Threaded Binary Search Tree | Deletion

A threaded binary tree node looks like following.

C++

struct Node {
    struct Node *left, *right;
    int info;

    // false if left pointer points to predecessor
    // in Inorder Traversal
    bool lthread;

    // false if right pointer points to predecessor
    // in Inorder Traversal
    bool rthread;
};

Java

static class Node {
    Node left, right;
    int info;

    // True if left pointer points to predecessor
    // in Inorder Traversal
    boolean lthread;

    // True if right pointer points to predecessor
    // in Inorder Traversal
    boolean rthread;
};


// This code contributed by aashish1995

Python3

class Node:
    def __init__(self):
        self.info = 0;
        self.left = None;
        self.right = None;

        # True if left pointer points to predecessor
        # in Inorder Traversal
        self.lthread = False;;

        # True if right pointer points to predecessor
        # in Inorder Traversal
        self.rthread = False;

# This code contributed by umadevi9616

C#

public
  class Node
  {
    public
      Node left,
    right;
    public
      int info;

    // True if left pointer points to predecessor
    // in Inorder Traversal
    public
      bool lthread;

    // True if right pointer points to predecessor
    // in Inorder Traversal
    public
      bool rthread;
  };

// This code is contributed by aashish1995

Javascript

<script>
 class Node {
     constructor(){

     this.left = null, this.right = null;
     this.info = 0;

    // True if left pointer points to predecessor
    // in Inorder Traversal
    this.lthread = false;

    // True if right pointer points to predecessor
    // in Inorder Traversal
    this.rthread = false;
}
}
// This code contributed by aashish1995
</script>

We have already discussed Insertion of Threaded Binary Search Tree

In deletion, first the key to be deleted is searched, and then there are different cases for deleting the Node in which key is found. 

C++

// Deletes a key from threaded BST with given root and
// returns new root of BST.
struct Node* delThreadedBST(struct Node* root, int dkey)
{
    // Initialize parent as NULL and ptrent
    // Node as root.
    struct Node *par = NULL, *ptr = root;

    // Set true if key is found
    int found = 0;

    // Search key in BST : find Node and its
    // parent.
    while (ptr != NULL) {
        if (dkey == ptr->info) {
            found = 1;
            break;
        }
        par = ptr;
        if (dkey < ptr->info) {
            if (ptr->lthread == false)
                ptr = ptr->left;
            else
                break;
        }
        else {
            if (ptr->rthread == false)
                ptr = ptr->right;
            else
                break;
        }
    }

    if (found == 0)
        printf("dkey not present in tree\n");

    // Two Children
    else if (ptr->lthread == false && ptr->rthread == false)
        root = caseC(root, par, ptr);

    // Only Left Child
    else if (ptr->lthread == false)
        root = caseB(root, par, ptr);

    // Only Right Child
    else if (ptr->rthread == false)
        root = caseB(root, par, ptr);

    // No child
    else
        root = caseA(root, par, ptr);

    return root;
}

Java

// Deletes a key from threaded BST with given root and
// returns new root of BST.
Node delThreadedBST(Node root, int dkey)
{
    // Initialize parent as null and ptrent
    // Node as root.
    Node par = null, ptr = root;

    // Set true if key is found
    int found = 0;

    // Search key in BST : find Node and its
    // parent.
    while (ptr != null) {
        if (dkey == ptr.info) {
            found = 1;
            break;
        }
        par = ptr;
        if (dkey < ptr.info) {
            if (ptr.lthread == false)
                ptr = ptr.left;
            else
                break;
        }
        else {
            if (ptr.rthread == false)
                ptr = ptr.right;
            else
                break;
        }
    }

    if (found == 0)
        System.out.printf("dkey not present in tree\n");

    // Two Children
    else if (ptr.lthread == false && ptr.rthread == false)
        root = caseC(root, par, ptr);

    // Only Left Child
    else if (ptr.lthread == false)
        root = caseB(root, par, ptr);

    // Only Right Child
    else if (ptr.rthread == false)
        root = caseB(root, par, ptr);

    // No child
    else
        root = caseA(root, par, ptr);

    return root;
}

// This code is contributed by gauravrajput1

Python3

# Deletes a key from threaded BST with given root and
# returns new root of BST.
def delThreadedBST(root, dkey):

    # Initialize parent as None and ptrent
    # Node as root.
    par = None;
    ptr = root;

    # Set True if key is found
    found = 0;

    # Search key in BST : find Node and its
    # parent.
    while (ptr != None):
        if (dkey == ptr.info):
            found = 1;
            break;

        par = ptr;
        if (dkey < ptr.info):
            if (ptr.lthread == False)
                ptr = ptr.left;
            else
                break;

        else:
            if (ptr.rthread == False)
                ptr = ptr.right;
            else
                break;

    if (found == 0):
        print("dkey not present in tree");

    # Two Children
    else if(ptr.lthread == False and ptr.rthread == False):
        root = caseC(root, par, ptr);

    # Only Left Child
    else if(ptr.lthread == False):
        root = caseB(root, par, ptr);

    # Only Right Child
    else if(ptr.rthread == False):
        root = caseB(root, par, ptr);

    # No child
    else:
        root = caseA(root, par, ptr);

    return root;

# This code is contributed by Rajput-Ji

C#

// Deletes a key from threaded BST with given root and
// returns new root of BST.
Node delThreadedBST(Node root, int dkey)
{
    // Initialize parent as null and ptrent
    // Node as root.
    Node par = null, ptr = root;

    // Set true if key is found
    int found = 0;

    // Search key in BST : find Node and its
    // parent.
    while (ptr != null) {
        if (dkey == ptr.info) {
            found = 1;
            break;
        }
        par = ptr;
        if (dkey < ptr.info) {
            if (ptr.lthread == false)
                ptr = ptr.left;
            else
                break;
        }
        else {
            if (ptr.rthread == false)
                ptr = ptr.right;
            else
                break;
        }
    }

    if (found == 0)
        Console.Write("dkey not present in tree\n");

    // Two Children
    else if (ptr.lthread == false && ptr.rthread == false)
        root = caseC(root, par, ptr);

    // Only Left Child
    else if (ptr.lthread == false)
        root = caseB(root, par, ptr);

