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<b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">#define IS_FULL (ptr ) (!(ptr ))
#define FALSE = 0
#define TRUE = 1
typedef struct {
int key;
}<font color="#FF0000">element</font>;
typedef struct tree_node *tree_pointer;
struct tree_node {
tree_pointer lefe_child;
element data;
short int bf;
tree_pointer right_child;
};
int unbalanced = FALSE;
tree_pointer root = NULL;
<font color="#FF0000">avl_insert</font> (&root, x, &unbalanced )
void <font color="#FF0000">avl_insert</font>( tree_pointer *parent , element x , int *unbalanced )
{ if ( !*parent ){ <i><font size="3" color="#CC0099"> /* insert element into null tree */</font></i>
*unbalanced = TRUE ;
*parent = ( tree_pointer ) malloc( sizeof( tree_node ) ) ;
if ( IS_FULL( *parent ) ){
fprintf( stderr , "The memory is full\n" ) ;
exit( 1 ) ;
}
( *parent )->left_child = ( *parent )->right_child = NULL ;
( *parent )->bf = 0 ;
( *parent )->data = x ;
}
else if ( x.key < ( *parent )->data.key ){
avl_insert( &( *parent )->left_child , x , unbalanced ) ;
if ( *unbalanced )
<i><font size="3" color="#CC0099"> /* left branch has grown higher */</font></i>
switch( ( *parent )->bf ){
case -1: ( *parent )->bf = 0 ;
*unbalanced = FALSE ; break ;
case 0: ( *parent )->bf = 1 ; break ;
case 1: left_rotation( parent , unbalanced ) ;
}
}
else if ( x.key > ( *parent )->data.key ){
avl_insert( &( *parent )->right_child , x , unbalanced ) ;
if ( *unbalanced )
<i><font size="3" color="#CC0099"> /* right branch has grown higher */
</font></i><font size="3" color="#CC0099"><font size="4" color="#000000"> switch ( ( *parent )->bf ){</font></font>
case 1: ( *parent )->bf = 0 ;
*unbalanced = FALSE ; break ;
case 0: ( *parent )->bf = -1 ; break ;
case -1: right_rotation( parent , unbalanced ) ;
}
}
else { *unbalanced = FALSE ;
printf( "The key is already in the tree" ) ;
}
}
void <font color="#FF0000">left_rotation</font>( tree_pointer *parent , int *unbalanced )
{
tree_pointer grand_child , child ;
child = ( *parent )->left_child ;
if ( child->bf == 1 ){
<i><font size="3" color="#CC0099"> /* LL rotation */</font></i>
( *parent )->left_child = child->right_child ;
child->right_child = *parent ;
( *parent )->bf = 0 ;
( *parent ) = child ;
}
else {
<i><font size="3" color="#CC0099"> /* LR rotation */</font></i>
grand_child = child->right_child ;
child->right_child = grand_child->left_child ;
grand_child->left_child = child ;
( *parent )->left_child = grand_child->right_child ;
grand_child->right_child = *parent ;
switch( grand_child->bf ){
case 1: ( *parent )->bf = -1 ;
child->bf = 0 ;
break ;
case 0: ( *parent )->bf = child->bf = 0 ;
break ;
case -1: ( *parent )->bf = 0 ;
child->bf = 1 ;
}
*parent = grand_child ;
}
( *parent )->bf = 0 ;
*unbalanced = FALSE ;
}
<font color="#FF0000">complexity</font>
h -- the height of the tree before insertion
the worst case - O( log n )
<font color="#FF0000">probability:</font>
rebalance -- 0.5349
single rotation ( LL or RR ) --- 0.2324
double rotation ( LR or RL ) --- 0.2324 </font></b>
<img src="image/table.gif" width="570" height="168"></pre>
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