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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. 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). 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. Let x be any arbitary node of a tree.