If I understand your question correctly, you want to know how to maintain the balance-factor of a given node. The best way to keep the track is when doing an "insert" in the tree. This is because you know whether your new node is going to the left or the right side of the "current" node. When it goes to the left, you decrement the balance and when it goes to the right, you increment the balance. The idea is to have the tree already balanced before you exit the "insert" method.
Another approach I have seen is NOT doing the balancing during the "insert". You simply insert like you would in BST. After the insert, you begin your balancing act where you get the left subtree and right subtree height at each node and start shuffling pointers. This is not a good approach since you incur O(logn) for every node in finding the height and since you would do that for every node, it results into n*O(logn).
I am posting the "insert" method that I once wrote that keeps the tree balanced at every insert and does NOT compute the height separately at any point during the insert. See if it helps:
Node*
AVL::insert(Node* node, int key, int value)
{
if(node == NULL)
node = new Node(key, value);
else if (key <= node->key)
{
node->balance--;
node->left = insert(node->left, key, value);
}
else if (key > node->key)
{
node->balance++;
node->right = insert(node->right, key, value);
}
// Right Tree Heavy
if (node->balance == 2)
{
// Left tree unbalanced
if (node->right && node->right->balance == 1)
{
// LL
node = singleLeftRotation(node);
node->balance = 0;
node->left->balance = 0;
}
if (node->right && node->right->balance == -1)
{
// LR
int nodeRLBalance = node->right->left->balance;
node = doubleLeftRotation(node);
node->balance = 0;
node->left->balance = nodeRLBalance == 1 ? -1 : 0;
node->right->balance = nodeRLBalance == -1 ? 1 : 0;
}
}
// Left Tree Heavy
if (node->balance == -2)
{
// Right tree unbalanced
if (node->left && node->left->balance == -1)
{
// RR
node = singleRightRotation(node);
node->balance = 0;
node->right->balance = 0;
}
if (node->left && node->left->balance == 1)
{
// RL
int nodeLRBalance = node->left->right->balance;
node = doubleRightRotation(node);
node->balance = 0;
node->left->balance = nodeLRBalance == 1 ? -1 : 0;
node->right->balance = nodeLRBalance == -1 ? 1 : 0;
}
}
return node;
}
