# Binary Search Tree – Programming Praxis solution

Earlier this year I was influenced by two things that got me to re-think what I work on in my free time. The first was this podcast from Software Engineering Radio with “Uncle Bob” Bob Martin on software craftsmanship. The second was a blog on the value of fundamentals in software development. As a result I am now focusing on incorporating puzzles as well as learning new languages or frameworks . This entry is a solution to the Binary Search Tree problem from Programming Praxis. While this post does not aim to be a thorough explanation of how a binary search tree works, I will present my code and briefly explain it.

The problem asked you to implement search, insert delete and enlist ( I took enlist to mean generate a list of values from the tree in order). Since I use Java on the day job, and I want to get better in other languages, I implemented my solution in Ruby. Here are the public methods that fufill the requirements of the problem.

require 'node' module Trees class BinarySearchTree attr_reader :root def initialize(root = nil) @root = root end def search(value) search_for_node(@root,Node.new(value)) end def insert(value) @root = insert_value(@root,value) end def delete(value) @root = delete_node(@root,Node.new(value)) end def in_order_list vals = [] inorder(vals,@root) vals end

These methods just delegate to private methods that actually do the work. Let’s consider search and insert first.

private def search_for_node(tnode,node) if tnode.nil? return nil end if tnode == node tnode = node elsif node < tnode tnode = search_for_node(tnode.left,node) else tnode = search_for_node(tnode.right,node) end tnode end def insert_value(tnode,value) if tnode.nil? tnode = Node.new(value) elsif value < tnode.value tnode.left = insert_value(tnode.left,value) elsif value > tnode.value tnode.right = insert_value(tnode.right,value) elsif value == tnode.value tnode.value = value end tnode end

Search and insert work almost identically. With search you keep traversing the tree until you find your value, or return nil when you have exhausted your options. With insert you actually want to keep going until you find a nil node, then you know thats where to insert. One thing I did in my insert method was that if you supply a value that already exists in the tree I simply update the node with that value. I’m sure there are better ways of handling that situation, but I felt simply updating with an existing value causes no harm. Now, deleting is not quite so straight forward, although still not that difficult.

def delete_node(tnode,node) if tnode == node tnode = remove(tnode) elsif node < tnode tnode.left = delete_node(tnode.left,node) else tnode.right = delete_node(tnode.right,node) end tnode end def remove(node) if node.left.nil? && node.right.nil? node = nil elsif !node.left.nil? && node.right.nil? node = node.left elsif node.left.nil? && !node.right.nil? node = node.right else node = replace_parent(node) end node end

When deleting a node from the tree there are 4 cases to consider:

- The node has no children
- The node has a left child only
- The node has a right child only
- The node has both a right and left child

The first three are pretty straight forward to handle. With no
children, obviously the node to be deleted is just set to null. If the
node only has one child you merely set the reference of the node to be
deleted to that of it's child. The situation of 0-1 child nodes is
handled by the first three branches of the if-else statements in the **remove** method. The following methods are used to handle the case of a node with 2 children.

def replace_parent(node) node.value = successor_value(node.right) node.right = update(node.right) node end def successor_value(node) unless node.left.nil? successor_value(node.left) end node.value end def update(node) unless node.left.nil? node.left = update(node) end node.right end

Deleting a node with 2 children is handled in two steps. First you
update the value of the node to be deleted with the value of the node's
in-order successor or predecessor. Then the duplicate node needs to be
deleted and handle the case if it has a child node. It is worth noting
due to the properties of binary trees, an in-order successor or
predecessor will only ever have a right or left child.

For me it seemed more natural to use the in-order successor. The **replace_parent** method first updates the value of the node to be deleted with the value returned from the **successor_value**
method. Then duplicate node is then removed and the right child of the
newly updated node is set to the right child of the in-order successor
or null. This last part is handled by the **update** method. Here is the code to get a list of the values from the tree in ascending order

def inorder(list, node) unless node.nil? inorder(list, node.left) list.push(node.value) inorder(list, node.right) end end

Finally here is the code for the **Node** class:

module Trees class Node include Comparable attr_accessor :left,:right,:value def initialize(value = nill, left = nil, right = nil) @value = value @left = left @right = right end def <=>(otherNode) @value <=> otherNode.value end def to_s "[value: #{@value} left=> #{@left} right=> #{@right}]" end end end

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