From 643b41b5be0992998a9b2971821bcd982df9d290 Mon Sep 17 00:00:00 2001
From: umbridge <44002678+umbridge@users.noreply.github.com>
Date: Mon, 5 Oct 2020 08:23:33 +0530
Subject: [PATCH] =?UTF-8?q?Create=20Prim=E2=80=99s=20Minimum=20Spanning=20?=
 =?UTF-8?q?Tree=20(MST).cpp?=
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---
 ...\200\231s Minimum Spanning Tree (MST).cpp" | 105 ++++++++++++++++++
 1 file changed, 105 insertions(+)
 create mode 100644 "Algorithms/Graph Algorithms/Prim\342\200\231s Minimum Spanning Tree (MST).cpp"

diff --git "a/Algorithms/Graph Algorithms/Prim\342\200\231s Minimum Spanning Tree (MST).cpp" "b/Algorithms/Graph Algorithms/Prim\342\200\231s Minimum Spanning Tree (MST).cpp"
new file mode 100644
index 00000000..b011cc06
--- /dev/null
+++ "b/Algorithms/Graph Algorithms/Prim\342\200\231s Minimum Spanning Tree (MST).cpp"	
@@ -0,0 +1,105 @@
+// A C++ program for Prim's Minimum 
+// Spanning Tree (MST) algorithm. The program is 
+// for adjacency matrix representation of the graph 
+#include <bits/stdc++.h>
+using namespace std;
+
+// Number of vertices in the graph 
+#define V 5 
+
+// A utility function to find the vertex with 
+// minimum key value, from the set of vertices 
+// not yet included in MST 
+int minKey(int key[], bool mstSet[]) 
+{ 
+	// Initialize min value 
+	int min = INT_MAX, min_index; 
+
+	for (int v = 0; v < V; v++) 
+		if (mstSet[v] == false && key[v] < min) 
+			min = key[v], min_index = v; 
+
+	return min_index; 
+} 
+
+// A utility function to print the 
+// constructed MST stored in parent[] 
+void printMST(int parent[], int graph[V][V]) 
+{ 
+	cout<<"Edge \tWeight\n"; 
+	for (int i = 1; i < V; i++) 
+		cout<<parent[i]<<" - "<<i<<" \t"<<graph[i][parent[i]]<<" \n"; 
+} 
+
+// Function to construct and print MST for 
+// a graph represented using adjacency 
+// matrix representation 
+void primMST(int graph[V][V]) 
+{ 
+	// Array to store constructed MST 
+	int parent[V]; 
+	
+	// Key values used to pick minimum weight edge in cut 
+	int key[V]; 
+	
+	// To represent set of vertices included in MST 
+	bool mstSet[V]; 
+
+	// Initialize all keys as INFINITE 
+	for (int i = 0; i < V; i++) 
+		key[i] = INT_MAX, mstSet[i] = false; 
+
+	// Always include first 1st vertex in MST. 
+	// Make key 0 so that this vertex is picked as first vertex. 
+	key[0] = 0; 
+	parent[0] = -1; // First node is always root of MST 
+
+	// The MST will have V vertices 
+	for (int count = 0; count < V - 1; count++)
+	{ 
+		// Pick the minimum key vertex from the 
+		// set of vertices not yet included in MST 
+		int u = minKey(key, mstSet); 
+
+		// Add the picked vertex to the MST Set 
+		mstSet[u] = true; 
+
+		// Update key value and parent index of 
+		// the adjacent vertices of the picked vertex. 
+		// Consider only those vertices which are not 
+		// yet included in MST 
+		for (int v = 0; v < V; v++) 
+
+			// graph[u][v] is non zero only for adjacent vertices of m 
+			// mstSet[v] is false for vertices not yet included in MST 
+			// Update the key only if graph[u][v] is smaller than key[v] 
+			if (graph[u][v] && mstSet[v] == false && graph[u][v] < key[v]) 
+				parent[v] = u, key[v] = graph[u][v]; 
+	} 
+
+	// print the constructed MST 
+	printMST(parent, graph); 
+} 
+
+// Driver code
+int main() 
+{ 
+	/* Let us create the following graph 
+		2 3 
+	(0)--(1)--(2) 
+	| / \ | 
+	6| 8/ \5 |7 
+	| / \ | 
+	(3)-------(4) 
+			9	 */
+	int graph[V][V] = { { 0, 2, 0, 6, 0 }, 
+						{ 2, 0, 3, 8, 5 }, 
+						{ 0, 3, 0, 0, 7 }, 
+						{ 6, 8, 0, 0, 9 }, 
+						{ 0, 5, 7, 9, 0 } }; 
+
+	// Print the solution 
+	primMST(graph); 
+
+	return 0; 
+}