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Problem solution · Java

Graph Connectivity With Threshold

Graph Connectivity With Threshold: a Java solution using disjoint set union. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Disjoint set union
Source
walkccc LeetCode Solutions
Length
51 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Disjoint set union

For Graph Connectivity With Threshold, the implementation maintains connected components and merges them as relationships are processed.

  1. Give each element a component representative.
  2. Merge representatives when a connection is accepted.
  3. Answer connectivity or component queries from the compressed representatives.

Code notes

  • 51 lines of Java from the credited upstream file 1627.java.
  • The implementation visibly relies on sequence storage.
  • 4 loop blocks detected.

Complexity

Account for every find and union operation; with path compression and ranked merging, the amortized cost is nearly constant per operation.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeGraph Connectivity With Threshold · JavaJava
Use this to learn the idea, then write your own version.
class UnionFind {  public UnionFind(int n) {    id = new int[n];    rank = new int[n];    for (int i = 0; i < n; ++i)      id[i] = i;  }   public boolean unionByRank(int u, int v) {    final int i = find(u);    final int j = find(v);    if (i == j)      return false;    if (rank[i] < rank[j]) {      id[i] = j;    } else if (rank[i] > rank[j]) {      id[j] = i;    } else {      id[i] = j;      ++rank[j];    }    return true;  }   public int find(int u) {    return id[u] == u ? u : (id[u] = find(id[u]));  }   private int[] id;  private int[] rank;} class Solution {  public List<Boolean> areConnected(int n, int threshold, int[][] queries) {    List<Boolean> ans = new ArrayList<>();    UnionFind uf = new UnionFind(n + 1);     for (int z = threshold + 1; z <= n; ++z)      for (int x = z * 2; x <= n; x += z)        uf.unionByRank(z, x);     for (int[] query : queries) {      final int a = query[0];      final int b = query[1];      ans.add(uf.find(a) == uf.find(b));    }     return ans;  }}

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