/// <summary>
/// Checks if a binary tree is balanced.
///
/// The definition of balance is with CLRS [1]. Under this definition, a balanced tree is:
///
/// 1. Left and right subtree are balanced
/// 2. The left and right trees' height difference is no larger than 1
///
/// The definition of tree height is with CLRS and Wikipedia [2]. With this definition, the following holds:
///
/// 1. A single node tree has height 0
/// 2. A null node has height -1
///
/// [1]: http://books.google.com/books?id=NLngYyWFl_YC&lpg=PA296&vq=avl&pg=PA296#v=onepage&q&f=false
/// [2]: http://en.wikipedia.org/wiki/Tree_(data_structure)#Terminology
/// </summary>
/// <param name="tree"></param>
/// <param name="height"></param>
/// <returns></returns>
static bool IsBalanced(Node tree, out int height)
{
if (tree == null)
{
height = -1;
return true;
}
if (!IsBalanced(tree.Left, out height))
{
return false;
}
int heightLeft = height;
if (!IsBalanced(tree.Right, out height))
{
return false;
}
if (Math.Abs(height - heightLeft) > 1)
{
return false;
}
height = Math.Max(height, heightLeft) + 1;
return true;
}
static void Main(string[] args)
{
int height;
Node tree = null;
Debug.Assert(IsBalanced(tree, out height) == true && height == -1);
tree = new Node();
Debug.Assert(IsBalanced(tree, out height) == true && height == 0);
tree = new Node(
left: new Node(),
right: null);
Debug.Assert(IsBalanced(tree, out height) == true && height == 1);
tree = new Node(
left: new Node(
left: new Node()),
right: new Node(
right: new Node()));
Debug.Assert(IsBalanced(tree, out height) == true && height == 2);
tree = new Node(
left: new Node(
left: new Node(
left: new Node())),
right: new Node(
right: new Node(
right: new Node())));
Debug.Assert(IsBalanced(tree, out height) == false); // don't need to check height
Console.WriteLine("passed.");
Console.Read();
}
public Node(Node left = null, Node right = null)
{
Left = left; Right = right;
}