hacktoberfest2022

CPP/prims algo.cpp

@@ -0,0 +1,83 @@
+#include <iostream>
+
+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[]
+int printMST(int parent[], int n, int graph[V][V])
+{
+    cout<<"Edge   Weight\n";
+    for (int i = 1; i < V; i++)
+        printf("%d - %d    %d \n", parent[i], i, graph[i][parent[i]]);
+}
+
+// Function to construct and print MST for a graph represented using adjacency
+// matrix representation
+void primMST(int graph[V][V])
+{
+    int parent[V]; // Array to store constructed MST
+    int key[V]; // Key values used to pick minimum weight edge in cut
+    bool mstSet[V]; // To represent set of vertices not yet included in MST
+
+    // 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.
+    key[0] = 0; // Make key 0 so that this vertex is picked as first vertex
+    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 thd 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, V, graph);
+}
+
+// driver program to test above function
+int main()
+{
+
+    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;
+}