    // Only Right Child
    else if (ptr.rthread == false)
        root = caseB(root, par, ptr);

    // No child
    else
        root = caseA(root, par, ptr);

    return root;
}

// This code is contributed by gauravrajput1

Javascript

<script>
// Deletes a key from threaded BST with given root and
// returns new root of BST.
function delThreadedBST(root , dkey)
{
    // Initialize parent as null and ptrent
    // Node as root.
    var par = null, ptr = root;

    // Set true if key is found
    var found = 0;

    // Search key in BST : find Node and its
    // parent.
    while (ptr != null) {
        if (dkey == ptr.info) {
            found = 1;
            break;
        }
        par = ptr;
        if (dkey < ptr.info) {
            if (ptr.lthread == false)
                ptr = ptr.left;
            else
                break;
        }
        else {
            if (ptr.rthread == false)
                ptr = ptr.right;
            else
                break;
        }
    }

    if (found == 0)
        document.write("dkey not present in tree\n");

    // Two Children
    else if (ptr.lthread == false && ptr.rthread == false)
        root = caseC(root, par, ptr);

    // Only Left Child
    else if (ptr.lthread == false)
        root = caseB(root, par, ptr);

    // Only Right Child
    else if (ptr.rthread == false)
        root = caseB(root, par, ptr);

    // No child
    else
        root = caseA(root, par, ptr);

    return root;
}

// This code is contributed by gauravrajput1
</script>

Case A: Leaf Node need to be deleted

In BST, for deleting a leaf Node the left or right pointer of parent was set to NULL. Here instead of setting the pointer to NULL it is made a thread. 
If the leaf Node is to be deleted is left child of its parent then after deletion, left pointer of parent should become a thread pointing to its predecessor of the parent Node after deletion. 

par -> lthread = true;
par -> left = ptr -> left;

If the leaf Node to be deleted is right child of its parent then after deletion, right pointer of parent should become a thread pointing to its successor. The Node which was inorder successor of the leaf Node before deletion will become the inorder successor of the parent Node after deletion. 

C++

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
struct Node* caseA(struct Node* root, struct Node* par,
                   struct Node* ptr)
{
    // If Node to be deleted is root
    if (par == NULL)
        root = NULL;

    // If Node to be deleted is left
    // of its parent
    else if (ptr == par->left) {
        par->lthread = true;
        par->left = ptr->left;
    }
    else {
        par->rthread = true;
        par->right = ptr->right;
    }

    // Free memory and return new root
    free(ptr);
    return root;
}

Java

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
Node caseA(Node root, Node par,
                   Node ptr)
{

    // If Node to be deleted is root
    if (par == null)
        root = null;

    // If Node to be deleted is left
    // of its parent
    else if (ptr == par.left) {
        par.lthread = true;
        par.left = ptr.left;
    }
    else {
        par.rthread = true;
        par.right = ptr.right;
    }

    return root;
}

// This code is contributed by gauravrajput1

Python3

# Here 'par' is pointer to parent Node and 'ptr' is
# pointer to current Node.
def caseA(root,par,ptr):

  # If Node to be deleted is root
    if (par == None):
        root = None

     # If Node to be deleted is left
    # of its parent
    elif(ptr == par.left):
        par.lthread = true
        par.left = ptr.left
    else:
        par.rthread = true
        par.right = ptr.right
return root

# This code is contributed by Patel2127.

C#

// Here 'par' is pointer to parent Node and
// 'ptr' is pointer to current Node.
Node caseA(Node root, Node par, Node ptr)
{

    // If Node to be deleted is root
    if (par == null)
        root = null;

    // If Node to be deleted is left
    // of its parent
    else if (ptr == par.left)
    {
        par.lthread = true;
        par.left = ptr.left;
    }
    else
    {
        par.rthread = true;
        par.right = ptr.right;
    }
    return root;
}

// This code is contributed by rutvik_56

Javascript

<script>

// Here 'par' is pointer to parent Node and
// 'ptr' is pointer to current Node.
function caseA(root, par, ptr)
{

    // If Node to be deleted is root
    if (par == null)
        root = null;

    // If Node to be deleted is left
    // of its parent
    else if (ptr == par.left)
    {
        par.lthread = true;
        par.left = ptr.left;
    }
    else
    {
        par.rthread = true;
        par.right = ptr.right;
    }
    return root;
}

// This code is contributed by rag2127

</script>

Case B: Node to be deleted has only one child
After deleting the Node as in a BST, the inorder successor and inorder predecessor of the Node are found out. 

s = inSucc(ptr);
p = inPred(ptr);

If Node to be deleted has left subtree, then after deletion right thread of its predecessor should point to its successor. 

p->right = s;

Before deletion 15 is predecessor and 2 is successor of 16. After deletion of 16, the Node 20 becomes the successor of 15, so right thread of 15 will point to 20. 
If Node to be deleted has right subtree, then after deletion left thread of its successor should point to its predecessor. 

s->left = p;

Before deletion of 25 is predecessor and 34 is successor of 30. After deletion of 30, the Node 25 becomes the predecessor of 34, so left thread of 34 will point to 25. 

C++

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
struct Node* caseB(struct Node* root, struct Node* par,
                   struct Node* ptr)
{
    struct Node* child;

    // Initialize child Node to be deleted has
    // left child.
    if (ptr->lthread == false)
        child = ptr->left;

    // Node to be deleted has right child.
    else
        child = ptr->right;

    // Node to be deleted is root Node.
    if (par == NULL)
        root = child;

    // Node is left child of its parent.
    else if (ptr == par->left)
        par->left = child;
    else
        par->right = child;

    // Find successor and predecessor
    Node* s = inSucc(ptr);
    Node* p = inPred(ptr);

    // If ptr has left subtree.
    if (ptr->lthread == false)
        p->right = s;

    // If ptr has right subtree.
    else {
        if (ptr->rthread == false)
            s->left = p;
    }

    free(ptr);
    return root;
}

Java

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
static Node caseB(Node root, Node par,
                   Node ptr)
{
    Node child;

    // Initialize child Node to be deleted has
    // left child.
    if (ptr.lthread == false)
        child = ptr.left;

    // Node to be deleted has right child.
    else
        child = ptr.right;

    // Node to be deleted is root Node.
    if (par == null)
        root = child;

