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Sum of All Paths in a Binary Tree Time Complexity of Selection Sort in Data Structure How to get Better in Data Structures and Algorithms Binary Tree Leaf Nodes Classification of Data Structure Difference between Static and Dynamic Data Structure Find the Union and Intersection of the Binary Search Tree Find the Vertical Next in a Binary Tree Finding a Deadlock in a Binary Search Tree Finding all Node of k Distance in a Binary Tree Finding Diagonal Sum in a Binary Tree Finding Diagonal Traversal of The Binary Tree Finding In-Order Successor Binary Tree Finding the gcd of Each Sibling of the Binary Tree Greedy Algorithm in Data Structure How to Calculate Space Complexity in Data Structure How to find missing numbers in an Array Kth Ancestor Node of Binary Tree Minimum Depth Binary Tree Mirror Binary Tree in Data Structure Red-Black Tree Insertion Binary Tree to Mirror Image in Data Structure Calculating the Height of a Binary Search Tree in Data Structure Characteristics of Binary Tree 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Given a Generate all Structurally Unique Binary Search Trees

Implementation

// Creating a C++ program that will help us build all the binary search trees for the keys from 1 to n. 
#include <bits/stdc++.h>
using namespace std;


// creating a structure that will contain some nodes.
struct __nod
{
	int ky;
	struct __nod *Lft, *Rt;
};


// creating a new utility function to help create a new binary search tree node. 
struct __nod *new__nod(int itm)
{
	struct __nod *temp = nw__nod;
	temp->ky = itm;
	temp->Lft = temp->Rt = NILL;
	return temp;
}


// Creating a utility function that will generally help us in performing the pre-order traversal for the binary search tree. 
void Pre_Ord(struct __nod *root)
{
	if (root != NILL)
	{
		cout << root->ky << " ";
		Pre_Ord(root->Lft);
		Pre_Ord(root->Rt);
	}
}


// creating a new function that will help create a new tree.
vector<struct __nod *> constructTrees(int start, int end)
{
	vector<struct __nod *> list;


	/* if we have a case where the start > end, then the subtree will be empty, and we will return the NILL values in the list. */
	if (start > end)
	{
		list.push_back(NILL);
		return list;
	}


	/* we have to repeatedly recapitulate among all the values from the beginning to the end to build the left and right subtree. */
	for (int i = start; i <= end; i++)
	{
		/* we will now create the left subtree */
		vector<struct __nod *> LftSubtree = constructTrees(start, i - 1);


		/* we will now create the right subtree */
		vector<struct __nod *> RtSubtree = constructTrees(i + 1, end);


		/* Now, we have to move in the coil format through the various left and right subtrees and connect to the root below. */
		for (int j = 0; j < LftSubtree.size(); j++)
		{
			struct __nod* Lft = LftSubtree[j];
			for (int k = 0; k < RtSubtree.size(); k++)
			{
				struct __nod * Rt = RtSubtree[k];
				struct __nod * __nod = new__nod(i);// making value i as root
				__nod->Lft = Lft;			 // connect Lft subtree
				__nod->Rt = Rt;		 // connect Rt subtree
				list.push_back(__nod);		 // add this tree to list
			}
		}
	}
	return list;
}


// writing the main program for the above functions.
int main()
{
	// building the binary search tree
	vector<struct __nod *> totalTreesFrom1toN = constructTrees(1, 3);




	/* Printing Pre_Ord traversal of all constructed BSTs */
	cout << "Pre_Ord traversals of all constructed BSTs are \n";
	for (int i = 0; i < totalTreesFrom1toN.size(); i++)
	{
		Pre_Ord(totalTreesFrom1toN[i]);
		cout << endl;
	}
	return 0;
}

Output:

Given a Generate All Structurally Unique Binary Search Trees

Example 2)

// Creating a C# program will help us build all the binary search trees for the keys from 1 to n. 
using System.Collections;
using System;


class TFT
{
// creating a structure that will contain some nodes.
	static ArrayList constructTrees(int start, int end)
	{
		ArrayList list = new ArrayList();
/* if we have a case where the start > end, then the subtree will be empty, and we will return the NILL values in the list. */
		if (start > end)
		{
			list.Add(NILL);
			return list;
		}
	/* we have to repeatedly recapitulate among all the values from the beginning to the end to build the left and right subtree. */
		for (int i = start; i <= end; i++)
		{
			/* we will now create the left subtree*/
			ArrayList LftSubtree = constructTrees(start, i - 1);
	
