gregghz - 5 months ago 26

C++ Question

I'm having the hardest time trying to figure out how to balance an AVL tree for my class. I've got it inserting with this:

`Node* Tree::insert(int d)`

{

cout << "base insert\t" << d << endl;

if (head == NULL)

return (head = new Node(d));

else

return insert(head, d);

}

Node* Tree::insert(Node*& current, int d)

{

cout << "insert\t" << d << endl;

if (current == NULL)

current = new Node(d);

else if (d < current->data) {

insert(current->lchild, d);

if (height(current->lchild) - height(current->rchild)) {

if (d < current->lchild->getData())

rotateLeftOnce(current);

else

rotateLeftTwice(current);

}

}

else if (d > current->getData()) {

insert(current->rchild, d);

if (height(current->rchild) - height(current->lchild)) {

if (d > current->rchild->getData())

rotateRightOnce(current);

else

rotateRightTwice(current);

}

}

return current;

}

My plan was to have the calls to balance() check to see if the tree needs balancing and then balance as needed. The trouble is, I can't even figure out how to traverse the tree to find the correct unbalanced node. I know how to traverse the tree recursively, but I can't seem to translate that algorithm into finding the lowest unbalanced node. I'm also having trouble writing an iterative algorithm. Any help would be appreciated. :)

Answer

You can measure the `height`

of a branch at a given point to calculate the unbalance

*(remember a difference in height (levels) >= 2 means your tree is not balanced)*

```
int Tree::Height(TreeNode *node){
int left, right;
if(node==NULL)
return 0;
left = Height(node->left);
right = Height(node->right);
if(left > right)
return left+1;
else
return right+1;
}
```

Depending on the unevenness then you can **rotate** as necessary

```
void Tree::rotateLeftOnce(TreeNode*& node){
TreeNode *otherNode;
otherNode = node->left;
node->left = otherNode->right;
otherNode->right = node;
node = otherNode;
}
void Tree::rotateLeftTwice(TreeNode*& node){
rotateRightOnce(node->left);
rotateLeftOnce(node);
}
void Tree::rotateRightOnce(TreeNode*& node){
TreeNode *otherNode;
otherNode = node->right;
node->right = otherNode->left;
otherNode->left = node;
node = otherNode;
}
void Tree::rotateRightTwice(TreeNode*& node){
rotateLeftOnce(node->right);
rotateRightOnce(node);
}
```

Now that we know how to rotate, lets say you want to **insert** a value in the tree... First we check whether the tree **is empty** or not

```
TreeNode* Tree::insert(int d){
if(isEmpty()){
return (root = new TreeNode(d)); //Is empty when root = null
}
else
return insert(root, d); //step-into the tree and place "d"
}
```

When the tree is not empty we use **recursion** to traverse the tree and get to where is needed

```
TreeNode* Tree::insert(TreeNode*& node, int d_IN){
if(node == NULL) // (1) If we are at the end of the tree place the value
node = new TreeNode(d_IN);
else if(d_IN < node->d_stored){ //(2) otherwise go left if smaller
insert(node->left, d_IN);
if(Height(node->left) - Height(node->right) == 2){
if(d_IN < node->left->d_stored)
rotateLeftOnce(node);
else
rotateLeftTwice(node);
}
}
else if(d_IN > node->d_stored){ // (3) otherwise go right if bigger
insert(node->right, d_IN);
if(Height(node->right) - Height(node->left) == 2){
if(d_IN > node->right->d_stored)
rotateRightOnce(node);
else
rotateRightTwice(node);
}
}
return node;
}
```

You should always check for balance *(and do rotations if necessary)* when modifying the tree, no point waiting until the end when the tree is a mess to balance it. That just complicates things...

**UPDATE**

There is a mistake in your implementation, in the code below you are not checking correctly whether the tree is unbalanced. You need to check whether the height is equals to 2 (therefore unbalance). As a result the code bellow...

```
if (height(current->lchild) - height(current->rchild)) { ...
if (height(current->rchild) - height(current->lchild)) {...
```

Should become...

```
if (height(current->lchild) - height(current->rchild) == 2) { ...
if (height(current->rchild) - height(current->lchild) == 2) {...
```

**Some Resources**