added prims algorithm c++ code to greedy algorithms

GreedyAlgorithms/prims_algorithm.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 not yet 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;  
+}