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Inserting a given item with a key k is similar in spirit to searching. Starting from the root, go down the tree, comparing keys as before, until a leaf node is reached. Now insert the item in a new node to the left or right of the leaf node as appropriate. The time taken is again O(h). Deleting an item from a binary search tree is slightly more complicated. First, using the search procedure, we locate the item in the tree. Let v be the node where the item resides. If v is a leaf, we just delete it, that is the appropriate child pointer of its parent is set to the special value NIL.

A full binary tree is a binary tree in which every internal node has exactly two children. A complete binary tree is a full binary tree with a block of rightmost leaves missing. Binary Search Trees. Data structures can be studied from at least two different perspectives. One is a low-level perspective that deals with how the data structure is implemented. In this section, we adopt a high-level approach where we are less concerned with implementation issues and more interested in the operations the structure can support.

They are also called languages and commonly denoted by the letter L when looked upon as subsets of ͚*. The function f defining L is then notated as L. A string x ʦ L iff L(x) ϭ 1. In this section, problem means decision problem, unless explicitly stated otherwise. An algorithm M is said to decide L if M when given input x returns 1 [in symbols, M(x) ϭ 1] if x ʦ L and 0 [in symbols, M(x) ϭ 0) otherwise. The time complexity of a problem is said to be T(n) if there is an algorithm to decide it that takes no more than T(n) steps on any input of length n bits.