From 17b8deec06b2e454d557366b3d479649b528e59b Mon Sep 17 00:00:00 2001
From: Himanshu Airan <62210670+Himanshu-77@users.noreply.github.com>
Date: Thu, 21 May 2020 20:55:53 +0530
Subject: [PATCH] Create Prim.cpp (#750)

* Create Prim.cpp

Created file for Prim's Algorithm in graph that was still missing.

* Update Prim.cpp

Edited indentation part

* Update Prim.cpp

indentation updated

* Update Prim.cpp

Indentation updated

* Rename Prim.cpp to prim.cpp

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 graph/prim.cpp | 58 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 graph/prim.cpp

diff --git a/graph/prim.cpp b/graph/prim.cpp
new file mode 100644
index 000000000..2923b5b25
--- /dev/null
+++ b/graph/prim.cpp
@@ -0,0 +1,58 @@
+// 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;
+}