Delete function for binary tree - c

Question

Given the below code what could I use to make a delete function? I have tried multiple things and I keep getting snagged on trying to get it to work. My main problem is trying to delete a node that has a left and right child. For a node that has no children I can just set its parent to point to null and free the node. For one child just set the parent to point to the child and free the node. How would I do it for a node with two children both conceptually and in my code?
#include<stdlib.h>
#include<stdio.h>
struct bin_tree {
int data;
struct bin_tree * right, * left;
} bin_tree;
typedef struct bin_tree node;
void help()//help
{
printf("Options:\n");
printf(" # -Put in any number to add it to the tree if not already there\n");
printf(" s # -Put in s and a number to search the tree for the number\n");
printf(" d # -Delete the number from the tree\n");
printf(" p -Put in p to print the tree\n");
printf(" ? -At any time you can press ? to display the help message\n");
printf(" Q -If you decide the leave the realm of the tree then you can press Q to quit this program\n");
}
int max(int a,int b)//max tree length
{
if(a>b)
return a;
else
return b;
}
int height(node* tree)//height
{
if(tree != NULL)
return(1 + max(height(tree->left),height(tree->right)));
else
return 0;
}
void insert(node ** tree, int val)//insert
{
node *temp = NULL;
if(!(*tree))
{
temp = (node *)malloc(sizeof(node));
temp->left = temp->right = NULL;
temp->data = val;
*tree = temp;
return;
}
if(val < (*tree)->data)
{
insert(&(*tree)->left, val);
}
else if(val > (*tree)->data)
{
insert(&(*tree)->right, val);
}
}
void print(node * tree)//print
{
if (tree)
{
print(tree->left);
printf("[%d] ",tree->data);
print(tree->right);
}
}
node* search(node ** tree, int val)
{//search
if(!(*tree))
{
return NULL;
}
if(val < (*tree)->data)
{
search(&((*tree)->left), val);
}
else if(val > (*tree)->data)
{
search(&((*tree)->right), val);
}
else if(val == (*tree)->data)
{
return *tree;
}
}
void main()
{
node *root;
node *tmp;
int no;
char ch, buff[500];
root = NULL;
printf("Options:\n");
printf(" # -Put in any intiger to add it to the tree if not already there\n");
printf(" s # -Put in s and a number to search the tree for the number\n");
printf(" d # -Delete the number from the tree\n");
printf(" p -Print the tree\n");
printf(" ? -At any time you can press ? to display the help message\n");
printf(" Q -If you decide the leave the realm of the tree then you can press Q to quit this program\n");
while(1){
printf(">");
fgets(buff,499,stdin); //grabs input from user
if(sscanf(buff,"%i",&no)==1){//decides if just a number
tmp = search(&root, no);//looks for number in the tree
if (tmp)
{
printf("Node already in tree!\n", tmp->data);
}
else
{
insert(&root, no);//if not in tree insert it
}
}
else if(sscanf(buff,"%c %i",&ch,&no)>=1)//checks if character
{
switch(ch)
{
case 's'://search for number
{
tmp = search(&root, no);
if (tmp)
{
printf("Node found=%d\n", tmp->data);
}
else
{
printf("Node not found in tree.\n");
}
break;
}
case 'd':
tmp = search(&root, no);
if (tmp)
{
//Call delete function
printf("Node %i deleted", no);
break;
}
else
{
printf("Node not found in tree.\n");
break;
}
case 'Q'://quit
exit(0);
case 'p'://print tree
printf("\n\n");
print(root);
printf("\nHeight= %i\n\n",height(root));
break;
case '?'://display help
help();
break;
default://idiot >.>
printf("Invalid input!\n\n");
help();
break;
}
}
}
return;
}

Answer 1

Either the largest of the nodes to the left or the smallest of the nodes to the right will take it's place!
Simply put one of these where the deleted node was (and delete them from your previous position) and your tree will still be a valid binary search tree. Take a look at this example:
15
/ \
… 25
/ \
20 30
\
23
Suppose you wanted to delete node 25:
By the properties of the binary search tree you already know that all children have to be larger than the parent (15), therefore using one of them instead of the 25 is valid. ✓
If you choose the largest node from the left sub tree (23) it will be larger than any of the nodes to the left, but it also will be smaller than any of the nodes to the right, therefore it fits nicely in the middle and can take the place of the deleted node. ✓
The same is true for the smallest node from the right sub tree (30). ✓
In case the chosen node is a leaf everything is fine and you can delete it. Otherwise perform the delete operation on your chosen node.
You can also take a look at the Wikipedia article of the binary search tree for a pseudocode implementation.