From 7f0ff584b9f51b9740e98ed8d3a15eab32a9ded4 Mon Sep 17 00:00:00 2001
From: Aayush Vyas <70998175+AayushVyasKIIT@users.noreply.github.com>
Date: Fri, 27 Aug 2021 16:07:27 +0530
Subject: [PATCH] Add files via upload

# Class Based DSU
-Using Path Compression to get the best time complexity O(1)
-Using Union Rank to keep track of changes using parent(p) O(logN)
---
 data_structures/DSU_path_compresssion.cpp | 111 ++++++++++++++++++++++
 data_structures/DSU_union_rank.cpp        |  58 +++++++++++
 2 files changed, 169 insertions(+)
 create mode 100644 data_structures/DSU_path_compresssion.cpp
 create mode 100644 data_structures/DSU_union_rank.cpp

diff --git a/data_structures/DSU_path_compresssion.cpp b/data_structures/DSU_path_compresssion.cpp
new file mode 100644
index 000000000..e0874e86b
--- /dev/null
+++ b/data_structures/DSU_path_compresssion.cpp
@@ -0,0 +1,111 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define vi vector<int>
+
+class DSU{
+    private:
+        vi p,depth,setSize,maxElement,minElement;
+    public:
+        DSU(int n){
+            p.assign(n,0);
+            //initially all of them are their parents.
+            for(int i=0;i<n;i++){
+                p[i] = i;
+            }
+            //initially all have depth =0
+            depth.assign(n,0);
+            maxElement.assign(n,0);
+            minElement.assign(n,0);
+            for(int i=0;i<n;i++){
+                depth[i] = 0;
+                maxElement[i] = i;
+                minElement[i] = i;
+            }
+            setSize.assign(n,0);
+            //initially set size will be 1
+            for(int i=0;i<n;i++){
+                setSize[i]=1;
+            }
+        }
+
+        //returns the leader/representative of the set
+        int findSet(int i){
+            if(p[i]==i){
+                return i;
+            }
+            //path compression
+            return (p[i] = findSet(p[i]));
+        }
+        //union of 2 sets
+        void UnionSet(int i,int j){
+            if(isSame(i,j)){
+                return;
+            }
+
+            //we find the representative of the i and j
+            int x = findSet(i);
+            int y = findSet(j);
+
+            //always keeping the min as x
+            //shallow tree
+            if(depth[x]>depth[y]){
+                swap(x,y);
+            }
+            //making the shallower root's parent the deeper root
+            p[x] = y;
+            
+            if(depth[x] == depth[y]){
+                depth[y]++;
+            }
+            //total size of the resultant set.  
+            setSize[y] += setSize[x];
+            maxElement[y] = max(maxElement[x],maxElement[y]);
+            minElement[y] = min(minElement[x],minElement[y]);
+        }
+        //checks if both sets equal
+
+        bool isSame(int i,int j){
+            if(findSet(i) == findSet(j)){
+                return true;
+            }
+            return false;
+        }
+        void get(int i){
+            cout << get_min(i) << " " << get_max(i) << " " <<size(i) << endl; 
+        }
+        //number of elements of each set
+        int size(int i){
+            return setSize[findSet(i)];
+        }
+        int get_max(int i){
+            return maxElement[findSet(i)];
+        }
+        int get_min(int i){
+            return minElement[findSet(i)];
+        }
+
+};
+
+int main(){
+    std::ios_base::sync_with_stdio(0);std::cin.tie(0);std::cout.tie(0);
+    int n,q;cin>>n;cin>>q;
+
+    DSU d(n+1);
+
+    while(q--){
+        string op;cin>>op;
+        if(op == "union"){
+            int i,j;
+            cin >> i >> j;
+            d.UnionSet(i,j);
+        }else{
+            int i;
+            cin >> i;
+            d.get(i);
+        }
+    }
+    
+    
+}
diff --git a/data_structures/DSU_union_rank.cpp b/data_structures/DSU_union_rank.cpp
new file mode 100644
index 000000000..535f71ebf
--- /dev/null
+++ b/data_structures/DSU_union_rank.cpp
@@ -0,0 +1,58 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define vi vector<int> 
+class DSU{
+    private:
+        vi p,depth,setSize;
+    public:
+        DSU(int n){
+            p.assign(n,0);
+            depth.assign(n,0);
+            setSize.assign(n,0);
+            for(int i=0;i<n;i++){
+                p[i] = i;
+                depth[i] = 0;
+                setSize[i] = 1;
+            }
+        }
+        int findSet(int i){
+            while(i!=p[i]){
+                i = p[i];
+            }
+            return i;
+        }
+        void unionSet(int i,int j){
+            if(isSame(i,j)){
+                return;
+            }
+            int x = findSet(i);
+            int y = findSet(j);
+
+            if(depth[x]>depth[y]){
+                swap(x,y);
+            }
+            p[x] = y;
+            if(depth[x] == depth[y]){
+                depth[y]++;
+            }
+            setSize[y]+=setSize[x];
+        }
+        bool isSame(int i,int j){
+            if(findSet(i) == findSet(j)){
+                return true;
+            }
+            return false;
+        }
+        
+};
+
+int main(){
+    int n;cin>>n;
+
+    DSU d(n+1);
+    d.unionSet(2,4);
+    d.unionSet(3,4);
+    cout <<  d.findSet(2) <<endl;
+}
\ No newline at end of file