    // Node is left child of its parent.
    else if (ptr == par.left)
        par.left = child;
    else
        par.right = child;

    // Find successor and predecessor
    Node s = inSucc(ptr);
    Node p = inPred(ptr);

    // If ptr has left subtree.
    if (ptr.lthread == false)
        p.right = s;

    // If ptr has right subtree.
    else {
        if (ptr.rthread == false)
            s.left = p;
    }
    return root;
}

// This code is contributed by gauravrajput1

Python3

# Here 'par' is pointer to parent Node and 'ptr' is
# pointer to current Node.
def caseB(root, par, ptr):
    child = None;

    # Initialize child Node to be deleted has
    # left child.
    if (ptr.lthread == False):
        child = ptr.left;

    # Node to be deleted has right child.
    else:
        child = ptr.right;

    # Node to be deleted is root Node.
    if (par == None):
        root = child;

    # Node is left child of its parent.
    elif(ptr == par.left):
        par.left = child;
    else:
        par.right = child;

    # Find successor and predecessor
    s = inSucc(ptr);
    p = inPred(ptr);

    # If ptr has left subtree.
    if (ptr.lthread == False):
        p.right = s;

    # If ptr has right subtree.
    else:
        if (ptr.rthread == False):
            s.left = p;

    return root;

# This code is contributed by umadevi9616

C#

// Here 'par' is pointer to parent Node and
// 'ptr' is pointer to current Node.
static Node caseB(Node root, Node par,
                  Node ptr)
{
    Node child;

    // Initialize child Node to be deleted
    // has left child.
    if (ptr.lthread == false)
        child = ptr.left;

    // Node to be deleted has right child.
    else
        child = ptr.right;

    // Node to be deleted is root Node.
    if (par == null)
        root = child;

    // Node is left child of its parent.
    else if (ptr == par.left)
        par.left = child;
    else
        par.right = child;

    // Find successor and predecessor
    Node s = inSucc(ptr);
    Node p = inPred(ptr);

    // If ptr has left subtree.
    if (ptr.lthread == false)
        p.right = s;

    // If ptr has right subtree.
    else
    {
        if (ptr.rthread == false)
            s.left = p;
    }
    return root;
}

// This code is contributed by gauravrajput1

Javascript

<script>

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
function caseB(root,par,ptr)
{
    let child;

    // Initialize child Node to be deleted has
    // left child.
    if (ptr.lthread == false)
        child = ptr.left;

    // Node to be deleted has right child.
    else
        child = ptr.right;

    // Node to be deleted is root Node.
    if (par == null)
        root = child;

    // Node is left child of its parent.
    else if (ptr == par.left)
        par.left = child;
    else
        par.right = child;

    // Find successor and predecessor
    let s = inSucc(ptr);
    let p = inPred(ptr);

    // If ptr has left subtree.
    if (ptr.lthread == false)
        p.right = s;

    // If ptr has right subtree.
    else {
        if (ptr.rthread == false)
            s.left = p;
    }
    return root;
}



// This code is contributed by avanitrachhadiya2155

</script>

Case C: Node to be deleted has two children

We find inorder successor of Node ptr (Node to be deleted) and then copy the information of this successor into Node ptr. After this inorder successor Node is deleted using either Case A or Case B. 

C++

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
struct Node* caseC(struct Node* root, struct Node* par,
                   struct Node* ptr)
{
    // Find inorder successor and its parent.
    struct Node* parsucc = ptr;
    struct Node* succ = ptr->right;

    // Find leftmost child of successor
    while (succ->left != NULL) {
        parsucc = succ;
        succ = succ->left;
    }

    ptr->info = succ->info;

    if (succ->lthread == true && succ->rthread == true)
        root = caseA(root, parsucc, succ);
    else
        root = caseB(root, parsucc, succ);

    return root;
}

Java

// Here 'par' is pointer to parent Node and 'ptr' is
    // pointer to current Node.
    static Node caseC(Node root, Node par,
                      Node ptr)
    {

        // Find inorder successor and its parent.
        Node parsucc = ptr;
        Node succ = ptr.right;

        // Find leftmost child of successor
        while (succ.lthread == false) {
            parsucc = succ;
            succ = succ.left;
        }

        ptr.info = succ.info;

        if (succ.lthread == true && succ.rthread == true)
            root = caseA(root, parsucc, succ);
        else
            root = caseB(root, parsucc, succ);

        return root;
    }

// This code is contributed by umadevi9616

C#

// Here 'par' is pointer to parent Node and 'ptr' is
    // pointer to current Node.
    static Node caseC(Node root, Node par,
                      Node ptr)
    {
        // Find inorder successor and its parent.
        Node parsucc = ptr;
        Node succ = ptr.right;

        // Find leftmost child of successor
        while (succ.lthread == false) {
            parsucc = succ;
            succ = succ.left;
        }

        ptr.info = succ.info;

        if (succ.lthread == true && succ.rthread == true)
            root = caseA(root, parsucc, succ);
        else
            root = caseB(root, parsucc, succ);

        return root;
    }

// This code is contributed by umadevi9616

Javascript

<script>
 // Here 'par' is pointer to parent Node and 'ptr' is
      // pointer to current Node.
      function caseC(root, par, ptr)
      {

        // Find inorder successor and its parent.
        var parsucc = ptr;
        var succ = ptr.right;

        // Find leftmost child of successor
        while (succ.lthread == false) {
          parsucc = succ;
          succ = succ.left;
        }

        ptr.info = succ.info;

        if (succ.lthread == true && succ.rthread == true)
          root = caseA(root, parsucc, succ);
        else root = caseB(root, parsucc, succ);

        return root;
      }

      // This code is contributed by gauravrajput1
</script>

Python3

# Here 'par' is pointer to parent Node and 'ptr' is
# pointer to current Node.
def caseC(root, par, ptr):

    # Find inorder successor and its parent.
    parsucc = ptr;
    succ = ptr.right;

    # Find leftmost child of successor
    while (succ.lthread == False):
        parsucc = succ;
        succ = succ.left;


    ptr.info = succ.info;

    if (succ.lthread == True and succ.rthread == True):
        root = caseA(root, parsucc, succ);
    else:
        root = caseB(root, parsucc, succ);

    return root;


