/// <summary>
/// Checks various properties to determine if the tree is a valid AA Tree.
/// Throws exceptions if properties are violated.
/// Useful for debugging.
/// </summary>
/// <remarks>
/// The properties that are checked are:
/// <list type="number">
/// <item>The level of every leaf node is one.</item>
/// <item>The level of every left child is exactly one less than that of its parent.</item>
/// <item>The level of every right child is equal to or one less than that of its parent.</item>
/// <item>The level of every right grandchild is strictly less than that of its grandparent.</item>
/// <item>Every node of level greater than one has two children.</item>
/// </list>
/// More information: https://en.wikipedia.org/wiki/AA_tree .
/// </remarks>
/// <param name="node">The node to check from.</param>
/// <returns>true if node passes all checks, false otherwise.</returns>
private static bool Validate <T>(AaTreeNode <T>?node)
{
if (node is null)
{
return(true);
}
// Check level == 1 if node if a leaf node.
var leafNodeCheck = CheckLeafNode(node);
// Check level of left child is exactly one less than parent.
var leftCheck = CheckLeftSubtree(node);
// Check level of right child is equal or one less than parent.
var rightCheck = CheckRightSubtree(node);
// Check right grandchild level is less than node.
var grandchildCheck = CheckRightGrandChild(node);
// Check if node has two children if not leaf.
var nonLeafChildrenCheck = CheckNonLeafChildren(node);
var thisNodeResult = leafNodeCheck && leftCheck && rightCheck;
thisNodeResult = thisNodeResult && grandchildCheck && nonLeafChildrenCheck;
return(thisNodeResult && Validate(node.Left) && Validate(node.Right));
}
/// <summary>
/// Checks if right node's level is either equal to or one less than node's level.
/// </summary>
/// <param name="node">The node to check.</param>
/// <returns>true if node passes check, false otherwise.</returns>
private static bool CheckRightSubtree <T>(AaTreeNode <T> node)
{
var condition = node.Right is not null &&
node.Level - node.Right.Level != 1 &&
node.Level != node.Right.Level;
return(!condition);
}
/// <summary>
/// Checks if node is not a leaf, and if so if it has two children.
/// </summary>
/// <param name="node">The node to check.</param>
/// <returns>true if node passes check, false otherwise.</returns>
private static bool CheckNonLeafChildren <T>(AaTreeNode <T> node)
{
var condition = node.Level > 1 && (node.Left is null || node.Right is null);
return(!condition);
}
/// <summary>
/// Checks if right grandchild's (right node's right node) level is less than node.
/// </summary>
/// <param name="node">The node to check.</param>
/// <returns>true if node passes check, false otherwise.</returns>
private static bool CheckRightGrandChild <T>(AaTreeNode <T> node)
{
var condition = node.Right?.Right is not null && node.Right.Level < node.Right.Right.Level;
return(!condition);
}
/// <summary>
/// Checks if node is a leaf, and if so if its level is 1.
/// </summary>
/// <param name="node">The node to check.</param>
/// <returns>true if node passes check, false otherwise.</returns>
private static bool CheckLeafNode <T>(AaTreeNode <T> node)
{
var condition = node.Left is null && node.Right is null && node.Level != 1;
return(!condition);
}
