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When it would be optimal to prefer Red-black trees over AVL trees?

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1.
Consider the below formations of red-black tree. All the below formations are incorrect for it to be a redblack tree. Then what may be the correct order?

data-structure-questions-answers-red-black-tree-q3
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2.
Can a tree stored in an array using either one of inorder or post order or pre order traversals be again reformed?
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3.
What is one of the most common operations that is performed on trees?
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4.
Consider the below left-left rotation pseudo code where the node contains value pointers to left, right child nodes and a height value and Height() function returns height value stored at a particular node.
What is missing?

avltree leftrotation(avltreenode z):
   avltreenode w =x-left
   x-left=w-right
   w-right=x
   x-height=max(Height(x-left),Height(x-right))+1 
   w-height=max(missing)+1   
  return w
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5.
What is a Cartesian tree?
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