This document provides an overview of binary search trees (BST) including their basic operations like insertion, deletion, and traversal in C programming. It outlines functions for inserting nodes, searching for values, and finding minimum and maximum values in the tree. The document also includes code snippets demonstrating the implementation of these operations.

1. DATA STRUCTURES
Binary Search Tree
Santhiya S
Assistant Professor
Department of AI
Kongu Engineering College

2. Binary search tree -8, 3, 6,1,10, 4, 9, 8.5, 50,35
8
10
3
6
1
4
9
8.5
50
35

3. Basic Operations
• The basic operations of a BST
• Search
• Insert
• Find minimum value
• Find maximum value
• Delete
• Traversal
• Pre-order Traversal
• In-order Traversal
• Post-order Traversal

4. #include<stdio.h>
#include<stdlib.h>
struct node
{
int data;
struct node*left;
struct node*right;
}*root;
void insert()
{
struct node *temp, *parent;
struct node *newnode= (struct
node*)malloc(sizeof(struct node));
scanf("%d",&newnode-> data);
newnode-> left=NULL;
newnode->right=NULL;
if(root==NULL)
{
root=newnode;
}
else
{
temp = root;
while(temp)
{
parent=temp;
if(newnode-> data<temp->data)
{
temp = temp-> left;
}
else
{
temp = temp-> right;
}
}
if(newnode-> data< parent->data)
{
parent-> left = newnode;
}
else
{
parent-> right = newnode;
}
}
}
void inorder(struct node *T)
{
if (T==NULL)
return;
inorder(T->left);
printf(" %d ",T->data);
inorder(T->right);
}
int main()
{
//struct node *root=NULL;
int n;
printf("n enter no. of term:- ");
scanf("%d",&n);
while(n!=0)
{
insert();
n--;
}
inorder(root);
print(“Enter the value to search”);
scanf(“%d”, &item);
search(item);
}

5. void insert()
{
struct node *temp, *parent;
struct node *newnode= (struct
node*)malloc(sizeof(struct node));
scanf("%d",&newnode-> data);
newnode-> left=NULL;
newnode->right=NULL;
if(root==NULL)
{
root=newnode;
}
else
{
temp = root;
while(temp)
{
parent=temp;
if(newnode-> data<temp->data)
{
temp = temp-> left;
}
else
{
temp = temp-> right;
}
}
if(newnode-> data< parent->data)
{
parent-> left = newnode;
}
else
{
parent-> right = newnode;
}
}
}
30
root
100
100
temp
100
parent
100
while(100), true
20<30, true
400
0 0
20<30, true
0
0
20
200
200
0 0
25
300
while(100), true
25<30, true
while(NULL),False
200
while(200),true
200
if 25<20, false
while(NULL),False
300
0 0
15
400
if 25<20, false
while(100), true
15<30, true
while(200),true
if15<20, true
if15<20, true
0 0 0
40
while(100), true
if 40<30, false
while(NULL),False
600
600
if 40<30, false

6. void search(int item)
{
struct node *parent=NULL, *temp=NULL;
temp = root;
while(temp->data != item)
{
//parent=temp;
if(temp != NULL)
{
printf("%d ",temp->data);
if(item<temp->data )
{
temp = temp->left;
}
else
{
temp = temp->right;
}
if(temp == NULL)
{
printf(“Element Not Found”);
break;
}
}
}
printf("nSearched value (or) least right node value :
%dn",temp->data);
}
30
root
100
100
20
200
300
0 0
15
400
400 0 0
40
600
600
0 0
25
300
200
item
temp
parent
25
100
100
while 30!=25,true
if 100!=NULL,true //op 30
25<30,true
200
200==NULL,false
while 20!=25,true
200
if 200!=NULL,true
//op 20
25<20,false
300
300==NULL,false
while 25!=25, False
op Searched value
(or) least right node
value :25

7. void deletion(int item)
{
struct node *parent=NULL, *temp=NULL;
temp = root;
search(item); (2)
if (temp == NULL)
return;
if (temp->left == NULL && temp->right ==
NULL) //No child
{
if (temp != root)
{
if (parent->left == temp)
parent->left = NULL;
else
parent->right = NULL;
}
else
root = NULL;
free(temp);
}
else if (temp->left !=NULL&& temp-
>right!=NULL) // if 2 child
{
// find the min value in right sub tree
temp1=temp;
t1=temp1- >right;
while(t1->left!=NULL)
{
t1=t1->left;
}
int val = t1->data;(4)
deletion(t1->data);
temp1->data = val;
}
else //if one child
{
struct node* child = (temp->left!=NULL)? temp-
>left: temp->right;
if (temp != root)
{
if (temp == parent->left)
parent->left = child;
temp->left=NULL;
else
parent->right = child;
temp->right=NULL;
}
else
{
root = child;
}
free(temp);
}
}

