+	// Find the middle point
+	int mid = n/2;
+	Point midPoint = P[mid];
+
+	// Consider the vertical line passing through the middle point
+	// calculate the smallest distance dl on left of middle point and dr on right side
+	float dl = closestUtil(P, mid);
+	float dr = closestUtil(P + mid, n-mid);
+
+	// Find the smaller of two distances
+	float d = min(dl, dr);
+
+	// Build an array strip[] that contains points close (closer than d) to the line passing through the middle point
+	Point strip[n];
+	int j = 0;
+	for (int i = 0; i < n; i++)
+		if (abs(P[i].x - midPoint.x) < d)
+			strip[j] = P[i], j++;
+
+	// Find the closest points in strip. Return the minimum of d and closest distance is strip[]
+	return min(d, stripClosest(strip, j, d) );
+}
+
+// The main function that finds the smallest distance
+// This method mainly uses closestUtil()
+float closest(Point P[], int n)
+{
+	qsort(P, n, sizeof(Point), compareX);
+
+	// Use recursive function closestUtil() to find the smallest distance
+	return closestUtil(P, n);
+}
+
+// Driver program to test above functions
+int main()
+{
+	Point P[] = {{2, 3}, {12, 30}, {40, 50}, {5, 1}, {12, 10}, {3, 4}};
+	int n = sizeof(P) / sizeof(P[0]);
+	printf("The smallest distance is %f ", closest(P, n));
+	return 0;
+}