From bf000284bca891f95b31bf70f8bbfc50a0c56679 Mon Sep 17 00:00:00 2001
From: Akshit Kharbanda <akshit.kharbanda04@gmail.com>
Date: Sun, 31 Oct 2021 14:44:20 -0500
Subject: [PATCH] add prims.cpp

---
 .../Graph Theory Algorithms/prims.cpp         | 102 ++++++++++++++++++
 1 file changed, 102 insertions(+)
 create mode 100644 C++/Algorithms/Graph Theory Algorithms/prims.cpp

diff --git a/C++/Algorithms/Graph Theory Algorithms/prims.cpp b/C++/Algorithms/Graph Theory Algorithms/prims.cpp
new file mode 100644
index 000000000..0a435c4ce
--- /dev/null
+++ b/C++/Algorithms/Graph Theory Algorithms/prims.cpp	
@@ -0,0 +1,102 @@
+#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;
+}
\ No newline at end of file