C-Plus-Plus/data_structures/dsu_path_compresssion.cpp

#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);
    
    
}