Skip to main content

Binary tree deletion - non-recursive

In the previous post we have seen how to delete a node of a binary search tree using recursion.

Today we will see how to delete a node of BST using a non-recursive function.

Let us revisit the 3 scenarios here
  1. Deleting a node with no children
    • just link the parent to NULL
  2. Deleting a node with one child
    • link the parent to  non-null child of node to be deleted
  3. Deleting a node with both children
    • select the successor of node to be deleted
    • copy successor's value into this node
    • delete the successor
In order to start, we need a function to search for a node in binary search tree. Did you know that searching in  a BST is very fast, and is of the order O(logn).

To search
  • Start with root
  • Repeat until value is found or node is NULL
    • If the search value is greater than node branch to right
    • If the search value is lesser than node branch to left. 
Here is the function


NODEPTR find_node(NODEPTR root,NODEPTR *parent,int delval)
{
 NODEPTR nd = root;
    NODEPTR pa = root;
     if(root->val==delval)
 {
   *parent = NULL;
          return root;
 }
 while(1 )
 {
   
  if(nd==NULL)
      return NULL;
  
  if(delval < nd->val)
  {
   pa = nd;
   nd = nd->left;    
  }
  else if(delval>nd->val)
  {
   pa = nd;
   nd = nd->right;    
  }  
  else
  {/* we found a match */    
     
      *parent = pa;
      return nd;
  }
  
 }
}

What is this function? Looks complicated? Not really. We have just added some codes to find the parent also. Remember we need parent of the node to be deleted too. Before we branch to left or to right, we set current node as parent.

Next we have to write deletion function


NODEPTR delete_non_recursive( NODEPTR root,NODEPTR delnode,NODEPTR parent)
{
 NODEPTR pa;
  
 if (delnode->left!=NULL && delnode->right!=NULL)/*has both subtrees*/
  {
   
   NODEPTR succ = find_rightst_min(delnode,&parent);
   delnode->val = succ->val;
   delnode=succ;
  }
 if (delnode->left!=NULL)
 {
  /*has only left child*/
  if(parent==NULL){
                       /*we are deleting root*/
   root = delnode->left;
  }else
  {
   if(parent->left ==delnode)
    parent->left = delnode->left;
   else
    parent->right = delnode->left;
  }
  free(delnode);
 }
 else if(delnode->right!=NULL)
 {/*has only right subtree*/
  if(parent==NULL)/*we are deleting root*/
  {
   root = delnode->right;
  }
  else{
   /*has only right child*/
   if(parent->left==delnode)
    parent->left = delnode->right;
   else
    parent->right = delnode->right;
  }
  free(delnode);
 }
 else{ 
   
     /* leaf node */
   if(parent==NULL)
   {
    root = NULL;
   }
   else{
    if(parent->left==delnode)
    {
       parent->left = NULL;
     free(delnode);
    }
    else
    {
     parent->right = NULL;
     free(delnode);
    }
   }
  }
     return root;
}

The special case here is what about deletion of root? If we delete the root, there is no parent. Parent has been set to NULL in find_node function for this case. So in each of the 3 scenarios, we check if parent is null. If parent is null then root is reconfigured to either a non-null child of node to be deleted or to null if root is the only node in the tree.

Now it is time for complete program.


#include<stdio.h>
#include<stdlib.h>
struct node
{
   int val;
   struct node *left;
   struct node *right;
};
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;
     return temp;
}

NODEPTR insert_node(NODEPTR nd,NODEPTR newnode)
{
    if(nd==NULL)
       return newnode;/* newnode becomes root of tree*/
    if(newnode->val > nd->val)
        nd->right = insert_node(nd->right,newnode);
    else if(newnode->val <  nd->val)
        nd->left = insert_node(nd->left,newnode); 
    return nd;   
}

void in_order(NODEPTR nd)
{
   if(nd!=NULL)
    {
        in_order(nd->left);
        printf("%d---",nd->val);
        in_order(nd->right);
     }
}

void pre_order(NODEPTR nd)
{
   if(nd!=NULL)
    {
        printf("%d---",nd->val);   
        pre_order(nd->left);
        pre_order(nd->right);
            
     }
}

void post_order(NODEPTR nd)
{
   if(nd!=NULL)
    {    
 post_order(nd->left);
        post_order(nd->right);
        printf("%d---",nd->val);
     }
}


/*go left till you reach null*/
NODEPTR find_rightst_min(NODEPTR nd,NODEPTR *parent)
{
     NODEPTR pa = nd;
     nd = nd->right;
     while(nd->left)
     {
        pa = nd;
        nd = nd->left;
      }
      *parent = pa;
      return nd;
}
 

