From fff01336e5ce82ed234a83b9797ae97c2e05c919 Mon Sep 17 00:00:00 2001
From: Dinesh Garg <dinesh.garg@students.iiit.ac.in>
Date: Wed, 20 Oct 2021 15:38:17 +0530
Subject: [PATCH 1/2] Update 1.cpp

---
 1.cpp | 33 +++++++++++++++++++++++----------
 1 file changed, 23 insertions(+), 10 deletions(-)

diff --git a/1.cpp b/1.cpp
index e7095b9..50c92b0 100644
--- a/1.cpp
+++ b/1.cpp
@@ -91,15 +91,7 @@ class subset
   
 // A utility function to find set of an element i  
 // (uses path compression technique)  
-int find(subset subsets[], int i)  
-{  
-    // find root and make root as parent of i  
-    // (path compression)  
-    if (subsets[i].parent != i)  
-        subsets[i].parent = find(subsets, subsets[i].parent);  
-  
-    return subsets[i].parent;  
-}  
+
   
 // A function that does union of two sets of x and y  
 // (uses union by rank)  
@@ -122,7 +114,28 @@ void Union(subset subsets[], int x, int y)
         subsets[yroot].parent = xroot;  
         subsets[xroot].rank++;  
     }  
-}  
+} 
+
+void Union(subset subsets[], int x, int y)  
+{  
+    int xroot = find(subsets, x);  
+    int yroot = find(subsets, y);  
+  
+    // Attach smaller rank tree under root of high  
+    // rank tree (Union by Rank)  
+    if (subsets[xroot].rank < subsets[yroot].rank)  
+        subsets[xroot].parent = yroot;  
+    else if (subsets[xroot].rank > subsets[yroot].rank)  
+        subsets[yroot].parent = xroot;  
+  
+    // If ranks are same, then make one as root and  
+    // increment its rank by one  
+    else
+    {  
+        subsets[yroot].parent = xroot;  
+        subsets[xroot].rank++;  
+    }  
+} 
   
 // Compare two edges according to their weights.  
 // Used in qsort() for sorting an array of edges  

From 8924972e44ac2d1418a012c8fc39da73e00bef74 Mon Sep 17 00:00:00 2001
From: Dinesh Garg <dinesh.garg@students.iiit.ac.in>
Date: Wed, 20 Oct 2021 15:39:35 +0530
Subject: [PATCH 2/2] Update 2.cpp

---
 2.cpp | 9 +--------
 1 file changed, 1 insertion(+), 8 deletions(-)

diff --git a/2.cpp b/2.cpp
index 3b839e9..f9247dd 100644
--- a/2.cpp
+++ b/2.cpp
@@ -19,14 +19,7 @@ int minKey(int key[], bool mstSet[])
  
 // 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 
+ction to construct and print MST for 
 // a graph represented using adjacency 
 // matrix representation 
 void primMST(int graph[V][V])