Ternary Search Tree

Ternary Search Tree is a trie data structure commonly used as a low-memory alternative to trie in various applications such as spell check and looking for nearby neighbors. To comprehend the ternary search tree, we must first grasp the concept of the trie.

A trie, also known as a digital tree, radix tree, or prefix tree, is a type of search tree, an ordered tree data structure used to hold a dynamic set or associative array using strings as keys.

Representation of Ternary Search Trees

In the trie (standard) data structure, each node contains 26 pointers for its children, but in a ternary search tree, each node contains only 3 pointers:

The left pointer points to the node whose value is lower than the current node's value.
The equal pointer leads to a node whose value is the same as the current node's value.
The right pointer leads to the node whose value exceeds the current node's value.

Aside from the three-pointers mentioned above, each node contains a field for indicating data (character in the case of a dictionary) and a field for indicating the end of a string.

So, it's similar to BST, which saves data in a specific order. On the other hand, data in a ternary search tree is dispersed among the nodes. For example, you required the four nodes to store the term "Bird".

One advantage of ternary search trees over tries is that ternary search trees take up less space (only three-pointers per node compared to 26 in standard tries). In addition, ternary search trees may be utilized in any situation where a hash table is used to hold strings.

Tries are appropriate when there is the correct distribution of words throughout the alphabets, allowing for the most effective use of space. Ternary search trees are preferable when the strings to be stored all have the same prefix; ternary search trees are the most economical in terms of space.

Java Code

Now let's write a Java program to implement a ternary search tree.

/**
 ** A sample Java program to implement Ternary Search Tree
 **/
import java.util.Scanner;
import java.util.ArrayList;
/** class TSTNode **/
class TSTNode
{
    char data;
    boolean isEnd;
    TSTNode left, middle, right;
    /** Constructor **/
    public TSTNode(char data)
    {
        this.data = data;
        this.isEnd = false;
        this.left = null;
        this.middle = null;
        this.right = null;
    }        
} 
/** class TernarySearchTree **/
class TernarySearchTree
{
    private TSTNode root;
    private ArrayList<String> al;
 
    /** Constructor **/
    public TernarySearchTree()
    {
        root = null;
    }
    /** function to check if empty **/
    public boolean isEmpty()
    {
        return root == null;
    }
    /** function to clear **/
    public void makeEmpty()
    {
        root = null;
    }
    /** function to insert for a word **/
    public void insert(String word)
    {
        root = insert(root, word.toCharArray(), 0);
    }
    /** function to insert for a word **/
    public TSTNode insert(TSTNode r, char[] word, int ptr)
    {
        if (r == null)
            r = new TSTNode(word[ptr]);
        if (word[ptr] < r.data)
            r.left = insert(r.left, word, ptr);
        else if (word[ptr] > r.data)
            r.right = insert(r.right, word, ptr);
        else
        {
            if (ptr + 1 < word.length)
                r.middle = insert(r.middle, word, ptr + 1);
            else
                r.isEnd = true;
        }
        return r;
    } 
    /** function to delete a word **/
    public void delete(String word)
    {
        delete(root, word.toCharArray(), 0);
    }
    /** function to delete a word **/
    private void delete(TSTNode r, char[] word, int ptr)
    {
        if (r == null)
            return; 
        if (word[ptr] < r.data)
            delete(r.left, word, ptr);
        else if (word[ptr] > r.data)
            delete(r.right, word, ptr);
        else
        {
            /** to delete a word just make isEnd false **/
            if (r.isEnd && ptr == word.length - 1)
                r.isEnd = false;
            else if (ptr + 1 < word.length)
                delete(r.middle, word, ptr + 1);
        }        
    } 
    /** function to search for a word **/
    public boolean search(String word)
    {
        return search(root, word.toCharArray(), 0);
    }
    /** function to search for a word **/
    private boolean search(TSTNode r, char[] word, int ptr)
    {
        if (r == null)
            return false;
        if (word[ptr] < r.data)
            return search(r.left, word, ptr);
        else if (word[ptr] > r.data)
            return search(r.right, word, ptr);
        else
        {
            if (r.isEnd && ptr == word.length - 1)
                return true;
            else if (ptr == word.length - 1)
                return false;
            else
                return search(r.middle, word, ptr + 1);
        }        
    }
    /** function to print tree **/
    public String toString()
    {
        al = new ArrayList<String>();
        traverse(root, "");
        return "\nTernary Search Tree : "+ al;
    }
    /** function to traverse tree **/
    private void traverse(TSTNode r, String str)
    {
        if (r != null)
        {
            traverse(r.left, str);
            str = str + r.data;
            if (r.isEnd)
                al.add(str); 
            traverse(r.middle, str);
            str = str.substring(0, str.length() - 1); 
            traverse(r.right, str);
        }
    }
}
/** class TernarySearchTree **/
public class TernarySearchTreeTest
{
    public static void main(String[] args)
    {
        Scanner scan = new Scanner(System.in); 
        /* Creating object of TernarySearchTree */
        TernarySearchTree tst = new TernarySearchTree(); 
        System.out.println("Ternary Search Tree Test\n"); 
        char ch;
        /*  Perform tree operations  */
        do    
        {
            System.out.println("\nSelect one of the operation for Ternary Search Tree::");
            System.out.println("1. To insert a new word in the Ternary Search Tree.");
            System.out.println("2. To search an already existing word in the Ternary Search Tree.");
            System.out.println("3. To delete a word from the Ternary Search Tree");
            System.out.println("4. To check if the Ternary Tree is empty.");
            System.out.println("5. To make the Ternary Search Tree empty.");
            int choice = scan.nextInt();            
            switch (choice)
            {
            case 1 : 
                System.out.println("Enter word to insert");
                tst.insert( scan.next() );                     
                break;                          
            case 2 : 
                System.out.println("Enter word to search");
                System.out.println("Search result : "+ tst.search( scan.next() ));
                break; 
            case 3 : 
                System.out.println("Enter word to delete");
                tst.delete( scan.next() );                     
                break; 
            case 4 : 
                System.out.println("Empty Status : "+ tst.isEmpty() );                
                break;    
            case 5 : 
                System.out.println("Ternary Search Tree cleared"); 
                tst.makeEmpty();               
                break;                                        
            default : 
                System.out.println("Wrong Entry \n ");
                break;   
            }
            System.out.println(tst); 
            System.out.println("\nDo you want to continue (Type y or n) \n");
            ch = scan.next().charAt(0);                        
        } while (ch == 'Y'|| ch == 'y');        
    }
}

