The best way to calculate the height in a binary search tree? (balancing an AVL-tree)

Question

I\'m looking for the best way to calculate a nodes balance in an AVL-tree. I thought I had it working, but after some heavy inserting/updating I can see that it\'s not worki

Answer 1

Give BinaryTree::Node a subtreeHeight data member, initialized to 0 in its constructor, and update automatically every time with:

template 
inline void BinaryTree::Node::setLeft (std::shared_ptr& node) {
    const std::size_t formerLeftSubtreeSize = left ? left->subtreeSize : 0;
    left = node;
    if (node) {
        node->parent = this->shared_from_this();
        subtreeSize++;
        node->depthFromRoot = depthFromRoot + 1;
        const std::size_t h = node->subtreeHeight;
        if (right)
            subtreeHeight = std::max (right->subtreeHeight, h) + 1;
        else
            subtreeHeight = h + 1;
    }
    else {
        subtreeSize -= formerLeftSubtreeSize;
        subtreeHeight = right ? right->subtreeHeight + 1 : 0;
    }
}

template 
inline void BinaryTree::Node::setRight (std::shared_ptr& node) {
    const std::size_t formerRightSubtreeSize = right ? right->subtreeSize : 0;
    right = node;
    if (node) {
        node->parent = this->shared_from_this();
        subtreeSize++;
        node->depthFromRoot = depthFromRoot + 1;
        const std::size_t h = node->subtreeHeight;
        if (left)
            subtreeHeight = std::max (left->subtreeHeight, h) + 1;
        else
            subtreeHeight = h + 1;
    }
    else {
        subtreeSize -= formerRightSubtreeSize;
        subtreeHeight = left ? left->subtreeHeight + 1 : 0;
    }
}

Note that data members subtreeSize and depthFromRoot are also updated. These functions are called when inserting a node (all tested), e.g.

template 
inline std::shared_ptr::Node>
BinaryTree::Node::insert (BinaryTree& tree, const T& t, std::shared_ptr& node) {
    if (!node) {
        std::shared_ptr newNode = std::make_shared(tree, t);
        node = newNode;
        return newNode;
    }
    if (getComparator()(t, node->value)) {
        std::shared_ptr newLeft = insert(tree, t, node->left);
        node->setLeft(newLeft);
    }
    else {
        std::shared_ptr newRight = insert(tree, t, node->right);
        node->setRight(newRight);
    }
    return node;
}

If removing a node, use a different version of removeLeft and removeRight by replacing subtreeSize++; with subtreeSize--;. Algorithms for rotateLeft and rotateRight can be adapted without much problem either. The following was tested and passed:

template 
void BinaryTree::rotateLeft (std::shared_ptr& node) {  // The root of the rotation is 'node', and its right child is the pivot of the rotation.  The pivot will rotate counter-clockwise and become the new parent of 'node'.
    std::shared_ptr pivot = node->right;
    pivot->subtreeSize = node->subtreeSize;
    pivot->depthFromRoot--;
    node->subtreeSize--;  // Since 'pivot' will no longer be in the subtree rooted at 'node'.
    const std::size_t a = pivot->left ? pivot->left->subtreeHeight + 1 : 0;  // Need to establish node->heightOfSubtree before pivot->heightOfSubtree is established, since pivot->heightOfSubtree depends on it.
    node->subtreeHeight = node->left ? std::max(a, node->left->subtreeHeight + 1) : std::max(a,1);
    if (pivot->right) {
        node->subtreeSize -= pivot->right->subtreeSize;  // The subtree rooted at 'node' loses the subtree rooted at pivot->right.
        pivot->subtreeHeight = std::max (pivot->right->subtreeHeight, node->subtreeHeight) + 1;
    }
    else
        pivot->subtreeHeight = node->subtreeHeight + 1;
    node->depthFromRoot++;
    decreaseDepthFromRoot(pivot->right);  // Recursive call for the entire subtree rooted at pivot->right.
    increaseDepthFromRoot(node->left);  // Recursive call for the entire subtree rooted at node->left.
    pivot->parent = node->parent;
    if (pivot->parent) {  // pivot's new parent will be its former grandparent, which is not nullptr, so the grandparent must be updated with a new left or right child (depending on whether 'node' was its left or right child).
        if (pivot->parent->left == node)
            pivot->parent->left = pivot;
        else
            pivot->parent->right = pivot;
    }
    node->setRightSimple(pivot->left);  // Since pivot->left->value is less than pivot->value but greater than node->value.  We use the NoSizeAdjustment version because the 'subtreeSize' values of 'node' and 'pivot' are correct already.
    pivot->setLeftSimple(node);
    if (node == root) {
        root = pivot;
        root->parent = nullptr; 
    }
}

where

inline void decreaseDepthFromRoot (std::shared_ptr& node) {adjustDepthFromRoot(node, -1);}
inline void increaseDepthFromRoot (std::shared_ptr& node) {adjustDepthFromRoot(node, 1);}

template 
inline void BinaryTree::adjustDepthFromRoot (std::shared_ptr& node, int adjustment) {
    if (!node)
        return;
    node->depthFromRoot += adjustment;
    adjustDepthFromRoot (node->left, adjustment);
    adjustDepthFromRoot (node->right, adjustment);
}

Here is the entire code: http://ideone.com/d6arrv