Binary Tree – Deleting a Node

The possibilities which may arise during deleting a node from a binary tree are as follows:

• Node is a terminal node: In this case, if the node is a left child of its parent, then the left pointer of its parent is set to NULL. Otherwise if the node is a right child of its parent, then the right pointer of its parent is set to NULL
• Node has only one child: In this case, the appropriate pointer of its parent is set to child node.
• Node has two children: Predecessor replaces the node value, and then the predecessor of the node is deleted.

Since the node has both, right and left child, if right sub-tree is opted find the smallest node. If left sub-tree is opted then find the largest node.

Since node->right = node->left = NULL, delete the node and place NULL in the parent node.

Node Removal Operation

If the node to be removed is a leaf node, it can be deleted immediately. If the node has one child, the node can be deleted after its parent adjusts a link to bypass the deleted node.

What if the node numbered 2 is deleted?

t à right

set t = t à right

If the node to be removed has two children, the general strategy is to replace the data of this node with the smallest data of the right sub-tree. Then the node with the smallest data is now removed (this case is easy since this node cannot have two children).

Remove the numbered 2 again.

C++ implementation for deleting a node

void del(int item) { node *parent,*location; if(root==NULL) { cout<<"Tree empty"); return; } find(item,&parent,&location); if(location==NULL) { cout<<"Item not present in tree"; return; } if(location->lchild==NULL && location->rchild==NULL) case_a(parent,location); if(location->lchild!=NULL && location->rchild==NULL) case_b(parent,location); if(location->lchild==NULL && location->rchild!=NULL) case_b(parent,location); if(location->lchild!=NULL && location->rchild!=NULL) case_c(parent,location); free(location); }/*End of del()*/ void find(int item,node **par,node **loc) { node *ptr,*ptrsave; if(root==NULL) /*tree empty*/ { *loc=NULL; *par=NULL; return; } if(item==root->info) /*item is at root*/ { *loc=root; *par=NULL; return; } /*Initialize ptr and ptrsave*/ if(item<root->info) ptr=root->lchild; else ptr=root->rchild; ptrsave=root; while(ptr!=NULL) { if(item==ptr->info) { *loc=ptr; *par=ptrsave; return; } ptrsave=ptr; if(item<ptr->info) ptr=ptr->lchild; else ptr=ptr->rchild; }/*End of while */ *loc=NULL; /*item not found*/ *par=ptrsave; }/*End of find()*/