Trees

BST Insert

Insert values into a binary search tree by comparing at each node.

Algorithm

The canonical tree is 4(2(1,3),6(5,7)), so this Ruby DSA implementation can be compared directly with the rest of the DSA track.

Basic Implementation

basic.rb 
class Node
  attr_accessor :value, :left, :right
  def initialize(value, left = nil, right = nil)
    @value = value
    @left = left
    @right = right
  end
end
def render(node)
  return "_" if node.nil?
  return node.value.to_s if node.left.nil? && node.right.nil?
  "#{node.value}(#{render(node.left)},#{render(node.right)})"
end
def sample_tree
  Node.new(4, Node.new(2, Node.new(1), Node.new(3)), Node.new(6, Node.new(5), Node.new(7)))
end
def insert(root, value); return Node.new(value) if root.nil?; value < root.value ? root.left = insert(root.left, value) : root.right = insert(root.right, value); root; end
root = nil
[4, 2, 6, 1, 3, 5, 7].each { |value| root = insert(root, value) }
puts render(root)

Complexity

  • Time: O(h) per insert
  • Space: O(n)

Implementation notes

  • Render tree structure explicitly instead of printing node objects.
  • The replay highlights the node, traversal state, queue, path, or search cursor that changes at each step.
binary search tree Values smaller than a node go left; larger values go right.