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Binary Search Trees. |
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Reading
Main: p479-494 |
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A Binary Tree such that: |
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Every node entry has a unique key. |
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All the keys in the left subtree of a node are less
than the key of the node. |
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All the keys in the right subtree of a node are greater
than the key of the node. |
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Inorder traversal of a Binary Search Tree always
gives the sorted order of the keys. |
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Inorder traversal of a Binary Search Tree always
gives the sorted order of the keys. |
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Inorder traversal of a Binary Search Tree always
gives the sorted order of the keys. |
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Inorder traversal of a Binary Search Tree always
gives the sorted order of the keys. |
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if target key is less than current node’s key,
search the left sub-tree. |
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else, if target key is greater than current
node’s key, search the right sub-tree. |
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returns: |
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if found, or if target key is equal to current
node’s key, a pointer to node containing target key. |
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otherwise, NULL pointer. |
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private TreeNode search( TreeNode ptr, TreeData
key) { |
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if ( ptr==null ) return null; |
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else |
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if ( ptr.data.equals(key) ) return ptr; |
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else |
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if ( key.compareTo(ptr.data) < 0 )
return search( ptr.left, key); |
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else return search( ptr.right, key); |
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} |
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public boolean includes( TreeData key ) { |
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return (search( root, key ) != null ); |
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} |
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public TreeData retrieve( TreeData key ); { |
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TreeNode ptr; |
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ptr = search( root, key ); |
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if (ptr == null) return null; |
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else return ptr.data; |
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} |
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Create new node for the item. |
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Find a parent node. |
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Attach new node as a leaf. |
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parameters: |
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pointer to current node (initially: root node). |
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item to be inserted. |
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If current node is NULL |
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Create a new node and return it. |
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Else if item’s key is less (greater) than
current node’s key: |
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otherwise, let the left (right) child node be
the current node, setting the parent left (right) link equal that node, and
repeat recursively. |
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parameter: item to be inserted |
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steps: |
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allocate memory for the new node |
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check if memory allocation is successful |
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if so, put item into the new node |
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set left and right branches to NULL |
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returns: pointer to (i.e. address of) new node |
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To sort a sequence of items: |
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Insert items into a Binary Search Tree. |
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Then Inorder Traverse the tree. |
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Average Case:
O(n log(n)) |
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Notes