Instructions
- Read through all the provided source code to make sure that you understand the context. A class named BinarySearchTree with an add method plus various utility methods is provided for you. You must not change any provided method with a body that is already complete. Note that linked nodes are used to implement the BinarySearchTree class. Note also that the data type allowed in the BinarySearchTree is constrained to be a class that implements the Comparable interface and thus has a natural total order defined.
- The min method of the BinarySearchTree class currently has no body. You must provide a correct body for the min method.
- A sample main method is provided to illustrate building a simple binary search tree and then using the min method to search for particular values.
Problem Description: Finding the Minimum Value in a Binary Search Tree
Complete the body of the min method so that it returns the minimum value in the binary search tree.
The following table lists an example call to min and the expected return value when called in the context of the binary search tree pictured below.
Method CallExpected Return Value
min() 1
/**
* Complete the min method in the nested BinarySearchTree class below.
*
*/
public class BSTMin {
/** Provides an example. */
public static void main(String[] args) {
BinarySearchTree iBst = new BinarySearchTree<>();
iBst.add(10);
iBst.add(12);
iBst.add(8);
iBst.add(2);
iBst.add(6);
iBst.add(4);
Integer imin = iBst.min();
// The following statement should print 2.
System.out.println(imin);
BinarySearchTree sBst = new BinarySearchTree<>();
sBst.add(“W”);
sBst.add(“A”);
sBst.add(“R”);
sBst.add(“E”);
sBst.add(“A”);
sBst.add(“G”);
sBst.add(“L”);
sBst.add(“E”);
String smin = sBst.min();
// The following statement should print A.
System.out.println(smin);
}
/** Defines a binary search tree. */
static class BinarySearchTree> {
// the root of this binary search tree
private Node root;
// the number of nodes in this binary search tree
private int size;
/** Defines the node structure for this binary search tree. */
private class Node {
T element;
Node left;
Node right;
/** Constructs a node containing the given element. */
public Node(T elem) {
element = elem;
left = null;
right = null;
}
}
/* >>>>>>>>>>>>>>>>>> YOUR WORK STARTS HERE <<<<<<<<<<<<<<<< */
///////////////////////////////////////////////////////////////////////////////
// I M P L E M E N T T H E M I N M E T H O D B E L O W //
///////////////////////////////////////////////////////////////////////////////
/**
* Returns the minimum value in the binary search tree.
*/
public T min() {
}
/* >>>>>>>>>>>>>>>>>> YOUR WORK ENDS HERE <<<<<<<<<<<<<<<< */
////////////////////////////////////////////////////////////////////
// D O N O T M O D I F Y B E L O W T H I S P O I N T //
////////////////////////////////////////////////////////////////////
////////////////////
// M E T R I C S //
////////////////////
/**
* Returns the number of elements in this bst.
*/
public int size() {
return size;
}
/**
* Returns true if this bst is empty, false otherwise.
*/
public boolean isEmpty() {
return size == 0;
}
/**
* Returns the height of this bst.
*/
public int height() {
return height(root);
}
/**
* Returns the height of node n in this bst.
*/
private int height(Node n) {
if (n == null) {
return 0;
}
int leftHeight = height(n.left);
int rightHeight = height(n.right);
return 1 + Math.max(leftHeight, rightHeight);
}
////////////////////////////////////
// A D D I N G E L E M E N T S //
////////////////////////////////////
/**
* Ensures this bst contains the specified element. Uses an iterative implementation.
*/
public void add(T element) {
// special case if empty
if (root == null) {
root = new Node(element);
size++;
return;
}
// find where this element should be in the tree
Node n = root;
Node parent = null;
int cmp = 0;
while (n != null) {
parent = n;
cmp = element.compareTo(parent.element);
if (cmp == 0) {
// don’t add a duplicate
return;
} else if (cmp < 0) {
n = n.left;
} else {
n = n.right;
}
}
// add element to the appropriate empty subtree of parent
if (cmp < 0) {
parent.left = new Node(element);
} else {
parent.right = new Node(element);
}
size++;
}
}
}