NODEPTR find_node(NODEPTR root,NODEPTR *parent,int delval)
{
 NODEPTR nd = root;
    NODEPTR pa = root;
     if(root->val==delval)
 {
   *parent = NULL;
          return root;
 }
 while(1 )
 {
   
  if(nd==NULL)
      return NULL;
  
  if(delval < nd->val)
  {
   pa = nd;
   nd = nd->left;    
  }
  else if(delval>nd->val)
  {
   pa = nd;
   nd = nd->right;    
  }  
  else
  {/* we found a match */    
     
      *parent = pa;
      return nd;
  }
  
 }
}
 
NODEPTR delete_non_recursive( NODEPTR root,NODEPTR delnode,NODEPTR parent)
{
 NODEPTR pa;
  
 if (delnode->left!=NULL && delnode->right!=NULL)
  {
   
   NODEPTR succ = find_rightst_min(delnode,&parent);
   delnode->val = succ->val;
   delnode=succ;
  }
 if (delnode->left!=NULL)
 {
  /*has only left child*/
  if(parent==NULL){
   root = delnode->left;
  }else/*we are not deleting root*/
  {
   if(parent->left ==delnode)
    parent->left = delnode->left;
   else
    parent->right = delnode->left;
  }
  free(delnode);
 }
 else if(delnode->right!=NULL)
 {
  if(parent==NULL)/*we are deleting root*/
  {
   root = delnode->right;
  }
  else{
   /*has only right child*/
   if(parent->left==delnode)
    parent->left = delnode->right;
   else
    parent->right = delnode->right;
  }
  free(delnode);
 }
 else{ 
   
     /* leaf node */
   if(parent==NULL)
   {
    root = NULL;
   }
   else{
    if(parent->left==delnode)
    {
       parent->left = NULL;
     free(delnode);
    }
    else
    {
     parent->right = NULL;
     free(delnode);
    }
   }
  }
     return root;
}

    
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);
      
       
       while(1){ 
  NODEPTR search_node,parent;   
   printf("Enter node to be searched(-1 to stop)");
         scanf("%d",&n);
  if(n==-1)
   break;
  search_node = find_node(root,&parent,n);
  if(search_node!=NULL){ 
            root = delete_non_recursive(root,search_node,parent);
   if(root==NULL)
   {
    printf("Now tree is empty");
    break;
   }
   else{
             printf("now tree is");
    in_order(root);printf("\n");
   }
  }else{
     printf("Node not found");
  } 
       } 
       return 0;
}

Happy binary trees :)
Labels:

Comments

Post a Comment

Popular posts from this blog

Program to create a Linked List in C

An array is a commonly used data structure in most of the languages. Because it is simple, it needs O(1) time for accessing elements. It is also compact. But an array has a serious drawback - it can not grow or shrink. You need to estimate the array size and define it during compile time. This drawback is not present a linked list. A linked list is a data structure which can grow or shrink dynamically.  A linked list has nodes each of which contain  contain  data and a link to next node . These nodes are dynamically allocated structures. If you need more nodes, you just need to allocate memory for these and link these nodes to the existing list. The nodes of a linked list have to be defined as self-referential structures in C. That is structures with data members and one member which is a pointer to the structure of same type.  This pointer will work as a link to next node. struct node { int data; struct node * next; //pointer to another node }...
1 comment
Read more

Mirror tree

Question : Write a function to mirror a binary tree. The mirror tree will have a left subtree and right subtree swapped. But this has to be done for each and every node. So to convert a tree to its mirror, we can write an algorithm like this               1) mirror left subtree recursively               2) mirror right subtree recursively               3) swap left and right children of the current node. Here is the function for it. void mirror_tree (NODEPTR root) { if (root != NULL ) { NODEPTR temp = root -> left; root -> left = root -> right; root -> right = temp; mirror_tree(root -> left); mirror_tree(root -> right); } }
Post a Comment
Read more

Josephus problem

Question: Write a function to delete every k th node from circular linked list until only one node is left. This has a story associated with it. Flavius Josephus was Jewish Historian from 1st century. He and 40 other soldiers were trapped in a cave by Romans. They decided to kill themselves rather than surrendering to Romans. Their method was like this. All the soldiers will stand in a circle and every k th soldier will be shot dead. Josephus said to have calculated the starting point so that he would remain alive. So we have similar problem at hand. We delete every kth node in a circular list. Eventually only one node will be left. e.g. Let us say this is our list And we are deleting every third node.  We will delete 30. Then we delete 60. Next we delete 10. Next it will be 50. Next to be deleted is 20. Next 80. This continues. Implementation   We can count k-1 nodes and delete next node. This can be repeated in  a loop. What must be the termina...
Post a Comment
Read more