# This code contributed by umadevi9616

Below is Complete code: 

C++

// Complete C++ program to demonstrate deletion
// in threaded BST
#include <bits/stdc++.h>
using namespace std;

struct Node {
    struct Node *left, *right;
    int info;

    // false if left pointer points to predecessor
    // in Inorder Traversal
    bool lthread;

    // false if right pointer points to predecessor
    // in Inorder Traversal
    bool rthread;
};

// Insert a Node in Binary Threaded Tree
struct Node* insert(struct Node* root, int ikey)
{
    // Searching for a Node with given value
    Node* ptr = root;
    Node* par = NULL; // Parent of key to be inserted
    while (ptr != NULL) {
        // If key already exists, return
        if (ikey == (ptr->info)) {
            printf("Duplicate Key !\n");
            return root;
        }

        par = ptr; // Update parent pointer

        // Moving on left subtree.
        if (ikey < ptr->info) {
            if (ptr->lthread == false)
                ptr = ptr->left;
            else
                break;
        }

        // Moving on right subtree.
        else {
            if (ptr->rthread == false)
                ptr = ptr->right;
            else
                break;
        }
    }

    // Create a new Node
    Node* tmp = new Node;
    tmp->info = ikey;
    tmp->lthread = true;
    tmp->rthread = true;

    if (par == NULL) {
        root = tmp;
        tmp->left = NULL;
        tmp->right = NULL;
    }
    else if (ikey < (par->info)) {
        tmp->left = par->left;
        tmp->right = par;
        par->lthread = false;
        par->left = tmp;
    }
    else {
        tmp->left = par;
        tmp->right = par->right;
        par->rthread = false;
        par->right = tmp;
    }

    return root;
}

// Returns inorder successor using left
// and right children (Used in deletion)
struct Node* inSucc(struct Node* ptr)
{
    if (ptr->rthread == true)
        return ptr->right;

    ptr = ptr->right;
    while (ptr->lthread == false)
        ptr = ptr->left;

    return ptr;
}

// Returns inorder successor using rthread
// (Used in inorder)
struct Node* inorderSuccessor(struct Node* ptr)
{
    // If rthread is set, we can quickly find
    if (ptr->rthread == true)
        return ptr->right;

    // Else return leftmost child of right subtree
    ptr = ptr->right;
    while (ptr->lthread == false)
        ptr = ptr->left;
    return ptr;
}

// Printing the threaded tree
void inorder(struct Node* root)
{
    if (root == NULL)
        printf("Tree is empty");

    // Reach leftmost Node
    struct Node* ptr = root;
    while (ptr->lthread == false)
        ptr = ptr->left;

    // One by one print successors
    while (ptr != NULL) {
        printf("%d ", ptr->info);
        ptr = inorderSuccessor(ptr);
    }
}

struct Node* inPred(struct Node* ptr)
{
    if (ptr->lthread == true)
        return ptr->left;

    ptr = ptr->left;
    while (ptr->rthread == false)
        ptr = ptr->right;
    return ptr;
}

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
struct Node* caseA(struct Node* root, struct Node* par,
                   struct Node* ptr)
{
    // If Node to be deleted is root
    if (par == NULL)
        root = NULL;

    // If Node to be deleted is left
    // of its parent
    else if (ptr == par->left) {
        par->lthread = true;
        par->left = ptr->left;
    }
    else {
        par->rthread = true;
        par->right = ptr->right;
    }

    // Free memory and return new root
    free(ptr);
    return root;
}

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
struct Node* caseB(struct Node* root, struct Node* par,
                   struct Node* ptr)
{
    struct Node* child;

    // Initialize child Node to be deleted has
    // left child.
    if (ptr->lthread == false)
        child = ptr->left;

    // Node to be deleted has right child.
    else
        child = ptr->right;

    // Node to be deleted is root Node.
    if (par == NULL)
        root = child;

    // Node is left child of its parent.
    else if (ptr == par->left)
        par->left = child;
    else
        par->right = child;

    // Find successor and predecessor
    Node* s = inSucc(ptr);
    Node* p = inPred(ptr);

    // If ptr has left subtree.
    if (ptr->lthread == false)
        p->right = s;

    // If ptr has right subtree.
    else {
        if (ptr->rthread == false)
            s->left = p;
    }

    free(ptr);
    return root;
}

// Here 'par' is pointer to parent Node and 'ptr' is
// pointer to current Node.
struct Node* caseC(struct Node* root, struct Node* par,
                   struct Node* ptr)
{
    // Find inorder successor and its parent.
    struct Node* parsucc = ptr;
    struct Node* succ = ptr->right;

    // Find leftmost child of successor
    while (succ->lthread==false) {
        parsucc = succ;
        succ = succ->left;
    }

    ptr->info = succ->info;

    if (succ->lthread == true && succ->rthread == true)
        root = caseA(root, parsucc, succ);
    else
        root = caseB(root, parsucc, succ);

    return root;
}

// Deletes a key from threaded BST with given root and
// returns new root of BST.
struct Node* delThreadedBST(struct Node* root, int dkey)
{
    // Initialize parent as NULL and ptrent
    // Node as root.
    struct Node *par = NULL, *ptr = root;

    // Set true if key is found
    int found = 0;

    // Search key in BST : find Node and its
    // parent.
    while (ptr != NULL) {
        if (dkey == ptr->info) {
            found = 1;
            break;
        }
        par = ptr;
        if (dkey < ptr->info) {
            if (ptr->lthread == false)
                ptr = ptr->left;
            else
                break;
        }
        else {
            if (ptr->rthread == false)
                ptr = ptr->right;
            else
                break;
        }
    }

    if (found == 0)
        printf("dkey not present in tree\n");

    // Two Children
    else if (ptr->lthread == false && ptr->rthread == false)
        root = caseC(root, par, ptr);

    // Only Left Child
    else if (ptr->lthread == false)
        root = caseB(root, par, ptr);

    // Only Right Child
    else if (ptr->rthread == false)
        root = caseB(root, par, ptr);

