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added about perfect binary tree in index.md (#26201)

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2019-03-06 03:01:41 +05:30
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guide/english/algorithms/binary-search-trees/index.md
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@ -350,8 +350,15 @@ Complete Binary Tree: A Binary Tree is complete Binary Tree if all levels are co
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### Augumenting a BST
Perfect Binary Tree A Binary tree is Perfect Binary Tree in which all internal nodes have two children and all leaves are at the same level.
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### Augumenting a BST
Sometimes we need to store some additional information with the traditional data structures to make our tasks easier.
For example, consider a scenario where you are supposed to find the ith smallest number in a set. You can use brute force here but we can reduce the complexity of the problem to O(lg n) by augumenting a red-black or any self-balancing tree (where n is the number of elements in the set). We can also compute rank of any element in O(lg n) time. Let us consider a case where we are augumenting a red-black tree to store the addional information needed. Besides the usual attributes, we can store number of internal nodes in the subtree rooted at x(size of the subtree rooted at x including the node itself).
Let x be any arbitary node of a tree.