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Why to prefer splay trees?

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1.
What is missing in this logic of finding a path in the tree for a given sum (i.e checking whether there will be a path from roots to leaf nodes with given sum)?

checkSum(struct bin-treenode *root , int sum) :
  if(root==null)
    return sum as 0
  else :
     leftover_sum=sum-root_node-->value
     //missing
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2.
What maximum difference in heights between the leafs of a AVL tree is possible?
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How can you save memory when storing color information in Red-Black tree?
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The null left pointer pointing to predecessor and null right pointer pointing to successor. how many types of threaded tree are possible with this convention?
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5.
Why to prefer red-black trees over AVL trees?
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