    // No child
    else
        root = caseA(root, par, ptr);

    return root;
}

// Driver Program
int main()
{
    struct Node* root = NULL;

    root = insert(root, 20);
    root = insert(root, 10);
    root = insert(root, 30);
    root = insert(root, 5);
    root = insert(root, 16);
    root = insert(root, 14);
    root = insert(root, 17);
    root = insert(root, 13);

    root = delThreadedBST(root, 20);
    inorder(root);

    return 0;
}

Java

// Complete Java program to demonstrate deletion
// in threaded BST
import java.util.*;
class solution {

    static class Node {
        Node left, right;
        int info;

        // True if left pointer points to predecessor
        // in Inorder Traversal
        boolean lthread;

        // True if right pointer points to predecessor
        // in Inorder Traversal
        boolean rthread;
    };

    // Insert a Node in Binary Threaded Tree
    static Node insert(Node root, int ikey)
    {
        // Searching for a Node with given value
        Node ptr = root;
        Node par = null; // Parent of key to be inserted
        while (ptr != null) {
            // If key already exists, return
            if (ikey == (ptr.info)) {
                System.out.printf("Duplicate Key !\n");
                return root;
            }

            par = ptr; // Update parent pointer

            // Moving on left subtree.
            if (ikey < ptr.info) {
                if (ptr.lthread == false)
                    ptr = ptr.left;
                else
                    break;
            }

            // Moving on right subtree.
            else {
                if (ptr.rthread == false)
                    ptr = ptr.right;
                else
                    break;
            }
        }

        // Create a new Node
        Node tmp = new Node();
        tmp.info = ikey;
        tmp.lthread = true;
        tmp.rthread = true;

        if (par == null) {
            root = tmp;
            tmp.left = null;
            tmp.right = null;
        }
        else if (ikey < (par.info)) {
            tmp.left = par.left;
            tmp.right = par;
            par.lthread = false;
            par.left = tmp;
        }
        else {
            tmp.left = par;
            tmp.right = par.right;
            par.rthread = false;
            par.right = tmp;
        }

        return root;
    }

    // Returns inorder successor using left
    // and right children (Used in deletion)
    static Node inSucc(Node ptr)
    {
        if (ptr.rthread == true)
            return ptr.right;

        ptr = ptr.right;
        while (ptr.lthread == false)
            ptr = ptr.left;

        return ptr;
    }

    // Returns inorder successor using rthread
    // (Used in inorder)
    static Node inorderSuccessor(Node ptr)
    {
        // If rthread is set, we can quickly find
        if (ptr.rthread == true)
            return ptr.right;

        // Else return leftmost child of right subtree
        ptr = ptr.right;
        while (ptr.lthread == false)
            ptr = ptr.left;
        return ptr;
    }

    // Printing the threaded tree
    static void inorder(Node root)
    {
        if (root == null)
            System.out.printf("Tree is empty");

        // Reach leftmost Node
        Node ptr = root;
        while (ptr.lthread == false)
            ptr = ptr.left;

        // One by one print successors
        while (ptr != null) {
            System.out.printf("%d ", ptr.info);
            ptr = inorderSuccessor(ptr);
        }
    }

    static Node inPred(Node ptr)
    {
        if (ptr.lthread == true)
            return ptr.left;

        ptr = ptr.left;
        while (ptr.rthread == false)
            ptr = ptr.right;
        return ptr;

    }

    // Here 'par' is pointer to parent Node and 'ptr' is
    // pointer to current Node.
    static Node caseA(Node root, Node par,
                      Node ptr)
    {
        // If Node to be deleted is root
        if (par == null)
            root = null;

        // If Node to be deleted is left
        // of its parent
        else if (ptr == par.left) {
            par.lthread = true;
            par.left = ptr.left;
        }
        else {
            par.rthread = true;
            par.right = ptr.right;
        }

        return root;
    }

    // Here 'par' is pointer to parent Node and 'ptr' is
    // pointer to current Node.
    static Node caseB(Node root, Node par,
                      Node ptr)
    {
        Node child;

        // Initialize child Node to be deleted has
        // left child.
        if (ptr.lthread == false)
            child = ptr.left;

        // Node to be deleted has right child.
        else
            child = ptr.right;

        // Node to be deleted is root Node.
        if (par == null)
            root = child;

        // Node is left child of its parent.
        else if (ptr == par.left)
            par.left = child;
        else
            par.right = child;

        // Find successor and predecessor
        Node s = inSucc(ptr);
        Node p = inPred(ptr);

        // If ptr has left subtree.
        if (ptr.lthread == false)
            p.right = s;

        // If ptr has right subtree.
        else {
            if (ptr.rthread == false)
                s.left = p;
        }

        return root;
    }

    // Here 'par' is pointer to parent Node and 'ptr' is
    // pointer to current Node.
    static Node caseC(Node root, Node par,
                      Node ptr)
    {
        // Find inorder successor and its parent.
        Node parsucc = ptr;
        Node succ = ptr.right;

        // Find leftmost child of successor
        while (succ.lthread == false) {
            parsucc = succ;
            succ = succ.left;
        }

        ptr.info = succ.info;

        if (succ.lthread == true && succ.rthread == true)
            root = caseA(root, parsucc, succ);
        else
            root = caseB(root, parsucc, succ);

        return root;
    }

    // Deletes a key from threaded BST with given root and
    // returns new root of BST.
    static Node delThreadedBST(Node root, int dkey)
    {
        // Initialize parent as null and ptrent
        // Node as root.
        Node par = null, ptr = root;

        // Set true if key is found
        int found = 0;

        // Search key in BST : find Node and its
        // parent.
        while (ptr != null) {
            if (dkey == ptr.info) {
                found = 1;
                break;
            }
            par = ptr;
            if (dkey < ptr.info) {
                if (ptr.lthread == false)
                    ptr = ptr.left;
                else
                    break;
            }
            else {
                if (ptr.rthread == false)
                    ptr = ptr.right;
                else
                    break;
            }
        }

        if (found == 0)
            System.out.printf("dkey not present in tree\n");

        // Two Children
        else if (ptr.lthread == false && ptr.rthread == false)
            root = caseC(root, par, ptr);

        // Only Left Child
        else if (ptr.lthread == false)
            root = caseB(root, par, ptr);

        // Only Right Child
        else if (ptr.rthread == false)
            root = caseB(root, par, ptr);

