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What maximum difference in heights between the leafs of a AVL tree is possible?

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1.
What is the below pseudo code trying to do, where pt is a node pointer and root pointer.

redblack(Node root, Node pt) :
    if (root == NULL)
       return pt
 
    if (pt.data < root.data)
    {
        root.left  =   redblack(root.left, pt);
        root.left.parent = root
    }
    else if (pt.data > root.data)
    {
        root.right = redblackt(root.right, pt)
        root.right.parent = root
    }
   return root
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2.
Cartesian trees are most suitable for?
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3.
When representing any algebraic expression E which uses only binary operations in a 2-tree,
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4.
The degree of a node is equal to the number of its__________.
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5.
Trees are often used in implementing _________ and hence it is considered as prime application of trees.
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