From 7d03ffdfea0ab633296cb5877087e80ab4cd0cc2 Mon Sep 17 00:00:00 2001
From: Apurwa lohia <74809495+apurwa-lohia@users.noreply.github.com>
Date: Fri, 21 Oct 2022 04:29:14 +0530
Subject: [PATCH 1/2] Create prim's-algorithm.cpp

---
 Coding/prim's-algorithm.cpp | 74 +++++++++++++++++++++++++++++++++++++
 1 file changed, 74 insertions(+)
 create mode 100644 Coding/prim's-algorithm.cpp

diff --git a/Coding/prim's-algorithm.cpp b/Coding/prim's-algorithm.cpp
new file mode 100644
index 00000000..1cd4a74d
--- /dev/null
+++ b/Coding/prim's-algorithm.cpp
@@ -0,0 +1,74 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define V 5
+
+int minKey(int key[], bool mstSet[])
+{
+	
+	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;
+}
+
+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";
+}
+
+
+void primMST(int graph[V][V])
+{
+	int parent[V];
+	int key[V];
+	bool mstSet[V];
+
+	for (int i = 0; i < V; i++)
+		key[i] = INT_MAX, mstSet[i] = false;
+
+	key[0] = 0;
+	parent[0] = -1;
+
+	for (int count = 0; count < V - 1; count++)
+	{
+		int u = minKey(key, mstSet);
+
+		mstSet[u] = true;
+
+		for (int v = 0; v < V; v++)
+
+			if (graph[u][v] && mstSet[v] == false && graph[u][v] < key[v])
+				parent[v] = u, key[v] = graph[u][v];
+	}
+
+	printMST(parent, graph);
+}
+
+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 } };
+
+	primMST(graph);
+
+	return 0;
+}
+
+
+/*
+Output: 
+Edge   Weight
+0 - 1    2
+1 - 2    3
+0 - 3    6
+1 - 4    5
+*/

From a5c84155ec01615c27d384ea4aac4be10bd82c76 Mon Sep 17 00:00:00 2001
From: Apurwa lohia <74809495+apurwa-lohia@users.noreply.github.com>
Date: Fri, 21 Oct 2022 04:30:33 +0530
Subject: [PATCH 2/2] Create kruskals_msp.cpp

---
 Coding/kruskals_msp.cpp | 36 ++++++++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)
 create mode 100644 Coding/kruskals_msp.cpp

diff --git a/Coding/kruskals_msp.cpp b/Coding/kruskals_msp.cpp
new file mode 100644
index 00000000..f3a42906
--- /dev/null
+++ b/Coding/kruskals_msp.cpp
@@ -0,0 +1,36 @@
+#include <iostream>
+using namespace std;
+
+#define V 6
+#define INFINITY 99999
+
+int graph[V][V] = {{0, 4, 1, 4, INFINITY, INFINITY},
+                   {4, 0, 3, 8, 3, INFINITY},
+                   {1, 3, 0, INFINITY, 1, INFINITY},
+                   {4, 8, INFINITY, 0, 5, 7},
+                   {INFINITY, 3, 1, 5, 0, INFINITY},
+                   {INFINITY, INFINITY, INFINITY, 7, INFINITY, 0}};
+
+void findMinimumEdge() {
+    for (int i = 0; i < V; i++) {
+        int min = INFINITY;
+        int minIndex = 0;
+        for (int j = 0; j < V; j++) {
+            if (graph[i][j] != 0 && graph[i][j] < min) {
+                min = graph[i][j];
+                minIndex = j;
+            }
+        }
+        cout << i << "  -  " << minIndex << "\t" << graph[i][minIndex] << "\n";
+    }
+}
+
+int main() {
+    findMinimumEdge();
+    return 0;
+}
+
+
+//1. Sort all the edges in non-decreasing order of their weight. 
+//2. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge. Else, discard it. 
+//3. Repeat step#2 until there are (V-1) edges in the spanning tree.