        // No child
        else
            root = caseA(root, par, ptr);

        return root;
    }

    // Driver Program
    public static void main(String args[])
    {
        Node root = null;

        root = insert(root, 20);
        root = insert(root, 10);
        root = insert(root, 30);
        root = insert(root, 5);
        root = insert(root, 16);
        root = insert(root, 14);
        root = insert(root, 17);
        root = insert(root, 13);

        root = delThreadedBST(root, 20);
        inorder(root);
    }
}
// This code is contributed by Arnab Kundu

Python3

# Complete Python program to demonstrate deletion
# in threaded BST

class Node:
    def __init__(self):
        self.info = 0;
        self.left = None;
        self.right = None;

        # True if left pointer points to predecessor
        # in Inorder Traversal
        self.lthread = False;

        # True if right pointer points to predecessor
        # in Inorder Traversal
        self.rthread = False;

# Insert a Node in Binary Threaded Tree
def insert(root, ikey):

    # Searching for a Node with given value
    ptr = root;
    par = None; # Parent of key to be inserted
    while (ptr != None):

        # If key already exists, return
        if (ikey == (ptr.info)):
            print("Duplicate Key !");
            return root;


        par = ptr; # Update parent pointer

        # Moving on left subtree.
        if (ikey < ptr.info):
            if (ptr.lthread == False):
                ptr = ptr.left;
            else:
                break;

        # Moving on right subtree.
        else:
            if (ptr.rthread == False):
                ptr = ptr.right;
            else:
                break;

    # Create a new Node
    tmp = Node();
    tmp.info = ikey;
    tmp.lthread = True;
    tmp.rthread = True;

    if (par == None):
        root = tmp;
        tmp.left = None;
        tmp.right = None;
    elif(ikey < (par.info)):
        tmp.left = par.left;
        tmp.right = par;
        par.lthread = False;
        par.left = tmp;
    else:
        tmp.left = par;
        tmp.right = par.right;
        par.rthread = False;
        par.right = tmp;

    return root;

# Returns inorder successor using left
# and right children (Used in deletion)
def inSucc(ptr):
    if (ptr.rthread == True):
        return ptr.right;

    ptr = ptr.right;
    while (ptr.lthread == False):
        ptr = ptr.left;

    return ptr;

# Returns inorder successor using rthread
# (Used in inorder)
def inorderSuccessor(ptr):

    # If rthread is set, we can quickly find
    if (ptr.rthread == True):
        return ptr.right;

    # Else return leftmost child of right subtree
    ptr = ptr.right;
    while (ptr.lthread == False):
        ptr = ptr.left;
    return ptr;

# Printing the threaded tree
def inorder(root):
    if (root == None):
        print("Tree is empty");

    # Reach leftmost Node
    ptr = root;
    while (ptr.lthread == False):
        ptr = ptr.left;

    # One by one print successors
    while (ptr != None):
        print( ptr.info, end=" ");
        ptr = inorderSuccessor(ptr);

def inPred(ptr):
    if (ptr.lthread == True):
        return ptr.left;

    ptr = ptr.left;
    while (ptr.rthread == False):
        ptr = ptr.right;
    return ptr;

# Here 'par' is pointer to parent Node and 'ptr' is
# pointer to current Node.
def caseA(root, par, ptr):

    # If Node to be deleted is root
    if (par == None):
        root = None;

    # If Node to be deleted is left
    # of its parent
    elif(ptr == par.left):
        par.lthread = True;
        par.left = ptr.left;
    else:
        par.rthread = True;
        par.right = ptr.right;

    return root;

# Here 'par' is pointer to parent Node and 'ptr' is
# pointer to current Node.
def caseB(root, par, ptr):
    child;

    # Initialize child Node to be deleted has
    # left child.
    if (ptr.lthread == False):
        child = ptr.left;

    # Node to be deleted has right child.
    else:
        child = ptr.right;

    # Node to be deleted is root Node.
    if (par == None):
        root = child;

    # Node is left child of its parent.
    elif(ptr == par.left):
        par.left = child;
    else:
        par.right = child;

    # Find successor and predecessor
    s = inSucc(ptr);
    p = inPred(ptr);

    # If ptr has left subtree.
    if (ptr.lthread == False):
        p.right = s;

    # If ptr has right subtree.
    else:
        if (ptr.rthread == False):
            s.left = p;
    return root;

# Here 'par' is pointer to parent Node and 'ptr' is
# pointer to current Node.
def caseC(root, par, ptr):

    # Find inorder successor and its parent.
    parsucc = ptr;
    succ = ptr.right;

    # Find leftmost child of successor
    while (succ.lthread == False):
        parsucc = succ;
        succ = succ.left;

    ptr.info = succ.info;

    if (succ.lthread == True and succ.rthread == True):
        root = caseA(root, parsucc, succ);
    else:
        root = caseB(root, parsucc, succ);

    return root;

# Deletes a key from threaded BST with given root and
# returns new root of BST.
def delThreadedBST(root, dkey):

    # Initialize parent as None and ptrent
    # Node as root.
    par = None;
    ptr = root;

    # Set True if key is found
    found = 0;

    # Search key in BST : find Node and its
    # parent.
    while (ptr != None):
        if (dkey == ptr.info):
            found = 1;
            break;

        par = ptr;
        if (dkey < ptr.info):
            if (ptr.lthread == False):
                ptr = ptr.left;
            else:
                break;
        else:
            if (ptr.rthread == False):
                ptr = ptr.right;
            else:
                break;

    if (found == 0):
        print("dkey not present in tree");

    # Two Children
    elif(ptr.lthread == False and ptr.rthread == False):
        root = caseC(root, par, ptr);

    # Only Left Child
    elif(ptr.lthread == False):
        root = caseB(root, par, ptr);

    # Only Right Child
    elif(ptr.rthread == False):
        root = caseB(root, par, ptr);

    # No child
    else:
        root = caseA(root, par, ptr);

    return root;

# Driver Program
if __name__ == '__main__':
    root = None;

    root = insert(root, 20);
    root = insert(root, 10);
    root = insert(root, 30);
    root = insert(root, 5);
    root = insert(root, 16);
    root = insert(root, 14);
    root = insert(root, 17);
    root = insert(root, 13);

    root = delThreadedBST(root, 20);
    inorder(root);

