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1101. The Earliest Moment When Everyone Become Friends 👍

  • Time: $O(n\log^* n)$
  • 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 earliestAcq(vector<vector<int>>& logs, int n) {
    UnionFind uf(n);

    // Sort `logs` by timestamp.
    ranges::sort(logs, ranges::less{},
                 [](const vector<int>& log) { return log[0]; });

    for (const vector<int>& log : logs) {
      const int timestamp = log[0];
      const int x = log[1];
      const int y = log[2];
      uf.unionByRank(x, y);
      if (uf.getCount() == 1)
        return timestamp;
    }

    return -1;
  }
};

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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 earliestAcq(int[][] logs, int n) {
    UnionFind uf = new UnionFind(n);

    // Sort `logs` by timestamp.
    Arrays.sort(logs, (a, b) -> Integer.compare(a[0], b[0]));

    for (int[] log : logs) {
      final int timestamp = log[0];
      final int x = log[1];
      final int y = log[2];
      uf.unionByRank(x, y);
      if (uf.getCount() == 1)
        return timestamp;
    }

    return -1;
  }
}

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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 earliestAcq(self, logs: list[list[int]], n: int) -> int:
    uf = UnionFind(n)

    # Sort `logs` by timestamp.
    logs.sort(key=lambda x: x[0])

    for timestamp, x, y in logs:
      uf.unionByRank(x, y)
      if uf.getCount() == 1:
        return timestamp

    return -1