Skip to main content

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;
}
Labels:

Comments

Post a Comment

Popular posts from this blog

Delete a node from doubly linked list

Deletion operation in DLL is simpler when compared to SLL. Because we don't have to go in search of previous node of to-be-deleted node.  Here is how you delete a node Link previous node of node of to-be-deleted to next node. Link next node of node of to-be-deleted to previous node. Free the memory of node of to-be-deleted Simple, isn't it. The code can go like this. prevnode = delnode->prev; nextnode = delnode->next; prevnode->next = nextnode; nextnode->prev = prevnode; free(delnode); And that is it. The node delnode is deleted. But we should always consider boundary conditions. What happens if we are trying to delete the first node or last node? If first node is to be deleted, its previous node is NULL. Hence step 3 should not be used.  And also, once head is deleted, nextnode becomes head . Similarly if last node is to be deleted, nextnode is NULL. Hence step 4 is as strict NO NO. And we should set prevnode to tail. After we put these things together, we have...
Post a Comment
Read more

Function to sort an array using bubble sort

Quick and dirty way of sorting an array is bubble sort. It is very easy to write and follow. But please keep in mind that it is not at all effecient. #include<iostream> using std::cin; using std::cout; void readArray(int arr[],int sz); void printArray(int arr[],int sz); void sortArray(int arr[],int sz); void swap(int &a,int &b); int main() {    int sz;    cout<<"Size of the array=";    cin>>sz;    int arr[sz];    readArray(arr,sz);     sortArray(arr,sz);   cout<<"Sorted array is ";   printArray(arr,sz); } void readArray(int arr[],int sz) {  for(int i=0;i<sz;i++)    {       cout<<"arr["<<i<<"]=";       cin>>arr[i];   } } void printArray(int arr[],int sz) {  for(int i=0;i<sz;i++)    {       cout<<"arr["<<i<<"]=";    ...
Post a Comment
Read more

Merge two binary search trees

How do you merge two binary search trees? I googled about the solutions. Most solutions told me to convert both trees into linked lists. Merge the lists. Then create a tree from the elements of the list. But why lists? Why can't we store the elements in an array? Because if the data of the tree is larger - not just integer keys, array manipulation becomes difficult. But again, we need not convert both the trees into lists. We can convert one tree into list - a doubly linked list. Then insert the elements of this list into the other tree. I tried this approach. To convert a tree into a sorted doubly linked list Create a doubly linked list. Let the prev and next links of nodes in this list be called left and right respectively. This way we can directly use the binary tree nodes in the list. Use a static variable previousnode  call the function recursively for left child of current node. link current node to the previousnode set next pointer of previousnode to curre...
Post a Comment
Read more