Balancing A Binary Tree

I came up with some code for a simple binary tree. I want to balance it but I am having trouble figuring out how to do this.

My idea was to create a malloced array of pointers to nodes then qsort them and rebuild the tree from that. The problem with this is that (AFAIK) I will need to use recursion to get at all the nodes which makes it tricky to keep track of the array index to place to node.

Heres my code:

Code:

#include <stdio.h>
#include <stdlib.h>

typedef struct node
{
	struct node *left;
	struct node *right;1
	int num;
}Node;

Node *CreateHeadNode(int num) // Creates a new tree
{
	Node *head = malloc(sizeof(Node)); 
	head->left = NULL;
	head->right = NULL;
	head->num = num;
	return head;
}

void AddNode(Node *head, int num)
{
	Node *new_node = malloc(sizeof(Node)); 
	new_node->left = NULL;
	new_node->right = NULL;
	new_node->num = num;

	Node *here = head;
	Node *next = (num < here->num)? here->left: here->right; 
	while(next)
	{
		here = next;
		next = (num < here->num)? here->left: here->right;	
	}
	//'here' will be the last node
	if(num < here->num)
		here->left = new_node;
	else
		here->right = new_node;
}

void PrintTree(Node *head)
{
	printf("Node: %2d\tL:%p \tR:%p\n", head->num, head->left, head->right);
	if(head->left) PrintTree(head->left);
	if(head->right)PrintTree(head->right); 
}

void TreeSize(Node *node, int *count)
{
	(*count)++;
	if(node->left)TreeSize(node->left, count);
	if(node->right)TreeSize(node->right, count);
}


void BalanceTree(Node *head)
{
	int size = 0;
	TreeSize(head, &size);
	Node **temp = malloc(size * sizeof(Node*));	
	// Stuck here
	free(temp);
}

int main()
{
	Node *head = CreateHeadNode(10);

	AddNode(head, 15);
	AddNode(head, 12);
	AddNode(head, 18);
	AddNode(head, 11);
	AddNode(head, 1);
	AddNode(head, 6);
	PrintTree(head);
	int count = 0;
	TreeSize(head, &count);
	printf("Node Count: %d\n", count);
	return 0;
}

Anyone got any suggestions as to the best way to go about this?

Cheers.

My idea when I was going to do this was to create a new tree and insert the nodes in such a way that the tree would be balanced.

So

1 2 3 4 5 6 7 8 9

Insert the middle number, 5, which creates two halves: 1 2 3 4 and 6 7 8 9

Now insert the middle of each halve, 3, 8 which also creates more halves 1 2 and 4 -- 6 7 and 9

Repeat.

Not sure if that made sense or if that results in a truly balanced binary tree.

Well thats basically what I was planning to do once had the address of all the nodes in a flat array. Maybe I'm missing something here but I cant see a simple way of going about this w/o first converting the tree to an array or list.

Somewhere i read that either you must "convert" tree to array to balance it, OR use self-balancing tree from start (and of course, insert/delete functions are a bit more complex then).

Example of self-balanced tree:
http://en.wikipedia.org/wiki/Red-black_tree
(I even heard kernel hackers are playing with this "toy" too)

>Somewhere i read that either you must "convert" tree to
>array to balance it, OR use self-balancing tree from start
That's not quite right. It's possible to globally balance a tree in-place without adding extra complexity to the base tree. One such algorithm is DSW.

Hey prelude, I managed to find your site again. The self balancing trees look cool, but I'll try get this version working first. Still not sure how I'll flatten it; guess maybe I should start with deleting nodes first and think about it later.