Quick-Find & Quick-Union with Path Compression

union_find.rb

class UnionFind

  attr_accessor :nodes, :sizes

  def initialize(num)
    self.nodes = []
    self.sizes = []

    num.times do |n|
      self.nodes[n] = n
      self.sizes[n] = 1
    end
  end

  def root(i)
    # Loop up the chain until reaching root
    while nodes[i] != i do
      # path compression for future lookups
      nodes[i] = nodes[nodes[i]]
      i = nodes[i]
    end
    i
  end

  def union(i, j)
    rooti = root i
    rootj = root j

    # already connected
    return if rooti == rootj

    # root smaller to root of larger
    if sizes[i] < sizes[j]
      nodes[rooti] = rootj
      sizes[rootj] += sizes[rooti]
    else
      nodes[rootj] = rooti
      sizes[rooti] += sizes[rootj]
    end
  end

  def connected?(i, j)
    root(i) == root(j)
  end

end


u = UnionFind.new(10)

p u.connected?(1, 4)

u.union(1,2)
u.union(2,3)
u.union(3,4)
u.union(5,2)
u.union(6,2)
u.union(6,7)
u.union(6,8)

p u.nodes

p u.connected?(1,4)
p u.connected?(2,4)
p u.connected?(1,8)

p u.nodes
p u.sizes