Lecture 21-22 - 1 CSC212 Data Structures 2  Consider the...

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1 CSC212: Data Structures
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2 Consider the search operation FindKey: find an element of a particular key value in a binary tree. In binary tree this operation is O(n) . In a binary tree of 10 6 nodes 10 6 steps required. In a Binary Search Tree (BST) this operation can be performed very efficiently: O(log 2 n) . A binary search tree of 10 6 nodes log 2 (10 6 ) 20 steps only are required.
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3 A Binary Search Tree (BST) is a binary tree such that for each node, say N, the following statements are true: 1. If L is any node in the left subtree of N, then L is less than N. 2. If R is any node in the right subtree of N, then R is greater than N.
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4 91 65 73 53 14 35 93 50 33 0 40 44 56 55 58 81 80 71 87 69
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5 Elements: the elements are nodes (BSTNode), each node contains the following data type: Type. Structure: hierarchical structure; each node can have two children: left or right child; there is a root node and a current node. If N is any node in the tree, nodes in the left subtree < N and nodes in the right subtree > N. Domain: the number of nodes in a BST is bounded; type/class name is BST
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6 Operations: 1. Method FindKey (int tkey, boolean found). requires: none. input: tkey. results: If bst contains a node whose key value is tkey, then that node is made the current node and found is set to true; otherwise found is set to false and either the tree is empty or the current node is the node to which the node with key = tkey would be attached as a child if it were added to the BST. output: found.
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7 2. Method Insert (int k, Type e, boolean inserted) requires: Full (bst) is false. input: key, e. results: if bst does not contain k then inserted is set to true and node with k and e is inserted and made the current element; otherwise inserted is set to false and current value does not change. output: inserted. 3. Method Remove_Key (int tkey, boolean removed) input: tkey results: Node with key value tkey is removed from the bst and removed set to true. If BST is not empty then root is made the current. output: removed
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8 4. Method Update(int key, Type e, boolean updated) requires: Empty(bst) is false. input: key, e. results: current node’s element is replaced with e. Output: updated. These operations have the same specification as ADT Binary Tree. 5. Method Traverse (Order ord) 6. Method DeleteSub ( ) 7. Method Retrieve (Type e) 8. Method Empty ( boolean empty ).
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9 9. Method Full (boolean full)
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10 public class BSTNode <T> { public int key; public T data; public BSTNode<T> left, right; /** Creates a new instance of BSTNode */ public BSTNode( int k, T val) { key = k; data = val; left = right = null ; } public BSTNode( int k, T val, BSTNode<T> l, BSTNode<T> r) { key = k; data = val; left = l; right = r; } }
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11 public class BST <T> { BSTNode<T> root, current; /** Creates a new instance of BST */ public BST() { root = current = null ; } public boolean empty() { return root == null ; } public boolean full() { return false ; } public T retrieve () { return current.data; }
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12 public class BST <T> { BSTNode<T> root, current; /** Creates a new instance of BST */ public BST() { root = current = null; } public boolean empty() { return root == null ; } public boolean full() { return false ; } public T retrieve () { return current.data; } R C null
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