# Trees Library

### Contents

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#### Tree Creation and Destruction Functions

One of the most useful features of the tree data structure is that it can grow dynamically. That is, at any point in your code, you can make a new node and add it to the tree. Because of this you do not need to know the number of nodes beforehand. As a result, our function which will provide a new tree structure will need to allocate memory. Recall that we have a tree_t data type, defined as follows:

```
typedef struct _tree {
int		data;
struct _tree	*left, *right;
} tree_t;
```

From this definition we can see that each node points to its left and right children. To make our node creation function mesh easily with the rest of our implementation, it should return a pointer to the memory we allocate. Here is one possible way to implementation such a function:

```
tree_t *new_tree(int	data)
{
tree_t	*tree;

if ((tree = (tree_t *) malloc (sizeof(tree_t))) == NULL) {
return NULL;
}
tree->data = data;
tree->left = NULL;
tree->right = NULL;

return tree;
}
```

Alternatively, you could write a version where the caller is allowed to specify the children.

```
tree_t *new_tree(int	data; tree_t *left; tree_t *right)
{
tree_t	*tree;

if ((tree = (tree_t *) malloc (sizeof(tree_t))) == NULL) {
return NULL;
}
tree->data = data;
tree->left = left;
tree->right = right;

return tree;
}
```

Since each node in the tree will necessarily be allocated dynamically, it must also be freed when it is no longer needed. The following function will take care of the freeing of an individual node.

```
void 	free_node (tree_t *tree)
{
if (tree != NULL) {
free(tree);
}
}
```

While it is useful to have a function that destroys an individual node, it would be far more useful if we could make one function call to destroy an entire tree. We mentioned in the introduction that trees are naturally recursive. This function will take advantage of that feature. Destroying a tree essentially requires destroying the tree headed by the left child and the tree headed by the right child along with the root of the tree itself. With that algorithm in mind, we produce the following function:

```
void	destroy_tree (tree_t *tree)
{
if (tree == NULL)
return;

destroy_tree(tree->left);
destroy_tree(tree->right);
free_node(tree);
}
```

To break down the function above, we see that there is a base case for the NULL tree, a recursive case for other trees, and finally a call to free_node to destroy the tree's root. You will find that this is a pattern that recurs frequently when writing functions to manipulate trees.

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