prim Algorithm
In abstract algebra, objects that behave in a generalized manner like prime numbers include prime components and prime ideals. A prime number (or a prime) is a natural number greater than 1 that is not a merchandise of two smaller natural numbers. method that are restricted to specific number forms include Pépin's test for Fermat numbers (1877), Proth's theorem (c. 1878), the Lucas – Lehmer primality test (originated 1856), and the generalized Lucas primality test.
// C++ program to implement Prim's Algorithm
#include <iostream>
#include <vector>
#include <queue>
const int MAX = 1e4 + 5;
typedef std:: pair<int, int> PII;
bool marked[MAX];
std:: vector <PII> adj[MAX];
int prim(int x) {
// priority queue to maintain edges with respect to weights
std:: priority_queue<PII, std:: vector<PII>, std:: greater<PII> > Q;
int y;
int minimumCost = 0;
PII p;
Q.push(std:: make_pair(0, x));
while (!Q.empty()) {
// Select the edge with minimum weight
p = Q.top();
Q.pop();
x = p.second;
// Checking for cycle
if (marked[x] == true)
continue;
minimumCost += p.first;
marked[x] = true;
for (int i = 0; i < adj[x].size(); ++i) {
y = adj[x][i].second;
if (marked[y] == false)
Q.push(adj[x][i]);
}
}
return minimumCost;
}
int main() {
int nodes, edges, x, y;
int weight, minimumCost;
std:: cin >> nodes >> edges; // number of nodes & edges in graph
if (nodes == 0 || edges == 0)
return 0;
// Edges with their nodes & weight
for (int i = 0; i < edges; ++i) {
std::cin >> x >> y >> weight;
adj[x].push_back(std:: make_pair(weight, y));
adj[y].push_back(std:: make_pair(weight, x));
}
// Selecting 1 as the starting node
minimumCost = prim(1);
std:: cout << minimumCost << std:: endl;
return 0;
}