# This code is contributed by Rajput-Ji

C#

// Complete C# program to demonstrate deletion
// in threaded BST
using System;

class GFG {

    public class Node {
        public Node left, right;
        public int info;

        // True if left pointer points to predecessor
        // in Inorder Traversal
        public bool lthread;

        // True if right pointer points to predecessor
        // in Inorder Traversal
        public bool rthread;
    };

    // Insert a Node in Binary Threaded Tree
    static Node insert(Node root, int ikey)
    {
        // Searching for a Node with given value
        Node ptr = root;
        Node par = null; // Parent of key to be inserted
        while (ptr != null) {
            // If key already exists, return
            if (ikey == (ptr.info)) {
                Console.Write("Duplicate Key !\n");
                return root;
            }

            par = ptr; // Update parent pointer

            // Moving on left subtree.
            if (ikey < ptr.info) {
                if (ptr.lthread == false)
                    ptr = ptr.left;
                else
                    break;
            }

            // Moving on right subtree.
            else {
                if (ptr.rthread == false)
                    ptr = ptr.right;
                else
                    break;
            }
        }

        // Create a new Node
        Node tmp = new Node();
        tmp.info = ikey;
        tmp.lthread = true;
        tmp.rthread = true;

        if (par == null) {
            root = tmp;
            tmp.left = null;
            tmp.right = null;
        }
        else if (ikey < (par.info)) {
            tmp.left = par.left;
            tmp.right = par;
            par.lthread = false;
            par.left = tmp;
        }
        else {
            tmp.left = par;
            tmp.right = par.right;
            par.rthread = false;
            par.right = tmp;
        }

        return root;
    }

    // Returns inorder successor using left
    // and right children (Used in deletion)
    static Node inSucc(Node ptr)
    {
        if (ptr.rthread == true)
            return ptr.right;

        ptr = ptr.right;
        while (ptr.lthread == false)
            ptr = ptr.left;

        return ptr;
    }

    // Returns inorder successor using rthread
    // (Used in inorder)
    static Node inorderSuccessor(Node ptr)
    {
        // If rthread is set, we can quickly find
        if (ptr.rthread == true)
            return ptr.right;

        // Else return leftmost child of right subtree
        ptr = ptr.right;
        while (ptr.lthread == false)
            ptr = ptr.left;
        return ptr;
    }

    // Printing the threaded tree
    static void inorder(Node root)
    {
        if (root == null)
            Console.Write("Tree is empty");

        // Reach leftmost Node
        Node ptr = root;
        while (ptr.lthread == false)
            ptr = ptr.left;

        // One by one print successors
        while (ptr != null) {
            Console.Write("{0} ", ptr.info);
            ptr = inorderSuccessor(ptr);
        }
    }

    static Node inPred(Node ptr)
    {
        if (ptr.lthread == true)
            return ptr.left;

        ptr = ptr.left;
        while (ptr.rthread == false)
            ptr = ptr.right;
        return ptr;
    }

    // Here 'par' is pointer to parent Node and 'ptr' is
    // pointer to current Node.
    static Node caseA(Node root, Node par,
                      Node ptr)
    {
        // If Node to be deleted is root
        if (par == null)
            root = null;

        // If Node to be deleted is left
        // of its parent
        else if (ptr == par.left) {
            par.lthread = true;
            par.left = ptr.left;
        }
        else {
            par.rthread = true;
            par.right = ptr.right;
        }

        return root;
    }

    // Here 'par' is pointer to parent Node and 'ptr' is
    // pointer to current Node.
    static Node caseB(Node root, Node par,
                      Node ptr)
    {
        Node child;

        // Initialize child Node to be deleted has
        // left child.
        if (ptr.lthread == false)
            child = ptr.left;

        // Node to be deleted has right child.
        else
            child = ptr.right;

        // Node to be deleted is root Node.
        if (par == null)
            root = child;

        // Node is left child of its parent.
        else if (ptr == par.left)
            par.left = child;
        else
            par.right = child;

        // Find successor and predecessor
        Node s = inSucc(ptr);
        Node p = inPred(ptr);

        // If ptr has left subtree.
        if (ptr.lthread == false)
            p.right = s;

        // If ptr has right subtree.
        else {
            if (ptr.rthread == false)
                s.left = p;
        }

        return root;
    }

    // Here 'par' is pointer to parent Node and 'ptr' is
    // pointer to current Node.
    static Node caseC(Node root, Node par,
                      Node ptr)
    {
        // Find inorder successor and its parent.
        Node parsucc = ptr;
        Node succ = ptr.right;

        // Find leftmost child of successor
        while (succ.lthread == false) {
            parsucc = succ;
            succ = succ.left;
        }

        ptr.info = succ.info;

        if (succ.lthread == true && succ.rthread == true)
            root = caseA(root, parsucc, succ);
        else
            root = caseB(root, parsucc, succ);

        return root;
    }

    // Deletes a key from threaded BST with given root and
    // returns new root of BST.
    static Node delThreadedBST(Node root, int dkey)
    {
        // Initialize parent as null and ptrent
        // Node as root.
        Node par = null, ptr = root;

        // Set true if key is found
        int found = 0;

        // Search key in BST : find Node and its
        // parent.
        while (ptr != null) {
            if (dkey == ptr.info) {
                found = 1;
                break;
            }
            par = ptr;
            if (dkey < ptr.info) {
                if (ptr.lthread == false)
                    ptr = ptr.left;
                else
                    break;
            }
            else {
                if (ptr.rthread == false)
                    ptr = ptr.right;
                else
                    break;
            }
        }

        if (found == 0)
            Console.Write("dkey not present in tree\n");

        // Two Children
        else if (ptr.lthread == false && ptr.rthread == false)
            root = caseC(root, par, ptr);

        // Only Left Child
        else if (ptr.lthread == false)
            root = caseB(root, par, ptr);

        // Only Right Child
        else if (ptr.rthread == false)
            root = caseB(root, par, ptr);