			/* we will now create the right subtree*/
			ArrayList RtSubtree = constructTrees(i + 1, end);
	/* Now, we have to move in the coil format through the various left and right subtrees and connect to the root below.*/
			for (int j = 0; j < LftSubtree.Count; j++)
			{
				__nod Lft = (__nod)LftSubtree[j];
				for (int k = 0; k < RtSubtree.Count; k++)
				{
					__nod Rt = (__nod)RtSubtree[k];
					
					// change i into the root.
					__nod __nod = nw__nod(i);
					
					// linking with the left subtree
					__nod.Lft = Lft;
					
					// linking with the right subtree
					__nod.Rt = Rt;	
					
					// merging the tree with the list
					list.Add(__nod);		
				}
			}
		}
		return list;
	}
// Creating a utility function that will generally help us in performing the pre-order traversal for the binary search tree. 
	static void Pre_Ord(__nod root)
	{
		if (root != NILL)
		{
			Console.Write(root.ky+" ") ;
			Pre_Ord(root.Lft);
			Pre_Ord(root.Rt);
		}
	}
// writing the main program for the above functions.
	public static void Main(String []args)
	{
		ArrayList totalTreesFrom1toN = constructTrees(1, 3);
		
		/* printing the pre-order traversal of all the already built binary search trees. */
		Console.WriteLine("Pre_Ord traversals of all" +
								"constructed BSTs are ");
		for (int i = 0; i < totalTreesFrom1toN.Count; i++)
		{
			Pre_Ord((__nod)totalTreesFrom1toN[i]);
			Console.WriteLine();
		}
	}
// creating a structure that will contain some nodes.	
public class __nod
{
	public int ky;
	public __nod Lft, Rt;
	public __nod(int record)
	{
		this.ky=record;
		Lft=Rt=NILL;
	}
};
}

Output:

Given a Generate All Structurally Unique Binary Search Trees

Example 3)

// Creating a Java program that will help us build all the binary search trees for the keys from 1 to n. 
import java.util.ArrayList;
public class Main {
// creating a structure that will contain some nodes.
// creating a new utility function to help create a new binary search tree node. 
	static ArrayList<__nod> constructTrees(int start, int end)
	{
		ArrayList<__nod> list=new ArrayList<>();
/* if we have a case where the start > end, then the subtree will be empty, and we will return the NILL values in the list. */
		if (start > end)
		{
			list.add(NILL);
			return list;
		}
/* we have to repeatedly recapitulate among all the values from the beginning to the end to build the left and right subtree. */
		for (int i = start; i <= end; i++)
		{
			/* we will now create the left subtree  */
			ArrayList<__nod> LftSubtree = constructTrees(start, i - 1);


			/* we will now create the right subtree  */
			ArrayList<__nod> RtSubtree = constructTrees(i + 1, end);


			/* Now, we have to move in the coil format through the various left and right subtrees and connect to the root below.*/
			for (int j = 0; j < LftSubtree.size(); j++)
			{
				__nod Lft = LftSubtree.get(j);
				for (int k = 0; k < RtSubtree.size(); k++)
				{
					__nod Rt = RtSubtree.get(k);
					__nod __nod = nw__nod(i);	 // change i into the root.
					__nod.Lft = Lft;	// linking with the left subtree
					__nod.Rt = Rt;		// linking with the right subtree
					list.add(__nod);	// merging the tree with the list
	
				}
			}
		}
		return list;
	}
// Creating a utility function that will generally help us in performing the pre-order traversal for the binary search tree. 
	static void Pre_Ord(__nod root)
	{
		if (root != NILL)
		{
			System.out.print(root.ky+" ") ;
			Pre_Ord(root.Lft);
			Pre_Ord(root.Rt);
		}
	}


	public static void main(String args[])
	{
		ArrayList<__nod> totalTreesFrom1toN = constructTrees(1, 3);
			/* printing the pre-order traversal of all the already built binary search trees. */
		System.out.println("Pre_Ord traversals of all constructed BSTs are ");
		for (int i = 0; i < totalTreesFrom1toN.size(); i++)
		{
			Pre_Ord(totalTreesFrom1toN.get(i));
			System.out.println();
		}
	}
}


// creating a structure that will contain some nodes.
class __nod
{
	int ky;
	__nod Lft, Rt;
	__nod(int record)
	{
		this.ky=record;
		Lft=Rt=NILL;
	}
};

