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3493. Properties Graph 👍

  • Time: $O(n^2\log^* n)$
  • Space: $O(n)$
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class UnionFind {
 public:
  UnionFind(int n) : count(n), id(n), rank(n) {
    iota(id.begin(), id.end(), 0);
  }

  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];
    }
    --count;
  }

  int getCount() const {
    return count;
  }

 private:
  int count;
  vector<int> id;
  vector<int> rank;

  int find(int u) {
    return id[u] == u ? u : id[u] = find(id[u]);
  }
};

class Solution {
 public:
  int numberOfComponents(vector<vector<int>>& properties, int k) {
    const int n = properties.size();
    const vector<set<int>> propertySets = getPropertySets(properties);
    UnionFind uf(n);

    for (int i = 0; i < n; ++i)
      for (int j = i + 1; j < n; ++j) {
        vector<int> intersection;
        std::set_intersection(propertySets[i].begin(), propertySets[i].end(),
                              propertySets[j].begin(), propertySets[j].end(),
                              std::back_inserter(intersection));
        if (intersection.size() >= k)
          uf.unionByRank(i, j);
      }

    return uf.getCount();
  }

 private:
  vector<set<int>> getPropertySets(const vector<vector<int>>& properties) {
    vector<set<int>> propertySets;
    for (const vector<int>& property : properties)
      propertySets.push_back({property.begin(), property.end()});
    return propertySets;
  }
};

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class UnionFind {
  public UnionFind(int n) {
    count = n;
    id = new int[n];
    rank = new int[n];
    for (int i = 0; i < n; ++i)
      id[i] = i;
  }

  public void unionByRank(int u, int v) {
    final int i = find(u);
    final 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];
    }
    --count;
  }

  public int getCount() {
    return count;
  }

  private int count;
  private int[] id;
  private int[] rank;

  private int find(int u) {
    return id[u] == u ? u : (id[u] = find(id[u]));
  }
}

class Solution {
  public int numberOfComponents(int[][] properties, int k) {
    final int n = properties.length;
    Set<Integer>[] propertySets = getPropertySets(properties);
    UnionFind uf = new UnionFind(n);

    for (int i = 0; i < n; ++i)
      for (int j = i + 1; j < n; ++j) {
        Set<Integer> intersection = new HashSet<>(propertySets[i]);
        intersection.retainAll(propertySets[j]);
        if (intersection.size() >= k)
          uf.unionByRank(i, j);
      }

    return uf.getCount();
  }

  private Set<Integer>[] getPropertySets(int[][] properties) {
    Set<Integer>[] propertySets = new Set[properties.length];
    for (int i = 0; i < properties.length; ++i)
      propertySets[i] = Arrays.stream(properties[i]).boxed().collect(Collectors.toSet());
    return propertySets;
  }
}

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class UnionFind:
  def __init__(self, n: int):
    self.count = n
    self.id = list(range(n))
    self.rank = [0] * n

  def unionByRank(self, u: int, v: int) -> None:
    i = self._find(u)
    j = self._find(v)
    if i == j:
      return
    if self.rank[i] < self.rank[j]:
      self.id[i] = j
    elif self.rank[i] > self.rank[j]:
      self.id[j] = i
    else:
      self.id[i] = j
      self.rank[j] += 1
    self.count -= 1

  def getCount(self) -> int:
    return self.count

  def _find(self, u: int) -> int:
    if self.id[u] != u:
      self.id[u] = self._find(self.id[u])
    return self.id[u]


class Solution:
  def numberOfComponents(self, properties: list[list[int]], k: int) -> int:
    n = len(properties)
    uf = UnionFind(n)
    propertySets = [set(property) for property in properties]

    for i, j in itertools.combinations(range(n), 2):
      if len(propertySets[i] & propertySets[j]) >= k:
        uf.unionByRank(i, j)

    return uf.getCount()