Data Structures & Algorithms
Union-Find/Disjoint-Set Interview Questions
Tackle coding interview questions on the Union-Find/Disjoint-Set data structure. Our AI-powered guide provides expert insights, practice problems, and personalized feedback to help you succeed.
Number of Connected Components in an Undirected Graph
Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to find the number of connected components in an undirected graph.
class Solution {
countComponents(n, edges) {
let parent = Array.from({length: n}, (_, i) => i);
let rank = Array(n).fill(1);
function find(i) { if (parent[i] === i) return i; parent[i] = find(parent[i]); return parent[i]; }
function union(i, j) { let rootI = find(i); let rootJ = find(j); if (rootI !== rootJ) { if (rank[rootI] > rank[rootJ]) { parent[rootJ] = rootI; } else if (rank[rootI] < rank[rootJ]) { parent[rootI] = rootJ; } else { parent[rootJ] = rootI; rank[rootI] += 1; } return 1; } return 0; }
let components = n; for (const [i, j] of edges) { components -= union(i, j); } return components; } }
function find(i) { if (parent[i] === i) return i; parent[i] = find(parent[i]); return parent[i]; }
function union(i, j) { let rootI = find(i); let rootJ = find(j); if (rootI !== rootJ) { if (rank[rootI] > rank[rootJ]) { parent[rootJ] = rootI; } else if (rank[rootI] < rank[rootJ]) { parent[rootI] = rootJ; } else { parent[rootJ] = rootI; rank[rootI] += 1; } return 1; } return 0; }
let components = n; for (const [i, j] of edges) { components -= union(i, j); } return components; } }
The Union-Find data structure is ideal for this problem. We initialize each node as a separate component. Then, we iterate through the edges, and for each edge, we union the two nodes. If they were not already in the same set, we decrement the number of components. The final count is the answer.
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