        // No child
        else
            root = caseA(root, par, ptr);

        return root;
    }

    // Driver code
    public static void Main(String[] args)
    {
        Node root = null;

        root = insert(root, 20);
        root = insert(root, 10);
        root = insert(root, 30);
        root = insert(root, 5);
        root = insert(root, 16);
        root = insert(root, 14);
        root = insert(root, 17);
        root = insert(root, 13);

        root = delThreadedBST(root, 20);
        inorder(root);
    }
}

// This code has been contributed by 29AjayKumar

Javascript

<script>

      // Complete JavaScript program to demonstrate deletion
      // in threaded BST
      class Node {
        constructor() {
          this.info = 0;
          // True if left pointer points to predecessor
          // in Inorder Traversal
          this.lthread = false;
          // True if right pointer points to predecessor
          // in Inorder Traversal
          this.rthread = false;
          this.left = null;
          this.right = null;
        }
      }

      // Insert a Node in Binary Threaded Tree
      function insert(root, ikey) {
        // Searching for a Node with given value
        var ptr = root;
        var par = null; // Parent of key to be inserted
        while (ptr != null) {
          // If key already exists, return
          if (ikey == ptr.info) {
            document.write("Duplicate Key !<br>");
            return root;
          }

          par = ptr; // Update parent pointer

          // Moving on left subtree.
          if (ikey < ptr.info) {
            if (ptr.lthread == false) ptr = ptr.left;
            else break;
          }

          // Moving on right subtree.
          else {
            if (ptr.rthread == false) ptr = ptr.right;
            else break;
          }
        }

        // Create a new Node
        var tmp = new Node();
        tmp.info = ikey;
        tmp.lthread = true;
        tmp.rthread = true;

        if (par == null) {
          root = tmp;
          tmp.left = null;
          tmp.right = null;
        } else if (ikey < par.info) {
          tmp.left = par.left;
          tmp.right = par;
          par.lthread = false;
          par.left = tmp;
        } else {
          tmp.left = par;
          tmp.right = par.right;
          par.rthread = false;
          par.right = tmp;
        }

        return root;
      }

      // Returns inorder successor using left
      // and right children (Used in deletion)
      function inSucc(ptr) {
        if (ptr.rthread == true) return ptr.right;

        ptr = ptr.right;
        while (ptr.lthread == false) ptr = ptr.left;

        return ptr;
      }

      // Returns inorder successor using rthread
      // (Used in inorder)
      function inorderSuccessor(ptr) {
        // If rthread is set, we can quickly find
        if (ptr.rthread == true) return ptr.right;

        // Else return leftmost child of right subtree
        ptr = ptr.right;
        while (ptr.lthread == false) ptr = ptr.left;
        return ptr;
      }

      // Printing the threaded tree
      function inorder(root) {
        if (root == null) document.write("Tree is empty");

        // Reach leftmost Node
        var ptr = root;
        while (ptr.lthread == false) ptr = ptr.left;

        // One by one print successors
        while (ptr != null) {
          document.write(ptr.info + " ");
          ptr = inorderSuccessor(ptr);
        }
      }

      function inPred(ptr) {
        if (ptr.lthread == true) return ptr.left;

        ptr = ptr.left;
        while (ptr.rthread == false) ptr = ptr.right;
        return ptr;
      }

      // Here 'par' is pointer to parent Node and 'ptr' is
      // pointer to current Node.
      function caseA(root, par, ptr) {
        // If Node to be deleted is root
        if (par == null) root = null;
        // If Node to be deleted is left
        // of its parent
        else if (ptr == par.left) {
          par.lthread = true;
          par.left = ptr.left;
        } else {
          par.rthread = true;
          par.right = ptr.right;
        }

        return root;
      }

      // Here 'par' is pointer to parent Node and 'ptr' is
      // pointer to current Node.
      function caseB(root, par, ptr) {
        var child;

        // Initialize child Node to be deleted has
        // left child.
        if (ptr.lthread == false) child = ptr.left;
        // Node to be deleted has right child.
        else child = ptr.right;

        // Node to be deleted is root Node.
        if (par == null) root = child;
        // Node is left child of its parent.
        else if (ptr == par.left) par.left = child;
        else par.right = child;

        // Find successor and predecessor
        var s = inSucc(ptr);
        var p = inPred(ptr);

        // If ptr has left subtree.
        if (ptr.lthread == false) p.right = s;
        // If ptr has right subtree.
        else {
          if (ptr.rthread == false) s.left = p;
        }

        return root;
      }

      // Here 'par' is pointer to parent Node and 'ptr' is
      // pointer to current Node.
      function caseC(root, par, ptr) {
        // Find inorder successor and its parent.
        var parsucc = ptr;
        var succ = ptr.right;

        // Find leftmost child of successor
        while (succ.lthread == false) {
          parsucc = succ;
          succ = succ.left;
        }

        ptr.info = succ.info;

        if (succ.lthread == true && succ.rthread == true)
          root = caseA(root, parsucc, succ);
        else root = caseB(root, parsucc, succ);

        return root;
      }

      // Deletes a key from threaded BST with given root and
      // returns new root of BST.
      function delThreadedBST(root, dkey) {
        // Initialize parent as null and ptrent
        // Node as root.
        var par = null,
          ptr = root;

        // Set true if key is found
        var found = 0;

        // Search key in BST : find Node and its
        // parent.
        while (ptr != null) {
          if (dkey == ptr.info) {
            found = 1;
            break;
          }
          par = ptr;
          if (dkey < ptr.info) {
            if (ptr.lthread == false)
            ptr = ptr.left;
            else break;
          } else {
            if (ptr.rthread == false)
            ptr = ptr.right;
            else break;
          }
        }

        if (found == 0)
        document.write("dkey not present in tree<br>");
        // Two Children
        else if (ptr.lthread == false && ptr.rthread == false)
          root = caseC(root, par, ptr);
        // Only Left Child
        else if (ptr.lthread == false)
        root = caseB(root, par, ptr);
        // Only Right Child
        else if (ptr.rthread == false)
        root = caseB(root, par, ptr);
        // No child
        else root = caseA(root, par, ptr);

        return root;
      }

      // Driver code
      var root = null;

      root = insert(root, 20);
      root = insert(root, 10);
      root = insert(root, 30);
      root = insert(root, 5);
      root = insert(root, 16);
      root = insert(root, 14);
      root = insert(root, 17);
      root = insert(root, 13);

      root = delThreadedBST(root, 20);
      inorder(root);

</script>

Output

5 10 13 14 16 17 30 

This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.