@Override
protected void balance(AVLNode<T> node) {
/* Rotation cases (N = node, C = child)
* Case 1:
* N
* /
* C
* /
* O
*
* Case 2:
* N
* /
* C
* \
* O
*
* Case 3:
* N
* \
* C
* \
* O
* Case 4:
* N
* \
* C
* /
* O
*/
if (node == null) return;
int bf = node.getBalanceFactor();
if (bf == 2) {
AVLNode<T> child = node.getLeftChild();
if (child.getBalanceFactor() == -1) // Case 2
rotateLeft(child);
rotateRight(node); // Case 1
} else if (bf == -2) {
AVLNode<T> child = node.getRightChild();
if (child.getBalanceFactor() == 1) // Case 4
rotateRight(child);
rotateLeft(node); // Case 3
} else balance(node.getParent()); // Recurrsively balance parent
}
/** {@inheritDoc} */
@Override
protected boolean validateNode(Node<T> node) {
boolean bst = super.validateNode(node);
if (!bst) return false;
AVLNode<T> avlNode = (AVLNode<T>) node;
int balanceFactor = avlNode.getBalanceFactor();
if (balanceFactor > 1 || balanceFactor < -1) {
return false;
}
if (avlNode.isLeaf()) {
if (avlNode.height != 1) return false;
} else {
AVLNode<T> avlNodeLesser = (AVLNode<T>) avlNode.lesser;
int lesserHeight = 1;
if (avlNodeLesser != null) lesserHeight = avlNodeLesser.height;
AVLNode<T> avlNodeGreater = (AVLNode<T>) avlNode.greater;
int greaterHeight = 1;
if (avlNodeGreater != null) greaterHeight = avlNodeGreater.height;
if (avlNode.height == (lesserHeight + 1) || avlNode.height == (greaterHeight + 1))
return true;
return false;
}
return true;
}
/**
* Balance the tree according to the AVL post-insert algorithm.
*
* @param node Root of tree to balance.
*/
private void balanceAfterInsert(AVLNode<T> node) {
int balanceFactor = node.getBalanceFactor();
if (balanceFactor > 1 || balanceFactor < -1) {
AVLNode<T> child = null;
Balance balance = null;
if (balanceFactor < 0) {
child = (AVLNode<T>) node.lesser;
balanceFactor = child.getBalanceFactor();
if (balanceFactor < 0) balance = Balance.LEFT_LEFT;
else balance = Balance.LEFT_RIGHT;
} else {
child = (AVLNode<T>) node.greater;
balanceFactor = child.getBalanceFactor();
if (balanceFactor < 0) balance = Balance.RIGHT_LEFT;
else balance = Balance.RIGHT_RIGHT;
}
if (balance == Balance.LEFT_RIGHT) {
// Left-Right (Left rotation, right rotation)
rotateLeft(child);
rotateRight(node);
} else if (balance == Balance.RIGHT_LEFT) {
// Right-Left (Right rotation, left rotation)
rotateRight(child);
rotateLeft(node);
} else if (balance == Balance.LEFT_LEFT) {
// Left-Left (Right rotation)
rotateRight(node);
} else {
// Right-Right (Left rotation)
rotateLeft(node);
}
child.updateHeight();
node.updateHeight();
}
}
/**
* Balance the tree according to the AVL post-delete algorithm.
*
* @param node Root of tree to balance.
*/
private void balanceAfterDelete(AVLNode<T> node) {
int balanceFactor = node.getBalanceFactor();
if (balanceFactor == -2 || balanceFactor == 2) {
if (balanceFactor == -2) {
AVLNode<T> ll = (AVLNode<T>) node.lesser.lesser;
int lesser = (ll != null) ? ll.height : 0;
AVLNode<T> lr = (AVLNode<T>) node.lesser.greater;
int greater = (lr != null) ? lr.height : 0;
if (lesser >= greater) {
rotateRight(node);
node.updateHeight();
if (node.parent != null) ((AVLNode<T>) node.parent).updateHeight();
} else {
rotateLeft(node.lesser);
rotateRight(node);
AVLNode<T> p = (AVLNode<T>) node.parent;
if (p.lesser != null) ((AVLNode<T>) p.lesser).updateHeight();
if (p.greater != null) ((AVLNode<T>) p.greater).updateHeight();
p.updateHeight();
}
} else if (balanceFactor == 2) {
AVLNode<T> rr = (AVLNode<T>) node.greater.greater;
int greater = (rr != null) ? rr.height : 0;
AVLNode<T> rl = (AVLNode<T>) node.greater.lesser;
int lesser = (rl != null) ? rl.height : 0;
if (greater >= lesser) {
rotateLeft(node);
node.updateHeight();
if (node.parent != null) ((AVLNode<T>) node.parent).updateHeight();
} else {
rotateRight(node.greater);
rotateLeft(node);
AVLNode<T> p = (AVLNode<T>) node.parent;
if (p.lesser != null) ((AVLNode<T>) p.lesser).updateHeight();
if (p.greater != null) ((AVLNode<T>) p.greater).updateHeight();
p.updateHeight();
}
}
}
}