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Kruskals.cpp
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Kruskals.cpp
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/*Kruskals Algorithm
Author: Phalesh Kolpe
Kruskals algorithm is used to Find the MST(Minimum Spaning Tree) of a graph it considers the edges and weight of the edge
Step 1: Sort all edges in increasing order of their edge weights.
Step 2: Pick the smallest edge.
Step 3: Check if the new edge creates a cycle or loop in a spanning tree.
Step 4: If it doesn’t form the cycle, then include that edge in MST. Otherwise, discard it.
Step 5: Repeat from step 2 until it includes |V| - 1 edges in MST.
Expected Output Of the code:-
Enter the number of vertices:
Enter the number of edges:
Enter the details of each edge (source, destination, weight):
Give input for the above line in the following manner
0 1 7
where 0 is the soucre of edge 1 is the destination and 7 is the weight of the edge*/
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
// Structure to represent an edge
struct edge {
int src, dest, weight;
};
// Structure to represent a graph
struct Graph {
int v, e;
vector<edge> edges;
};
int findParent(vector<int>& parent, int i) {
if (parent[i] == -1)
return i;
return findParent(parent, parent[i]);
}
// Function to perform union of two sets
void unionSets(vector<int>& parent, int x, int y) {
parent[x] = y;
}
// Function to compare two edges based on their weights
bool compareedges(const edge& a, const edge& b) {
return a.weight < b.weight;
}
// Function to apply Kruskal's algorithm and find the minimum spanning tree
void kruskalMST(Graph& graph) {
int v = graph.v;
vector<edge> result;
int e = 0;
int i = 0;
// Sort the edges in ascending order of their weights
sort(graph.edges.begin(), graph.edges.end(), compareedges);
// Allocate memory for parent array
vector<int> parent(v, -1);
// Process each edge and add it to the MST if it does not form a cycle
while (e < v - 1 && i < graph.e) {
edge nextedge = graph.edges[i++];
int x = findParent(parent, nextedge.src);
int y = findParent(parent, nextedge.dest);
if (x != y) {
result.push_back(nextedge);
unionSets(parent, x, y);
e++;
}
}
// Print the edges of the MST
cout << "Edges in the constructed MST:" << endl;
for (const edge& edge : result) {
cout << edge.src << " -- " << edge.dest << " => " << edge.weight << endl;
}
}
int main() {
int v, e;
cout << "Enter the number of vertices: ";
cin >> v;
cout << "Enter the number of edges: ";
cin >> e;
Graph graph;
graph.v = v;
graph.e = e;
cout << "Enter the details of each edge (source, destination, weight):" << endl;
for (int i = 0; i < e; i++) {
edge edge;
cin >> edge.src >> edge.dest >> edge.weight;
graph.edges.push_back(edge);
}
kruskalMST(graph);
return 0;
}