changed file name from upper case to lower case

data_structures/dsu_path_compresssion.cpp

@@ -0,0 +1,124 @@
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+//Disjoint set union 
+class DSU{
+    private:
+        // p: keeps track of parent of i
+        // depth: tracks the depth of i
+        // setSize: size of each chunk(set)
+        // maxElement : max of each set, using maxElement[representative]
+        // minElement : min of each set, using minElement[representative]
+        vector<int> p,depth,setSize,maxElement,minElement;
+    public:
+        // parameter : int n -> maximum number of items
+        DSU(int n){
+            p.assign(n,0);
+            //initially all of them are their own 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 i -> root(representative)
+            return (p[i] = findSet(p[i]));
+        }
+        //union of 2 sets
+        void UnionSet(int i,int j){
+            //check if both belongs to same set or not
+            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 same depth then increase one's depth
+            if(depth[x] == depth[y]){
+                depth[y]++;
+            }
+            //total size of the resultant set.  
+            setSize[y] += setSize[x];
+            //changing the maximum elements
+            maxElement[y] = max(maxElement[x],maxElement[y]);
+            minElement[y] = min(minElement[x],minElement[y]);
+        }
+        //checks if both belongs to same set
+        bool isSame(int i,int j){
+            if(findSet(i) == findSet(j)){
+                return true;
+            }
+            return false;
+        }
+        //returns min max size of i's set
+        void get(int i){
+            cout << "min:" << get_min(i) << " max:" << get_max(i) << " size of set:" <<size(i) << endl; 
+        }
+        //number of elements of each set
+        int size(int i){
+            return setSize[findSet(i)];
+        }
+        //returns max of the set whose part is i
+        int get_max(int i){
+            return maxElement[findSet(i)];
+        }
+        //returns min of the set whose part is i
+        int get_min(int i){
+            return minElement[findSet(i)];
+        }
+
+};
+
+//T(n) = O(n)
+int main(){
+    int n;
+    n = 10;
+    //n: number of items
+    DSU d(n+1);
+    //set 1
+    cout << "set 1:"<<endl;
+    d.UnionSet(1,2); //performs union operation on 1 and 2
+    d.UnionSet(1,4);
+    cout << "Representative of "<< 4 << " is "<< d.findSet(4) << endl; //find the representative of the set which 4 belongs to.
+    d.get(4); //print min max and size of set.
+
+    //set 2
+    cout << "\nset 2"<<endl;
+    d.UnionSet(3,5);
+    d.UnionSet(5,6);
+    d.UnionSet(5,7);
+    cout << "Representative of " << 7 <<" is " << d.findSet(7) << endl;
+    d.get(3);
+    
+    
+}

data_structures/dsu_union_rank.cpp

@@ -0,0 +1,96 @@
+#include <iostream>
+#include <vector>
+
+
+using namespace std;
+
+class DSU{
+    private:
+        // p: keeps track of parent of i
+        // depth: tracks the depth of i
+        // setSize: size of each chunk(set)
+        vector<int> p,depth,setSize;
+    public:
+        //parameter : int n -> maximum number of items
+        DSU(int n){
+            p.assign(n,0);
+            //initially all of them their own parents
+            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){
+            //union rank i - > p[i]
+            while(i!=p[i]){
+                i = p[i];
+            }
+            return i;
+        }
+        //union of 2 sets
+        void unionSet(int i,int j){
+            //check if both belongs to same set or not
+            if(isSame(i,j)){
+                return;
+            }
+            //we find representative of the i and j
+            int x = findSet(i);
+            int y = findSet(j);
+
+            //always keeping the min as x
+            //in order to create a shallow tree
+            if(depth[x]>depth[y]){
+                swap(x,y);
+            }
+            //making the shallower tree' root parent of the deeper root
+            p[x] = y;
+
+            //if same depth then increase one's depth
+            if(depth[x] == depth[y]){
+                depth[y]++;
+            }
+            //total size of the resultant set
+            setSize[y]+=setSize[x];
+        }
+        // checks if both belongs to same set
+        bool isSame(int i,int j){
+            if(findSet(i) == findSet(j)){
+                return true;
+            }
+            return false;
+        }
+        void getParents(int i){
+            while(p[i]!=i){
+                cout << i << " ->";
+                i = p[i];
+            }
+            cout << p[i] << endl;
+        }
+        
+};
+
+int main(){
+    int n;
+    n = 10; 
+    //n: number of items
+    DSU d(n+1);
+    d.unionSet(2,1); //performs union operation on 1 and 2
+    d.unionSet(1,4);
+    d.unionSet(8,1);
+    
+    d.unionSet(3,5);
+    d.unionSet(5,6);
+    d.unionSet(5,7);
+
+    d.unionSet(9,10);
+    d.unionSet(2,10);
+
+    //keeping track of the changes using parent pointers
+    d.getParents(7);
+    d.getParents(2);
+
+
+}