C++ Program to Implement Threaded Binary Tree

Threaded binary tree is a binary tree that provides the facility to traverse the tree in a particular order.

It makes inorder traversal faster and do it without stack and without recursion. There are two types of threaded binary trees.

Single Threaded Each node is threaded towards either left or right means in-order predecessor or successor. Here, all right null pointers will point to inorder successor or all left null pointers will point to inorder predecessor.

Double threaded Each node is threaded towards either left and right means in-order predecessor and successor. Here, all right null pointers will point to inorder successor and all left null pointers will point to inorder predecessor.

This is a C++ program to implement Threaded Binary Tree.

Functions and pseudocodes

function insert()

Insert node as root if tree is completely empty.
Otherwise, if newnode < current node then
   Go to left thread and set the newnode as left child.
else
   Go to right thread and set the newnode as right child.

function search()

If search key < root then
   Go to left thread
else
   Go to right thread

function delete()

Find Node and its parent. For deleting node there are three cases −

• Node which has two children.
• Has only left child.
• Has only right child.

Example

#include <iostream>
#include <cstdlib>
#define MAX_VALUE 65536
using namespace std;
class N { //node declaration
   public:
      int k;
   N *l, *r;
   bool leftTh, rightTh;
};
class ThreadedBinaryTree {
   private:
   N *root;
   public:
   ThreadedBinaryTree() { //constructor to initialize the variables
      root= new N();
      root->r= root->l= root;
      root->leftTh = true;
      root->k = MAX_VALUE;
   }
   void makeEmpty() { //clear tree
      root= new N();
      root->r = root->l = root;
      root->leftTh = true;
      root->k = MAX_VALUE;
   }
   void insert(int key) {
      N *p = root;
      for (;;) {
         if (p->k< key) { / /move to right thread
            if (p->rightTh)
               break;
            p = p->r;
         } else if (p->k > key) { // move to left thread
            if (p->leftTh)
               break;
            p = p->l;
         } else {
            return;
         }
      }
      N *temp = new N();
      temp->k = key;
      temp->rightTh= temp->leftTh= true;
      if (p->k < key) {
         temp->r = p->r;
         temp->l= p;
         p->r = temp;
         p->rightTh= false;
      } else {
         temp->r = p;
         temp->l = p->l;
         p->l = temp;
         p->leftTh = false;
      }
   }
   bool search(int key) {
      N *temp = root->l;
      for (;;) {
      if (temp->k < key) { //search in left thread
      if (temp->rightTh)
            return false;
         temp = temp->r;
      } else if (temp->k > key) { //search in right thread
         if (temp->leftTh)
            return false;
         temp = temp->l;
      } else {
         return true;
      }
   }
}
void Delete(int key) {
   N *dest = root->l, *p = root;
   for (;;) { //find Node and its parent.
      if (dest->k < key) {
         if (dest->rightTh)
            return;
         p = dest;
         dest = dest->r;
      } else if (dest->k > key) {
         if (dest->leftTh)
            return;
         p = dest;
         dest = dest->l;
      } else {
         break;
      }
   }
   N *target = dest;
   if (!dest->rightTh && !dest->leftTh) {
      p = dest;  //has two children
      target = dest->l;   //largest node at left child
      while (!target->rightTh) {
         p = target;
         target = target->r;
      }
      dest->k= target->k; //replace mode
   }
   if (p->k >= target->k) { //only left child
      if (target->rightTh && target->leftTh) {
         p->l = target->l;
         p->leftTh = true;
      } else if (target->rightTh) {
         N*largest = target->l;
         while (!largest->rightTh) {
            largest = largest->r;
         }
         largest->r = p;
         p->l= target->l;
      } else {
         N *smallest = target->r;
         while (!smallest->leftTh) {
            smallest = smallest->l;
         }
         smallest->l = target->l;
         p->l = target->r;
      }
   } else {//only right child
      if (target->rightTh && target->leftTh) {
         p->r= target->r;
         p->rightTh = true;
      } else if (target->rightTh) {
         N *largest = target->l;
         while (!largest->rightTh) {
            largest = largest->r;
         }
         largest->r= target->r;
         p->r = target->l;
      } else {
         N *smallest = target->r;
         while (!smallest->leftTh) {
            smallest = smallest->l;
         }
         smallest->l= p;
         p->r= target->r;
      }
   }
}
void displayTree() { //print the tree
   N *temp = root, *p;
   for (;;) {
      p = temp;
      temp = temp->r;
      if (!p->rightTh) {
         while (!temp->leftTh) {
            temp = temp->l;
         }
      }
      if (temp == root)
         break;
      cout<<temp->k<<" ";
   }
   cout<<endl;
}
};
int main() {
   ThreadedBinaryTree tbt;
   cout<<"ThreadedBinaryTree\n";
   char ch;
   int c, v;  
   while(1) {
      cout<<"1. Insert "<<endl;
      cout<<"2. Delete"<<endl;
      cout<<"3. Search"<<endl;
      cout<<"4. Clear"<<endl;
      cout<<"5. Display"<<endl;
      cout<<"6. Exit"<<endl;
      cout<<"Enter Your Choice: ";
      cin>>c;
      //perform switch operation
      switch (c) {
         case 1 :
            cout<<"Enter integer element to insert: ";
            cin>>v;
            tbt.insert(v);
            break;
         case 2 :
            cout<<"Enter integer element to delete: ";
            cin>>v;
            tbt.Delete(v);
            break;
         case 3 :
            cout<<"Enter integer element to search: ";
            cin>>v;
            if (tbt.search(v) == true)
               cout<<"Element "<<v<<" found in the tree"<<endl;
            else
               cout<<"Element "<<v<<" not found in the tree"<<endl;
            break;
         case 4 :
            cout<<"\nTree Cleared\n";
            tbt.makeEmpty();
            break;
         case 5:
            cout<<"Display tree: \n ";
            tbt.displayTree();
            break;
         case 6:
            exit(1);
         default:
            cout<<"\nInvalid type! \n";
      }
   }
   cout<<"\n";
   return 0;
}

Output

ThreadedBinaryTree
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 1
Enter integer element to insert: 10
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 1
Enter integer element to insert: 7
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 1
Enter integer element to insert: 6
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 1
Enter integer element to insert: 4
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 1
Enter integer element to insert: 5
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 1
Enter integer element to insert: 3
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 5
Display tree
3 4 5 6 7 10
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 3
Enter integer element to search: 7
Element 7 found in the tree
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 3
Enter integer element to search: 1
Element 1 not found in the tree
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 2
Enter integer element to delete: 3
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 5
Display tree
4 5 6 7 10
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 4

Tree Cleared
1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 5
Display tree

1. Insert
2. Delete
3. Search
4. Clear
5. Display
6. Exit
Enter Your Choice: 6