Working with Graphs & Trees

What optimization techniques are implemented in this Union-Find data structure?

class DisjointSet {
  constructor() {
    this.parent = {};
    this.rank = {};
  }
  
  makeSet(x) {
    this.parent[x] = x;
    this.rank[x] = 0;
  }
  
  find(x) {
    if (this.parent[x] !== x) {
      this.parent[x] = this.find(this.parent[x]);
    }
    return this.parent[x];
  }
  
  union(x, y) {
    const rootX = this.find(x);
    const rootY = this.find(y);
    if (rootX === rootY) return;
    
    if (this.rank[rootX] < this.rank[rootY]) {
      this.parent[rootX] = rootY;
    } else if (this.rank[rootX] > this.rank[rootY]) {
      this.parent[rootY] = rootX;
    } else {
      this.parent[rootY] = rootX;
      this.rank[rootX]++;
    }
  }
}

Path compression only
Union by rank only
Both path compression and union by rank
This implements both major Union-Find optimizations because: 1) Uses path compression in find operation by updating parent pointers, 2) Implements union by rank to keep trees balanced, 3) Combines both techniques for optimal performance, 4) Achieves near-constant time operations, 5) Reduces tree height during finds, 6) Prevents skewed trees during unions, 7) Essential for efficient graph connectivity queries, 8) Common in Kruskal's MST algorithm implementation.
Neither optimization

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