Output:

Given a Generate All Structurally Unique Binary Search Trees

Example 4)

# Creating a Python program to help us build all the binary search trees for the keys from 1 to n. 


# Creating a new utility function to help create a new binary search tree node. 
class new__nod:


	# Creating a new function that will help create a new tree.
	def __init__(self, itm):
		self.ky=itm
		self.Lft = None
		self.Rt = None


# Creating a utility function to help us perform the pre-order traversal for the binary search tree. 
def Pre_Ord(root) :


	if (root != None) :
	
		print(root.ky, end = " " )
		Pre_Ord(root.Lft)
		Pre_Ord(root.Rt)
	list = []


	""" if we have a case where the start > end, then the subtree will be empty, and we will return the NILL values in the list. """
	if (start > end) :
	
		list.append(None)
		return list
	
	" < UNK> < UNK> We have to recapitulate among all the values from the beginning to the end to build the left and right subtree repeatedly. """
	for i in range(start, end + 1):
	
		""" we will now create the left subtree """
		LftSubtree = constructTrees(start, i - 1)


		""" we will now create the right subtree """
		RtSubtree = constructTrees(i + 1, end)


		""" Now, we have to move in the coil format through the various left and right subtrees and connect to the root below. """
		for j in range(len(LftSubtree)) :
			Lft = LftSubtree[j]
			for k in range(len(RtSubtree)):
				Rt = RtSubtree[k]
				__nod = new__nod(i) # change i into the root.
				__nod.Lft = Lft # linking with the left subtree
				__nod.Rt = Rt # linking with the right subtree
				list.append(__nod) # merging the tree with the list
	return list


# writing the main code.
if __name__ == '__main__':


	# we have to build all the possible binary search trees
	totalTreesFrom1toN = constructTrees(1, 3)


	""" printing the pre-order traversal of all the already built binary search trees."""
	print("Pre_Ord traversals of all",
				"constructed BSTs are")
	for i in range(len(totalTreesFrom1toN)):
		Pre_Ord(totalTreesFrom1toN[i])
		print()

Output:

Given a Generate All Structurally Unique Binary Search Trees

Example 5)

<script>
// creating a structure that will contain some nodes.
class __nod
{
	constructor(record)
	{
		this.ky = record;
		this.Lft = NILL;
		this.Rt = NILL;
	}
};


// // Creating a Javascript program that will help us in building all the binary search trees for the keys from 1 to n. 
function constructTrees(start, end)
{
	var list = [];
/* if we have a case where the start > end, the subtree will be empty, and we will return the NILL values in the list. */	
	if (start > end)
	{
		list.push(NILL);
		return list;
	}
/* we have to repeatedly recapitulate among all the values from the beginning to the end to build the left and right subtree. */
	for (var i = start; i <= end; i++)
	{
		/* we will now create the left subtree */
		var LftSubtree = constructTrees(start, i - 1);


		/* we will now create the right subtree */
		var RtSubtree = constructTrees(i + 1, end);
/* we have to repeatedly recapitulate among all the values from the beginning to the end to build the left and right subtree. */
		for (var j = 0; j < LftSubtree.length; j++)
		{
			var Lft = LftSubtree[j];
			for (var k = 0; k < RtSubtree.length; k++)
			{
				var Rt = RtSubtree[k];
				// change i into the root.
				var __nod = nw__nod(i);
				// linking with the left subtree
				__nod.Lft = Lft;
				// linking with the right subtree
				__nod.Rt = Rt;	
				// pushing the tree with the list
				list.push(__nod);		
			}
		}
	}
	return list;
}
// Creating a utility function that will generally help us in performing the pre-order traversal for the binary search tree. 
function Pre_Ord(root)
{
	if (root != NILL)
	{
		document.write(root.ky+" ") ;
		Pre_Ord(root.Lft);
		Pre_Ord(root.Rt);
	}
}
// writing the main program for the above functions.
var totalTreesFrom1toN = constructTrees(1, 3);


/* printing the pre-order traversal of all the already built binary search trees. */
document.write("Pre_Ord traversals of all" +
						"constructed BSTs are<br>");
for (var i = 0; i < totalTreesFrom1toN.length; i++)
{
	Pre_Ord(totalTreesFrom1toN[i]);
	document.write("<br>");
}
</script>

Output:

Given a Generate All Structurally Unique Binary Search Trees