Skip to main content

Implementation of binary tree in C++


A binary tree is a non-linear data structure where every node has maximum two branches - left subtree and right subtree. An empty node is also a binary tree.

In earlier posts we have seen how to insert a node to binary tree, how to traverse a tree and how to delete nodes from tree.

The functions look almost similar in C++. Except that all these functions and root pointer are all parts of the class binary tree.

That is a good thing and a bad thing. If root is a data member (so private), how do we use root as a parameter in all the recursive functions - insert, delete, inorder etc?

Easy answer would be don't use recursion. Anyway no one like them.

So we can write insert and delete functions without using recursion and even search function. But traversal functions have to be recursive.

Ok, let us write a function to return root of the tree and use it as first parameter in all traversal functions.

Here is the complete class.

You can download this code along with test program from here


struct node
{
   int num;
   node *left;
   node *right;
};
class binarytree
{
   node *root;
public:
   binarytree();
   node* create_node(int val);
   void insert( int val); 
   void inorder(node *nd);
   void preorder(node *nd);
   void postorder(node *nd);
   node *search(node *nd,int val);
   void delete_node(int val);
   node*find_parent(node *nd);
   node*find_successor(node*nd,node**parent);
   node* get_root();
};
binarytree::binarytree()
{
    root = NULL;
}
node *binarytree::create_node(int val)
{
   node *newn = new node;
   newn->num = val;
   newn->left = NULL;
   newn->right = NULL;
   return newn;
}
void binarytree::insert( int val)
{//insert a node non-recursively
    node*newnode = create_node(val);
    if(root==NULL)
    {//tree is empty
       root = newnode;
       return;
    }
    node *temp = root;
    node *parent = NULL;
    while(temp!=NULL)
    {//find the location for new node
        parent = temp;
        if(temp->num >val)
           temp = temp->left;
        else
           temp = temp->right;
     }
     //which branch
     if(parent->num >val)
        parent->left = newnode;
     else
        parent->right = newnode;    
}

void binarytree::inorder(node *nd)
{
  if(nd!=NULL)
  {
     inorder(nd->left);
     cout<<nd->num<<"  ";
     inorder(nd->right);
   }
}
void binarytree::preorder(node *nd)
{
  if(nd!=NULL)
  {
     cout<<nd->num<<"  ";
     preorder(nd->left);   
     preorder(nd->right);
   }
}
void binarytree::postorder(node *nd)
{
  if(nd!=NULL)
  {
     postorder(nd->left);   
     postorder(nd->right);
     cout<<nd->num<<"  ";
   }
}
node* binarytree::search(node *nd, int val)
{
     if(nd==NULL)
       return nd;
     if(nd->num==val)
        return nd;
     if(nd->num > val)
       return search(nd->left,val);
     if(nd->num <val)
       return search(nd->right,val);
}
node *binarytree::find_parent(node *nd)
{
    if(nd==root)
    //root has no parent
       return NULL;
    node *temp = root;
    while(temp)
    {
       if(temp->left==nd || temp->right==nd)
          return temp;
       if(nd->num > temp->num)
         temp = temp->right;
       else if(nd->num <temp->num)
         temp = temp->left;
    }
    return NULL;
}
node*binarytree::find_successor(node*nd,node**parent)
{//successor is tree minimum of right subtree
   node*temp = nd->right;
   *parent = nd;
   while(temp->left!=NULL)
      {
      *parent=temp;
      temp = temp->left;
      }
   return temp;
}
         
void binarytree::delete_node(int val)
{
    node *dn = search(root,val);
    if(dn==NULL)
      {
        cout<<"value not found\n";
        return;
      }
     node*parent = find_parent(dn);
    if(dn->left!=NULL && dn->right!=NULL)
    {//node has both subtrees. delete successor instead
        node*successor = find_successor(dn,&parent);
        dn->num = successor->num;//copy data
        dn = successor;
    }    
   
    if(dn->left==NULL && dn->right==NULL)
    {//leaf node
       
        if(parent==NULL && dn==root)
           root = NULL;
        else if(parent==NULL)
           cout<<"Error";
        else
           if(dn==parent->left)
              parent->left = NULL;
           else if(dn==parent->right)
              parent->right = NULL;
        delete dn;
    }
    else if(dn->left==NULL||dn->right==NULL)
    {//has one child
         
         node* child = dn->left?dn->left:dn->right;
         if(dn==root)
             root = child;
         else{
            if(parent->left==dn)
              parent->left = child;
            else
             parent->right = child;
          }
          delete dn;
    }
}
node*binarytree::get_root()
{
   return root;
}
Labels:

Comments

Post a Comment

Popular posts from this blog

Program to delete a node from linked list

How do you remove a node from a linked list? If you have to delete a node, first you need to search the node. Then you should find its previous node. Then you should link the previous node to the next node. If node containing 8 has to be deleted, then n1 should be pointing to n2. Looks quite simple. Isn't it? But there are at least two special cases you have to consider. Of course, when the node is not found. If the node is first node of the list viz head. If the node to be deleted is head node, then if you delete, the list would be lost. You should avoid that and make the second node as the head node. So it becomes mandatory that you return the changed head node from the function.   Now let us have a look at the code. #include<stdio.h> #include<stdlib.h> struct node { int data; struct node * next; }; typedef struct node * NODEPTR; NODEPTR create_node ( int value) { NODEPTR temp = (NODEPTR) malloc( size...
3 comments
Read more

Function to add a node to binary search tree

Binary search tree (BST) is an ordered tree where each node has smaller values on the left sub tree and larger values on the right subtree. This is similar to binary search algorithm. And another useful fact is if you traverse the node in in-order method, the values of the tree will be in ascending order. Binary Search Tree with root as 50 Now as you can see from the diagram on the left child and their children of root (which in this case is 50), values are 40, 20 and 45. All are less than 50. On the other hand, on the right sub tree 50, the values are 60, 55 and 78 - larger than 50. And this rule follows for each and every node, not just root. Now if we have to  add a node - let us 43, where shall we add it, in such a way that the tree will still remain as BST. The new node must be a leaf node (i.e. the node with no child nodes) Let us traverse from root and find out where this new node fits. 43 is smaller than 50. Hence we must branch to left of 50. Now we get 40. 4...
Post a Comment
Read more

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