Output

The above Java code gives the following output.

Ternary Search Tree Test
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
red
Ternary Search Tree : [red]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
blur e
Ternary Search Tree : [blue, red]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
green
Ternary Search Tree : [blue, green, red]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
yellow
Ternary Search Tree : [blue, green, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
pink
Ternary Search Tree : [blue, green, pink, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
black
Ternary Search Tree : [black, blue, green, pink, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
grey
Ternary Search Tree : [black, blue, green, grey, pink, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
mustard
Ternary Search Tree : [black, blue, green, grey, mustard, pink, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
White
Ternary Search Tree : [White, black, blue, green, grey, mustard, pink, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
1
Enter the word to insert
purple
Ternary Search Tree : [White, black, blue, green, grey, mustard, pink, purple, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
2
Enter the word to search
black
Search result: true
Ternary Search Tree : [White, black, blue, green, grey, mustard, pink, purple, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
3
Enter the word to delete
blue mustard
Ternary Search Tree : [White, black, blue, green, grey, pink, purple, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
4
Empty Status: false
Ternary Search Tree : [White, black, blue, green, grey, pink, purple, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
3
Enter the word to delete
black
Ternary Search Tree : [White, blue, green, grey, pink, purple, red, yellow]
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Tree is empty.
5. To make the Ternary Search Tree empty.
5
Ternary Search Tree cleared
Ternary Search Tree : []
Do you want to continue (Type y or n)
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To delete a word from the Ternary Search Tree
4. To check if the Ternary Search Tree is empty.
5. To make the Ternary Search Tree empty.
4
Empty Status: true
Ternary Search Tree : []
Do you want to continue (Type y or n)
n

In the above Java code, we have implemented the ternary search tree data structure and various functions like adding new data in the ternary search tree, deleting the existing data from the ternary search tree, to check whether the ternary search tree is empty or not, there is also one operation to empty the tree that will delete all the content within the ternary search tree and the traversal of the ternary search tree.

For all these operations of the ternary search tree, there are different functions written, and then according to the need of the operation on the ternary search tree data structure, those functions are called.

C++ Code

Let's write the C++ code for the ternary search tree.

