Chapter 25 - A Binary Search Implementation
What is the worst-case performance of the getEntry method in a full binary search tree with linked nodes?
O(log n)
What is the worst-case performance of the remove method in a full binary search tree with linked nodes?
O(log n)
Write a pseudo code algorithm for searching a binary search tree.
If(binary search tree is empty) return false else if(object being searched for is equal to the root of the tree) return true else if(object being searched for is less than the root of the tree) recursively call the search algorithm on the left subtree else recursively call the search algorithm on the right subtree.
Given a binary search tree with n nodes and height h, what is the maximum number of comparisons that each operation requires for the method add?
O(h)
Given a binary search tree with n nodes and height h, what is the maximum number of comparisons that each operation requires for the method remove?
O(h)
Given a binary search tree with nnodes and height h, what is the maximum number of comparisons that each operation requires for the method getEntry?
O(h)
What is the worst-case performance of the addmethod in a full binary search tree with linked nodes?
O(log n)
What is the worst-case performance of the add method in a binary search tree with linked nodes?
O(n)
What is the worst-case performance of the getEntry method in a binary search tree with linked nodes?
O(n)
What is the worst-case performance of the remove method in a binary search tree with linked nodes?
O(n)
Why can't the two setTreemethods that are inherited from BinaryTree be used in the class BinrarySearchTree?
One could create a tree that does not have the properties of a binary search tree
When adding an entry to a binary search tree, when does the search ends?
When the item is found, At a leaf if the entry is not already in the tree
Binary search trees are not an efficient choice for searching if the data tends to remain stable.
False
Every addition to a binary search tree adds a new root.
False
For best performance, when you add entries to a binary search tree, you should add them in sorted order.
False
How does the class BinarySearchTree handle the two setTreemethods that are inherited from BinaryTree?
They are overridden with methods that throw an exception if called
Searching a binary search tree is like performing a binary search of an array.
True
The shape of a binary search tree affects the efficiency of the simple recursive search algorithm.
True
When adding an entry to a binary search tree, the search ends at a leaf if the entry is not already in the tree.
True
You can create different binary search trees from the same data.
True
You can implement the ADT dictionary using a binary search tree.
True
When you add entries to a binary search tree, if possible, you should not add them in sorted order. Explain.
adding them in sorted, or nearly sorted order produces a tree with a very large height yielding an O(n) performance on the add, remove and getEntry operations. if the data is entered in a ore random fashion, the height will be smaller, approaching the optimum performance of O(log n) for a full search tree.
In the interface SearchTreeInterface, the method getEntryreturns an object in the tree that matches the given entry according to the entry's _____ method.
compareTo
In a binary search tree, the getInorderIteratorinherited from the class BinaryTree sorts data
in ascending order
Every addition to a binary search tree adds a new
leaf
If a node x is the inorder predecessor of node y then node x must appear in y's _____ subtree.
left
The data in a node's _____ subtree are less than the data in a node's _____ subtree.
left, right
In the interface SearchTreeInterface, what does the method addreturn if the object being added doesn't exist?
null
In the interface SearchTreeInterface, what does the method getEntryreturn if the object being sought doesn't exist?
null
In the interface SearchTreeInterface, what does the method removereturn if the object being sought doesn't exist?
null
If a node x is the inorder successor of node y then node x must appear in y's _____ subtree.
right
In the interface SearchTreeInterface, what does the method addreturn if the object being added already exists in the tree?
the existing entry that matched the parameter
The inorder predecessor of a node N is
the largest entry in the N's left subtree
The inorder successor of a node N is
the smallest entry in the N's right subtree
The smallest entry in a node N's left subtree is
the subtree's leftmost node
The smallest entry in a node N's right subtree is
the subtree's leftmost node
The largest entry in a node N's left subtree is
the subtree's rightmost node
The largest entry in a node N's right subtree is
the subtree's rightmost node
How do you remove a node that is a leaf in a binary search tree?
you locate the parent node ans set the appropritate child reference in the parent node to null.
