Program to insert and delete a node from the binary search tree.

#include <"stdio.h">
#include <"conio.h">
#include <"alloc.h">

#define TRUE 1
#define FALSE 0

struct btreenode
{
struct btreenode *leftchild ;
int data ;
struct btreenode *rightchild ;
} ;

void insert ( struct btreenode **, int ) ;
void delete ( struct btreenode **, int ) ;
void search ( struct btreenode **, int, struct btreenode **,
struct btreenode **, int * ) ;
void inorder ( struct btreenode * ) ;

void main( )
{
struct btreenode *bt ;
int req, i = 0, num, a[ ] = { 11, 9, 13, 8, 10, 12, 14, 15, 7 } ;

bt = NULL ; /* empty tree */

clrscr( ) ;

while ( i <= 8 )
{
insert ( &bt, a[i] ) ;
i++ ;
}
clrscr( ) ;
printf ( "Binary tree before deletion:\n" ) ;
inorder ( bt ) ;

delete ( &bt, 10 ) ;
printf ( "\nBinary tree after deletion:\n" ) ;
inorder ( bt ) ;

delete ( &bt, 14 ) ;
printf ( "\nBinary tree after deletion:\n" ) ;
inorder ( bt ) ;

delete ( &bt, 8 ) ;
printf ( "\nBinary tree after deletion:\n" ) ;
inorder ( bt ) ;

delete ( &bt, 13 ) ;
printf ( "\nBinary tree after deletion:\n" ) ;
inorder ( bt ) ;
}

/* inserts a new node in a binary search tree */
void insert ( struct btreenode **sr, int num )
{
if ( *sr == NULL )
{
*sr = malloc ( sizeof ( struct btreenode ) ) ;

( *sr ) -> leftchild = NULL ;
( *sr ) -> data = num ;
( *sr ) -> rightchild = NULL ;
}
else /* search the node to which new node will be attached */
{
/* if new data is less, traverse to left */
if ( num < ( *sr ) -> data )
insert ( &( ( *sr ) -> leftchild ), num ) ;
else
/* else traverse to right */
insert ( &( ( *sr ) -> rightchild ), num ) ;
}
}

/* deletes a node from the binary search tree */
void delete ( struct btreenode **root, int num )
{
int found ;
struct btreenode *parent, *x, *xsucc ;

/* if tree is empty */
if ( *root == NULL )
{
printf ( "\nTree is empty" ) ;
return ;
}

parent = x = NULL ;

/* call to search function to find the node to be deleted */
search ( root, num, &parent, &x, &found ) ;

/* if the node to deleted is not found */
if ( found == FALSE )
{
printf ( "\nData to be deleted, not found" ) ;
return ;
}

/* if the node to be deleted has two children */
if ( x -> leftchild != NULL && x -> rightchild != NULL )
{
parent = x ;
xsucc = x -> rightchild ;

while ( xsucc -> leftchild != NULL )
{
parent = xsucc ;
xsucc = xsucc -> leftchild ;
}

x -> data = xsucc -> data ;
x = xsucc ;
}

/* if the node to be deleted has no child */
if ( x -> leftchild == NULL && x -> rightchild == NULL )
{
if ( parent -> rightchild == x )
parent -> rightchild = NULL ;
else
parent -> leftchild = NULL ;

free ( x ) ;
return ;
}

/* if the node to be deleted has only rightchild */
if ( x -> leftchild == NULL && x -> rightchild != NULL )
{
if ( parent -> leftchild == x )
parent -> leftchild = x -> rightchild ;
else
parent -> rightchild = x -> rightchild ;

free ( x ) ;
return ;
}

/* if the node to be deleted has only left child */
if ( x -> leftchild != NULL && x -> rightchild == NULL )
{
if ( parent -> leftchild == x )
parent -> leftchild = x -> leftchild ;
else
parent -> rightchild = x -> leftchild ;

free ( x ) ;
return ;
}
}

/*returns the address of the node to be deleted, address of its parent and
whether the node is found or not */
void search ( struct btreenode **root, int num, struct btreenode **par, struct
btreenode **x, int *found )
{
struct btreenode *q ;

q = *root ;
*found = FALSE ;
*par = NULL ;

while ( q != NULL )
{
/* if the node to be deleted is found */
if ( q -> data == num )
{
*found = TRUE ;
*x = q ;
return ;
}

*par = q ;

if ( q -> data > num )
q = q -> leftchild ;
else
q = q -> rightchild ;
}
}

/* traverse a binary search tree in a LDR (Left-Data-Right) fashion */
void inorder ( struct btreenode *sr )
{
if ( sr != NULL )
{
inorder ( sr -> leftchild ) ;

/* print the data of the node whose leftchild is NULL or the path has
already been traversed */
printf ( "%d\t", sr -> data ) ;

inorder ( sr -> rightchild ) ;
}
}