Remove BST keys outside the given range

PROBLEM :

Remove BST keys outside the given range

Given a Binary Search Tree (BST) and a range [min, max], remove all keys which are outside the given range. The modified tree should also be BST. For example, consider the following BST and range [-10, 13].



The given tree should be changed to following. Note that all keys outside the range [-10, 13] are removed and modified tree is BST.




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SIMPLE c++ IMPLEMENTATION :
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/*
typedef struct BST
{
int info ;
struct BST *left ;
struct BST *right ;
}tree ;                            */

tree* delete_element_tree(tree *,int ) ;

// L is the lower limit and H is the upper limit

tree* remove_range(tree* root,int L,int H)
{
if(root==NULL)
return NULL ;

if(root->info>=L&&root->info<=H)
{
root->left=remove_range(root->left,L,H) ;
root->right=remove_range(root->right,L,H) ;
}
else
{
root=delete_element_tree(root,root->info) ;
root=remove_range(root,L,H) ;
}
return root ;
}

tree* delete_element_tree(tree *root,int ele)
{
if(root==NULL)
return root ;

if(root->info>ele)
root->left=delete_element_tree(root->left,ele) ;

else if(root->info<ele)
root->right=delete_element_tree(root->right,ele) ;

else
{
if(root->right==NULL)
{
tree *temp=root->left ;
free(root) ;
return temp ;
}
if(root->left==NULL)
{
tree *temp=root->right ;
free(root) ;
return temp ;
}

tree *temp=getMin_tree(root->right) ;
root->info=temp->info ;
root->right=delete_element_tree(root->right,root->info) ;
}
}

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