From 5a1cb91748137c93748047d89ef10a2b43c4dc7d Mon Sep 17 00:00:00 2001
From: Prabhat <87269080+Prabhatsingh001@users.noreply.github.com>
Date: Thu, 24 Oct 2024 20:18:33 +0530
Subject: [PATCH] closest pair of points algorithm

---
 .../closest_pair_of_points.py                 | 98 +++++++++++++++++++
 1 file changed, 98 insertions(+)
 create mode 100644 Algorithms_and_Data_Structures/closest_pair_of_points/closest_pair_of_points.py

diff --git a/Algorithms_and_Data_Structures/closest_pair_of_points/closest_pair_of_points.py b/Algorithms_and_Data_Structures/closest_pair_of_points/closest_pair_of_points.py
new file mode 100644
index 00000000..82e0b52a
--- /dev/null
+++ b/Algorithms_and_Data_Structures/closest_pair_of_points/closest_pair_of_points.py
@@ -0,0 +1,98 @@
+import math
+
+class Point:
+	def __init__(self, x, y):
+		self.x = x
+		self.y = y
+
+#sort array of points according to X coordinate
+def compareX(a, b):
+	p1, p2 = a, b
+	return (p1.x != p2.x) * (p1.x - p2.x) + (p1.y - p2.y)
+
+#sort array of points according to Y coordinate
+def compareY(a, b):
+	p1, p2 = a, b
+	return (p1.y != p2.y) * (p1.y - p2.y) + (p1.x - p2.x)
+
+
+# A utility function to find the distance between two points
+def dist(p1, p2):
+	return math.sqrt((p1.x - p2.x)**2 + (p1.y - p2.y)**2)
+
+'''A Brute Force method to return the smallest distance between two points
+in P[] of size n'''
+def bruteForce(P, n):
+	min = float('inf')
+	for i in range(n):
+		for j in range(i+1, n):
+			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
+def min(x, y):
+	return x if x < y else 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.Note that this method seems to be a O(n^2) method, but it's a O(n) method as the inner loop runs at most 6 times'''
+def stripClosest(strip, size, d):
+	min = d
+	for i in range(size):
+		for j in range(i+1, size):
+			if (strip[j].y - strip[i].y) < min:
+				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 Px contains all points sorted according to x coordinates and Py contains all points sorted according to y coordinates'''
+def closestUtil(Px, Py, n):
+	if n <= 3:
+		return bruteForce(Px, n)
+
+	mid = n // 2
+	midPoint = Px[mid]
+
+	Pyl = [None] * mid
+	Pyr = [None] * (n-mid)
+	li = ri = 0
+	for i in range(n):
+		if ((Py[i].x < midPoint.x or (Py[i].x == midPoint.x and Py[i].y < midPoint.y)) and li<mid):
+			Pyl[li] = Py[i]
+			li += 1
+		else:
+			Pyr[ri] = Py[i]
+			ri += 1
+
+	dl = closestUtil(Px, Pyl, mid)
+	dr = closestUtil(Px[mid:], Pyr, n-mid)
+
+	d = min(dl, dr)
+	strip = [None] * n
+	j = 0
+	for i in range(n):
+		if abs(Py[i].x - midPoint.x) < d:
+			strip[j] = Py[i]
+			j += 1
+	return stripClosest(strip, j, d)
+
+
+def closest(P, n):
+	Px = P
+	Py = P
+	Px.sort(key=lambda x:x.x)
+	Py.sort(key=lambda x:x.y)
+
+	return closestUtil(Px, Py, n)
+
+#example usage
+if __name__ == '__main__':
+	P = [Point(2, 3), Point(12, 30), Point(40, 50), Point(5, 1), Point(12, 10), Point(3, 4)]
+	n = len(P)
+	print("The smallest distance is", closest(P, n))
+
+'''output
+The smallest distance is 1.4142135623730951
+'''