8. void deletion(int item)
{
struct node *parent=NULL, *temp=NULL
*temp1,*t1;
item,temp,parent =search(item);
if (temp == NULL)
return;
if (temp->left == NULL && temp->right == NULL)
//No child
{
if (temp != root)
{
if (parent->left == temp)
parent->left = NULL;
else
parent->right = NULL;
}
else
root = NULL;
free(temp);
}
}
temp
parent
30
root
100
100
20
200
300
0 0
15
400
400 0 0
40
600
600
0 0
25
300
200
300
200
item
25
300==NULL, false
0==NULL&&0==NULL,true,
no child condition
400==300,False
300!=100,true (only root node
with no child condition)
0
temp
parent
30
root
100
100
200 600
100
NULL
item
25
100==NULL, false
0==NULL&&0==NULL,true,
no child condition
100!=100,false (only root node
with no child condition)
0

9. void deletion(int item)
{
struct node *parent=NULL, *temp=NULL
*temp1,*t1;
temp = root;
item,temp,parent = search(item);
if (temp == NULL)
return;
if (temp->left == NULL && temp->right == NULL)
//No child
{
}
else if (temp->left !=NULL&& temp->right!=NULL)
// if 2 child
{
// find the min value in right sub tree
temp1=temp;
t1=temp1- >right;
while(t1->left!=NULL)
{
t1=t1->left;
}
int val = t1->data;
deletion(t1->data);
temp1->data = val;
}
else // one child
{
}
30
root
100
100
20
200
300
0 0
15
400
400 300 700
40
600
600
0 0
35
300
200
temp
parent
100
NULL
item
30
else if 200!=NULL && 600!=NULL, true,
2 child node condition
temp1 t1
100
600
0 0
60
700
while(300!=NULL),true,
to check whether right sub tree contain left node
300
while(0!=NULL),false
value
35
deletion(t1->data);
0
35
100==NULL,False
if (200===NULL &&600==NULL),false,
no child node condition temp
parent
300
600

10. void deletion(int item)
{
struct node *parent=NULL, *temp=NULL
*temp1,*t1;
temp = root;
item,temp,parent = search(item);
if (temp == NULL)
return;
if (temp->left == NULL && temp->right == NULL)
//No child
{
}
else if (temp->left !=NULL&& temp->right!=NULL)
// if 2 child
{
}
else // one child
{
struct node* child = (temp->left!=NULL)? temp-
>left: temp->right;
if (temp != root)
{
if (temp == parent->left)
{
parent->left = child;
if(temp->left!=NULL)
temp->left=NULL;
else
temp->right=NULL;
else
{
parent->right = child;
if(temp->left!=NULL)
temp->left=NULL;
else
temp->right=NULL;
}
}
else
{
root = child;
}
free(temp);
}
30
root
100
100
20
200
0
0 0
15
300
400 300 0
40
600
600
0 0
35
400
200
parent
100
item
40
else if 200!=NULL && 600!=NULL, false,
2 child node condition
temp
600
child=(300!=NULL)?300:NULL
if(600!=100), true
else (one child):
100==NULL,False
if (200===NULL &&600==NULL),false,
no child node condition
child= 300
if(600==200), false.enter to else part
300
0
if(300!=NULL), true

11. TRAVERSAL
inorder(root)
void inorder(struct node *root)
{
if (root!=NULL)
{
inorder(root->left);
printf(" %d “,root->data);
inorder(root->right);
}
}
7
2 9
1 5
14
r
o
o
t

12. TRAVERSAL
preorder(root)
void preorder(struct node *root)
{
if (root!=NULL)
{
printf(" %d ",root->data);
preorder(root->left);
preorder(root->right);
}
}
7
2 9
1 5
14
r
o
o
t

13. TRAVERSAL
postorder(root)
void postorder(struct node *root)
{
if (root!=NULL)
{
postorder(root->left);
postorder(root->right);
printf(" %d ",root->data);
}
}
7
2 9
1 5
14
r
o
o
t

14. FIND MAXIMUM
void max ()
{
if (root==NULL)
return root;
else
{
struct node*temp;
temp=root;
while(tempright !=NULL)
{
temp=temp  right;
}
printf(“n %d”, tempdata);
}
r
o
o
t
Maximum value:14
temp

15. FIND MNIMUM
void min ()
{
if (root==NULL)
return root;
else
{
struct node*temp;
temp=root;
while(templeft !=NULL)
{
temp=temp  left;
}
printf(“n %d”, tempdata);
}
temp
r
o
o
t
Minimum value:1