990. Satisfiability of Equality Equations

EquationsPossible.cs

public class Solution {
  public bool EquationsPossible(string[] equations) {    
    var uf = new UnionFind(26);
    static (int x, int y, bool isEqual) Parse(in string equation) =>
       (equation[0] - 'a',  equation[3] - 'a', equation[1] == '=');
    foreach(var equation in equations){
      var (x, y, isEqual) = Parse(equation);
      if(!isEqual)
        continue;
      if(x == y && !isEqual)
        return false;
      uf.Union(x, y);
    }
    
    foreach(var equation in equations){
      var (x, y, isEqual) = Parse(equation);      
      if(!isEqual && uf.IsConnected(x, y))
        return false;
    }
    
    return true;
  }
  private ref struct UnionFind {
    private readonly int[] _parents;
    private readonly int[] _ranks;
    
    public UnionFind(int size){
      _parents = new int[size];
      _ranks = new int[size];
      for(var i = 0; i < size; i++){
        _parents[i] = i;
        _ranks[i] = 1;
      }
    }
    
    public int Find(int val){
      if(_parents[val] == val)
        return val;
      return _parents[val] = Find(_parents[val]);
    }
    
    public void Union(int a, int b){
      if(IsConnected(a, b, out var parentA, out var parentB))
        return;
      if(_ranks[parentA] > _ranks[parentB])
        _parents[parentB] = parentA;
      else if(_ranks[parentA] < _ranks[parentB])
        _parents[parentA] = parentB;
      else{
        _parents[parentB] = parentA;
        _ranks[parentA]++;
      }
      return;
    }
    
    public bool IsConnected(int a, int b)
      => IsConnected(a, b, out var _, out var _);
    
    private bool IsConnected(int a, int b, out int parentA, out int parentB){
      parentA = Find(a);
      parentB = Find(b);
      return parentA == parentB;
    }
  }
}