/* 
 * C++ Program to implement Ternary Seach Tree
 */
#include <iostream>
#include <cstdlib>
#define MAX 50
using namespace std; 
/* 
 * Node Declaration
 */
struct Node
{
    char data;
    unsigned isEndOfString: 1;
    Node *left, *eq, *right;
};
/* 
 * create a new ternary search tree node
 */ 
Node* newNode(char data)
{
    Node* temp = new Node;
    temp->data = data;
    temp->isEndOfString = 0;
    temp->left = temp->eq = temp->right = NULL;
    return temp;
}
/* 
 * insert a new word in a Ternary Search Tree
 */ 
void insert(Node** root, char *word)
{
    if (!(*root))
        *root = newNode(*word);
    if ((*word) < (*root)->data)
        insert(&((*root)->left), word);
    else if ((*word) > (*root)->data)
        insert(&((*root)->right), word);
    else
    {
        if (*(word + 1))
            insert(&( (*root)->eq ), word + 1);
        else
            (*root)->isEndOfString = 1;
    }
}
/* 
 * traverse Utility function
 */  
void traverseTSTUtil(Node* root, char* buffer, int depth)
{
    if (root)
    {
        traverseTSTUtil(root->left, buffer, depth);
        buffer[depth] = root->data;
        if (root->isEndOfString)
        {
            buffer[depth + 1] = '\0';
            cout<<buffer<<endl;
        }
        traverseTSTUtil(root->eq, buffer, depth + 1);
        traverseTSTUtil(root->right, buffer, depth);
    }
}
/* 
 * traverse Ternary Search Tree
 */  
void traverseTST(Node* root)
{
    char buffer[MAX];
    traverseTSTUtil(root, buffer, 0);
}
/* 
 * search a given word in Ternary Search Tree
 */  
int searchTST(Node *root, char *word)
{
    if (!root)
        return 0;
    if (*word < (root)->data)
        return searchTST(root->left, word);
    else if (*word > (root)->data)
        return searchTST(root->right, word);
    else
    {
        if (*(word + 1) == '\0')
            return root->isEndOfString;
        return searchTST(root->eq, word+1);
    }
}
/* 
 * beginning of the Main function to call all the functions of the ternary search tree.
 */  
int main()
{
    Node *root = NULL;
    char s[100];
        char ch;
        /*  Perform tree operations  */
        do    
        {
            cout<<"\nSelect one of the operation for Ternary Search Tree::"<<endl;
            cout<<"1. To insert a new word in the Ternary Search Tree."<<endl;
            cout<<"2. To search an already exisitng word in the Ternary Search Tree."<<endl;
            cout<<"3. To Traverse the Ternary Search Tree."<<endl;             
            int choice;
            cin>>choice;            
            switch (choice)
            {
            case 1 : 
                cout<<"Enter word to insert"<<endl;
                cin>>s;
                insert(&root,s);                     
                break;                          
            case 2 : 
                cout<<"Enter word to search"<<endl;
                cin>>s;
                if (searchTST(root, s))
                    cout<<s<<" found in Ternary Search Tree"<<endl;
                else
                    cout<<s<<" not found in Ternary Search Tree"<<endl;
                break; 
            case 3 : 
                cout<<"Contents of the Ternary Search Tree are::"<<endl;
                traverseTST(root);
                break; 
            default : 
                cout<<"Wrong Entry \n ";
                break;   
            }
            cout<<"\nDo you want to continue (Type y or n) \n";
            cin>>ch;                        
        } while (ch == 'Y'|| ch == 'y');
return 0;
}

Output

The above C++ code gives the following output.

Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
1
Enter the word to insert
orange 
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
1
Enter the word to insert
banana
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
1
Enter the word to insert
grapes 
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
1
Enter the word to insert
apple
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
1
Enter the word to insert
watermelon
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
1
Enter the word to insert
guava
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
1
Enter the word to insert
Kiwi
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
3
Contents of the Ternary Search Tree are::
Kiwi
apple
Banana
Watermelon
guava
grapes
orange
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
2
Enter the word to search
Kiwi
Kiwi found in Ternary Search Tree
Do you want to continue (Type y or n) 
y
Select one of the operations for Ternary Search Tree::
1. To insert a new word in the Ternary Search Tree.
2. To search an already existing word in the Ternary Search Tree.
3. To Traverse the Ternary Search Tree.
2
Enter the word to search
mango
mango not found in Ternary Search Tree
Do you want to continue (Type y or n) 
n

In the above C++ code, we have implemented the ternary search tree data structure and various functions like adding new data, deleting the existing data, and the traversal of the ternary search tree. For all these operations of the ternary search tree, there are different functions written, and then according to the need of the operation on the ternary search tree data structure, those functions are called.

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