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2076. Process Restricted Friend Requests 👍

  • Time: $O(|\texttt{restrictions}||\texttt{requests}|\cdot\log n)$
  • Space: $O(n)$
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class UnionFind {
 public:
  UnionFind(int 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];
    }
  }

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

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

class Solution {
 public:
  vector<bool> friendRequests(int n, vector<vector<int>>& restrictions,
                              vector<vector<int>>& requests) {
    vector<bool> ans;
    UnionFind uf(n);

    for (const vector<int>& request : requests) {
      const int i = uf.find(request[0]);
      const int j = uf.find(request[1]);
      bool isValid = true;
      if (i != j)
        for (const vector<int>& restriction : restrictions) {
          const int x = uf.find(restriction[0]);
          const int y = uf.find(restriction[1]);
          if (i == x && j == y || i == y && j == x) {
            isValid = false;
            break;
          }
        }
      ans.push_back(isValid);
      if (isValid)
        uf.unionByRank(i, j);
    }

    return ans;
  }
};

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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 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];
    }
  }

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

  private int[] id;
  private int[] rank;
}

class Solution {
  public boolean[] friendRequests(int n, int[][] restrictions, int[][] requests) {
    boolean[] ans = new boolean[requests.length];
    UnionFind uf = new UnionFind(n);

    for (int i = 0; i < requests.length; ++i) {
      final int pu = uf.find(requests[i][0]);
      final int pv = uf.find(requests[i][1]);
      boolean isValid = true;
      if (pu != pv)
        for (int[] restriction : restrictions) {
          final int px = uf.find(restriction[0]);
          final int py = uf.find(restriction[1]);
          if (pu == px && pv == py || pu == py && pv == px) {
            isValid = false;
            break;
          }
        }
      ans[i] = isValid;
      if (isValid)
        uf.unionByRank(pu, pv);
    }

    return ans;
  }
}

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class UnionFind:
  def __init__(self, n: int):
    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

  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 friendRequests(self, n: int, restrictions: List[List[int]], requests: List[List[int]]) -> List[bool]:
    ans = []
    uf = UnionFind(n)

    for u, v in requests:
      pu = uf.find(u)
      pv = uf.find(v)
      isValid = True
      if pu != pv:
        for x, y in restrictions:
          px = uf.find(x)
          py = uf.find(y)
          if (pu, pv) in [(px, py), (py, px)]:
            isValid = False
            break
      ans.append(isValid)
      if isValid:
        uf.unionByRank(pu, pv)

    return ans