From d46fc541a941f5026ce713d381e637d535785672 Mon Sep 17 00:00:00 2001
From: HawkEye201 <imt_2019024@iiitm.ac.in>
Date: Thu, 15 Oct 2020 03:41:54 +0530
Subject: [PATCH] Added Kruskal ALgorithm

---
 C++/graph/Kruskal_Algorithm.cpp | 80 +++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 C++/graph/Kruskal_Algorithm.cpp

diff --git a/C++/graph/Kruskal_Algorithm.cpp b/C++/graph/Kruskal_Algorithm.cpp
new file mode 100644
index 0000000..8d5c82c
--- /dev/null
+++ b/C++/graph/Kruskal_Algorithm.cpp
@@ -0,0 +1,80 @@
+#include <algorithm>
+#include <iostream>
+#include <iomanip>
+#include <vector>
+#include <cmath>
+using std::vector;
+//create a point class
+struct point{
+	int x; int y; int parent; int rank;
+	point(int a, int b, int c, int d):x(a), y(b), parent(c), rank(d){}
+};
+//create a edge class
+struct Edge{
+	int indexa, indexb;
+	double length;
+	Edge(int a, int b, double c):indexa(a), indexb(b), length(c){}
+};
+//formula for finding distance between two coordinates
+double distance(int x1, int y1, int x2, int y2){
+	return sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2));
+}
+//custom sorting edges according to edges length
+struct sort_edges{
+	inline bool operator()(const Edge& struct1, const Edge& struct2){
+		return (struct1.length < struct2.length);
+	}
+};
+//finds parent of each vertices
+int find(int i, vector<point> &points){
+	int x=i;
+	while(i != points[i].parent)
+		i=points[i].parent;
+	points[x].parent=i;
+	return i;
+}
+//joins two vertices
+void Union(int a, int b, vector<point> &points){
+	if(points[a].rank < points[b].rank)
+		points[a].parent = b;
+	else {
+		points[b].parent = a;
+		if(points[a].rank == points[b].rank){
+			points[a].rank++;
+		}		
+	}	
+}
+//takes two arrays having x and y coordinates respectively and returns minimium distance between them
+double minimum_distance(vector<int> x, vector<int> y) {
+  double result = 0.0;
+  vector<point> points;
+  for(int i=0; i<x.size(); i++){
+  	points.push_back({x[i], y[i], i, 0});
+  }
+  vector<Edge> edges;
+  for(int i=0; i<x.size(); i++){
+  	for(int j=i+1; j<x.size(); j++){
+  		edges.push_back({i, j, distance(x[i], y[i], x[j], y[j])});//inserting edges(initial point, final point and distance between them)
+	}
+  }
+  std::sort(edges.begin(), edges.end(), sort_edges());
+  for(int i=0; i<edges.size(); i++){
+	int x=find(edges[i].indexa, points);
+	int y=find(edges[i].indexb, points);
+  	if(x!=y){
+  		result += edges[i].length;
+  		Union(x, y, points);
+	  }
+  };
+  return result;
+} 
+
+int main() {
+  size_t n;
+  std::cin >> n;
+  vector<int> x(n), y(n);//taking input x and y having x and y coordinate of points
+  for (size_t i = 0; i < n; i++) {
+    std::cin >> x[i] >> y[i];
+  }
+  std::cout << std::setprecision(10) << minimum_distance(x, y) << std::endl;
+}