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Threaded Binary Trees

You can download the complete program from here
 
Binary trees need to be traversed using recursion. All the three methods of traversal - inorder, preorder and post order methods employ recursion.

Recursion needs stack storage. In cases where the tree is highly unbalanced, the cost on this traversal would be high.

It would be nice where one could traverse a binary tree without using recursion.

That is where a threaded tree comes into picture. This utilizes the pointers which are wasted on leaf nodes and uses these to save threads pointing to inorder successor or inorder predecessor.

In the diagram above, node A does not have right child. Instead of NULL, a link to B is stored in A->right. Remember that B is the inorder successor of A. Similarly C does not have child nodes. So it has link to predecessor B as left thread and link to D as right thread.

Only A has left link as NULL because A has no predecessor. And I has no successor, so it has right link as NULL.

Types of threaded binary tree

A threaded binary tree can be single or double. A single threaded tree will have either in order successor for   nodes which do  not have a right children or in order predecessor for  nodes which do not have a left children. But not both.

Whereas a double threaded binary tree will have a thread for in order successor, and another thread for in order predecessor whenever a node does not have a left and right child nodes.

The diagram shown above is a double threaded binary tree.

Structure of threaded binary tree node


To differentiate between a thread and a link to child, a boolean is  used. So the threaded tree node will have two extra fields. I have called them  isleftthread and isrightthread. If isleftthread is 1, node->left is a thread to in order successor and it is not a link to child node. But if this value is 0, node->left is a link to left child.

Similarly if node->isrightthread is 1, node->right is a thread. If it is 0, node->right is a child node link.

struct node
{
    int val;
    struct node *left;
    struct node *right;
    int isleftthread;
    int isrightthread;
};


To insert a node into such a tree, you need to do the following
  1. node = root
  2. if node->val > key value, branch to left 
  3. if node->val <key value,  branch to right
  4. Repeat 2 to 3 until you  get a thread (thread means there is no child node present. which means we can insert the new node there)
  5. link the parent to newnode
  6. if newnode is right child of parent
    1. set newnode->right as parent->right (thread)
    2. set newnode->left as parent (thread)
    3. set parent->right as newnode (child)
    4. set parent->isrightthread as 0(false)
  7. if newnode is left child of parent
    1. set newnode->left as parent->left (thread)
    2. set newnode->right as parent (thread)
    3. set parent->left as newnode (child)
    4. set parent->isleftthread as 0(false)
Here is the C code for insert a value into threaded binary tree

NODEPTR insert_node(NODEPTR nd,NODEPTR newnode)
{
     NODEPTR parent = nd;
     NODEPTR root = nd;
     if(root == NULL)
        return newnode;
     while(nd!=NULL)
     {
 
        parent = nd;
        if(newnode->val > nd->val)
        {
        if(nd->isrightthread)
        {
           nd = nd->right;
           break;
         }
        else
           nd = nd->right; 
     }
  
    else if(newnode->val <nd->val){
        if(nd->isleftthread)
        {
          nd = nd->left;
          break;
        }
        else
                 nd = nd->left;
     }
        else
            {
              printf("Duplicate values not allowed");
              return NULL;
            }
     }

Next let us see how we can traverse such a threaded binary tree in order without using recursion.

  1. Traverse to the left most node and find the minimum of the tree.
  2. From this node, use the right link to traverse. 
  3. Repeat until NULL is encountered. 
And here is the code for inorder traversal of threaded binary tree.

void in_order(NODEPTR nd)
{
    /* find extreme left node*/
    while(!nd->isleftthread)
 nd = nd->left;
   /* traverse all nodes till extreme right end*/
    while(nd)
 {
   printf("%d  ",nd->val);
   if(nd->isrightthread)
             nd = nd->right;
          else 
            {
              nd = nd->right;
              while(nd!=NULL && !nd->isleftthread)
                nd = nd->left;
           }
 } 
}
Now we are ready to write the complete program.


#include<stdio.h>
#include<stdlib.h>
struct node
{
   int val;
   struct node *left;
   struct node *right;
   int isleftthread;
   int isrightthread;
};
typedef struct node *NODEPTR;

NODEPTR create_node(int num)
{
     NODEPTR temp = (NODEPTR)malloc(sizeof(struct node));
     temp->val = num;
     temp->left = NULL;
     temp->right = NULL;
     temp->isleftthread = 1;
     temp->isrightthread = 1;
     return temp;
}

NODEPTR insert_node(NODEPTR nd,NODEPTR newnode)
{
     NODEPTR parent = nd;
     NODEPTR root = nd;
     if(root == NULL)
        return newnode;
     while(nd!=NULL)
     {
 
 parent = nd;
        if(newnode->val > nd->val)
  {
    if(nd->isrightthread)
   {
   nd = nd->right;
   break;
  }
  else
   nd = nd->right; 
   }
  
        else if(newnode->val <nd->val){
         if(nd->isleftthread)
   {
   nd = nd->left;
   break;
   }
  else
                 nd = nd->left;
  }
        else
            {
  printf("Duplicate values not allowed");
  return NULL;
            }
     }
     if(newnode->val >parent->val)
 {
 newnode->right = parent->right;
 parent->right = newnode;
 parent->isrightthread=0;
 newnode->left = parent;
 }
     else
 {
 newnode->left = parent->left;
  parent->left = newnode;
 parent->isleftthread = 0;
 newnode->right = parent;
 }
     return root;
}
void in_order(NODEPTR nd)
{
    /* find extreme left node*/
    while(!nd->isleftthread)
 nd = nd->left;
   /* traverse all nodes till extreme right end*/
    while(nd)
 {
   printf("%d  ",nd->val);
   if(nd->isrightthread)
             nd = nd->right;
          else 
            {
              nd = nd->right;
              while(nd!=NULL && !nd->isleftthread)
                nd = nd->left;
           }
 } 
}

void pre_order(NODEPTR nd)
{
   if(nd!=NULL)
    {
        printf("%d---",nd->val);   
        pre_order(nd->left);
        pre_order(nd->right);
            
     }
} 
 
int main()
{
       NODEPTR root=NULL,delnode; 
       int n;
       do
       {
           NODEPTR newnode;
           printf("Enter value of node(-1 to exit):");
           scanf("%d",&n);
           if(n!=-1)
            {  
               newnode = create_node(n);
               root = insert_node(root,newnode);
             }
       } while (n!=-1);
       
       printf("\nInorder traversal\n");
       in_order(root);   
       return 0;
}
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