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Problem solution · C++

Count Connected Components in LCM Graph

Count Connected Components in LCM Graph: a C++ 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
44 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 Count Connected Components in LCM Graph, 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

  • 44 lines of C++ from the credited upstream file 3378.cpp.
  • The implementation visibly relies on sequence storage, hash lookup.
  • 3 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 codeCount Connected Components in LCM Graph · C++C++
Use this to learn the idea, then write your own version.
class UnionFind { public:  void unionByRank(int u, int v) {    const int i = find(u);    const int j = find(v);    if (i == j)      return;    if (rank[i] < rank[j]) {      id[i] = j;    } else if (rank[i] > rank[j]) {      id[j] = i;    } else {      id[i] = j;      ++rank[j];    }  }   int find(int u) {    if (!id.contains(u))      id[u] = u;    return id[u] == u ? u : id[u] = find(id[u]);  }  private:  unordered_map<int, int> id;  unordered_map<int, int> rank;}; class Solution { public:  int countComponents(vector<int>& nums, int threshold) {    UnionFind uf;     for (const int num : nums)      for (int multiple = 2 * num; multiple <= threshold; multiple += num)        uf.unionByRank(num, multiple);     unordered_set<int> components;    for (const int num : nums)      components.insert(uf.find(num));    return components.size();  }};

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