Disjoint Set Implementation

Computational_Algorithms/Disjoint Set Union/implementation.c++

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+//DISJOINT SET UNION - IMPLEMENTATION
+
+/*
+    Functionalities included:
+    1. Find Ultimate Parent of a node 
+    2. Union By Rank
+    3. Union By Size
+    4. Find whether two elements are part of same component or not
+    5. Print all the ultimate parents for all the nodes in the DSU
+*/
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+
+class DSU{
+private:
+    vector<int> rank;
+    vector<int> size;
+    vector<int> parent;
+
+public:
+    DSU(int n){
+        rank.resize(n + 1, 0);
+        parent.resize(n + 1);
+        size.resize(n + 1, 1);
+        for (int i = 0; i <= n; i++) parent[i] = i;
+    }
+
+    int findUltimateParent(int node){
+        if (node == parent[node]) return node;
+        int ultimateParent = findUltimateParent(parent[node]);
+        parent[node] = ultimateParent;   //Path Compression
+        return ultimateParent;
+    }
+
+    void unionByRank(int u, int v){
+        int ulp_u = findUltimateParent(u);
+        int ulp_v = findUltimateParent(v);
+        if (ulp_u == ulp_v) return;
+        if (rank[ulp_u] < rank[ulp_v]) parent[ulp_u] = ulp_v;
+        else if (rank[ulp_u] > rank[ulp_v]) parent[ulp_v] = ulp_u;
+        else {
+            parent[ulp_v] = ulp_u;
+            rank[ulp_u]++;
+        }
+    }
+
+    void unionBySize(int u, int v){
+        int ulp_u = findUltimateParent(u);
+        int ulp_v = findUltimateParent(v);
+        if (ulp_u == ulp_v) return;
+        if (size[ulp_u] < size[ulp_v]){
+            parent[ulp_u] = ulp_v;
+            size[ulp_v] += size[ulp_u];
+        }
+        else{
+            parent[ulp_v] = ulp_u;
+            size[ulp_u] += size[ulp_v];
+        }
+    }
+
+    bool inSameComponent(int u, int v){
+        return findUltimateParent(u) == findUltimateParent(v);
+    }
+
+    void printUltimateParents(){
+        for (int i : parent) cout << i << " ";
+        cout << "\n";
+    }
+};
+
+int main(){
+    DSU ds(5);
+    ds.unionBySize(1, 2);
+    ds.unionBySize(3, 2);
+    ds.unionBySize(4, 2);
+    ds.unionBySize(5, 3);
+    ds.unionBySize(1, 4);
+    if (ds.inSameComponent(1, 4)) cout << "YES, these two are in the same component" << endl;
+    else cout << "NO" << endl;
+    cout << "Parents of all nodes in the DSU -> ";
+    ds.printUltimateParents();
+}