text: /**
  952. Largest Component Size by Common Factor
  
  
  Given a non-empty array of unique positive integers A, consider the following graph:
  
  There are A.length nodes, labelled A[0] to A[A.length - 1];
  There is an edge between A[i] and A[j] if and only if A[i] and A[j] share a common factor greater than 1.
  Return the size of the largest connected component in the graph.
  
   
  
  Example 1:
  
  Input: [4,6,15,35]
  Output: 4
  
  Example 2:
  
  Input: [20,50,9,63]
  Output: 2
  
  Example 3:
  
  Input: [2,3,6,7,4,12,21,39]
  Output: 8
  
  Note:
  
  1 <= A.length <= 20000
  1 <= A[i] <= 100000
  
   */
  
  /**
   * @param {number[]} A
   * @return {number}
   */
  var largestComponentSize = function(A) {
      // union join
      const seq = [];
      for ( let i = 0 ; i < A.length ; i++ ) {
          seq.push( {
              parent: i, // who share the root
              val: 1, // max size
          })
      }
      
      let max = 1;
      const cacheFactor = {}; // factors
      const HelperUnion = (factor, i) => {
          if ( factor in cacheFactor ) { 
              // find the factor's root ele
              // 2 3 6 -> 3 6
              let factorRoot = cacheFactor[factor]; 
              while ( factorRoot !== seq[factorRoot].parent ) {
                  factorRoot = seq[factorRoot].parent;
              }
  
              let eleRoot = i;
              while ( eleRoot !== seq[eleRoot].parent ) {
                  eleRoot = seq[eleRoot].parent;
              }
  
              if ( factorRoot !== eleRoot ) { 
                  // console.log("hit", factor, factorRoot, i, eleRoot)
                  seq[factorRoot].val += seq[eleRoot].val;
                  seq[eleRoot].parent = factorRoot;
                  max = Math.max( seq[factorRoot].val, max );
              }
          } else {
              cacheFactor[factor] = i;  // set the initial if not exist
          }
      }
      
      
      for ( let i = 0 ; i < A.length ; i++ ) {
          for ( let j = 2 ; j <= Math.ceil(Math.sqrt(A[i])) ; j++ ) { 
              
              if ( A[i] % j === 0 ) {
                  const pairFactor = [j];
                  if ( A[i]/j > 1 && A[i]/j !== j ) pairFactor.push(A[i]/j)
                  // console.log("FACTORS", pairFactor);
                  pairFactor.forEach( factor => {
                      HelperUnion(factor, i)
                  });
              }      
              HelperUnion(A[i], i)
          }
          // console.log(i, ...seq , cacheFactor )
      }
      
      return max;
  };
  
  /**
  [4,6,15,35]
  [20,50,9,63]
  [2,3,6,7,4,12,21,39]
  [2,3,6,7,4,12,21,39,100000]
  [1]
  [1,3,7]
  [1,3,7,9]
  [4,6,15,35]
  [20,50,9,63]
  [2,3,6,7,4,12,21,39]
  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   */