Question

Please code in Java and ignore question 2, thank you!

1. Write a Java method that takes as its only input parameter a single integer, n, and returns the number of unique binary search trees that can be constructed with integers 1 through n. (Hint: You'll probably want to do this recursively.) (Note: This is not asking for the number of maximally tall BSTs. The BSTs can be any height.) 2. Work through the deletion exercises in 2-4-deletion-supplementary.pdf (attached above). Note: The PDF includes solutions 3. If we start off with an empty tree (null), what is the minimum number of insert and delete operations necessary to create the following 2-4 tree? (16) (12) (20) Sorry this diagram is not as fancy as the one below.)

Answer 1

CODE

================

import java.util.ArrayList;

public class Main {

// function for constructing trees

static ArrayList<Node> constructTrees(int start, int end)

{

ArrayList<Node> list=new ArrayList<>();

/* if start > end then subtree will be empty so returning NULL

in the list */

if (start > end)

{

list.add(null);

return list;

}

/* iterating through all values from start to end for constructing\

left and right subtree recursively */

for (int i = start; i <= end; i++)

{

/* constructing left subtree */

ArrayList<Node> leftSubtree = constructTrees(start, i - 1);

/* constructing right subtree */

ArrayList<Node> rightSubtree = constructTrees(i + 1, end);

/* now looping through all left and right subtrees and connecting

them to ith root below */

for (int j = 0; j < leftSubtree.size(); j++)

{

Node left = leftSubtree.get(j);

for (int k = 0; k < rightSubtree.size(); k++)

{

Node right = rightSubtree.get(k);

Node node = new Node(i); // making value i as root

node.left = left; // connect left subtree

node.right = right; // connect right subtree

list.add(node); // add this tree to list

}

}

}

return list;

}

// A utility function to do preorder traversal of BST

static void preorder(Node root)

{

if (root != null)

{

System.out.print(root.key+" ") ;

preorder(root.left);

preorder(root.right);

}

}

public static void main(String args[])

{

ArrayList<Node> totalTreesFrom1toN = constructTrees(1, 3);

System.out.println("Number of unique BSTs = " + totalTreesFrom1toN.size());

// IF YOU WANT TO PRINT THE TREES TOO, UNCOMMENT THE BELOW LINES OF CODE

// /* Printing preorder traversal of all constructed BSTs */

// System.out.println("Preorder traversals of all constructed BSTs are ");

// for (int i = 0; i < totalTreesFrom1toN.size(); i++)

// {

// preorder(totalTreesFrom1toN.get(i));

// System.out.println();

// }

}

}

// node structure

class Node

{

int key;

Node left, right;

Node(int data)

{

this.key=data;

left=right=null;

}

};

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