### Binary Search Trees! Simple Class in C++

Here is a really basic binary tree class, it just includes the basics of creating, inserting, erasing, and returning size. In later posts I will talk about printing and traversals.

This class also uses the Node.h talked about in this earlier post. You’ll notice that I really like to use recursion, I think this is cleaner than looping.

```#include <assert.h>
#include "Node.h"
using namespace std;

class Bst
{
public:

//constructor for when a head Node is provided and when it is not
Bst() {
root = nullptr;
}

Bst(Node *np) {
root = np;
}

//destroy the tree, we need to go through and destroy each node
~Bst() {
destroyTree(root);
}

//get the number of nodes in the tree
int size() {
return size(root);
}

//erase a value in the tree
void erase(int item) {
erase(item, root);
}

//insert a Node in the tree
void insert(int item) {
insert(item, root);
}

private:

Node* root;

//Go through each branch and recursively destroy all Nodes
void destroyTree(Node*& n) {
if (n != nullptr) {
destroyTree(n->left);
destroyTree(n->right);
delete n;
}
}

//For each Node return the number of left and right nodes
//Add it up recursively to get the total size
int size(Node* n) {
if (n != nullptr) {
int left = size(n->left);
int right = size(n->right);
int self = 1;
return left + self + right;
}
return 0;
}

//Find the minimum Node value
Node* findMin(Node* n){
assert(n != nullptr);
if (n->left != nullptr) {
return findMin(n->left);
}
return n;
}

//this one is a beast
//look through all the nodes recursively
//once you find the node value there are numerous cases we need to look for
//If the current node does not have left and right nodes, just delete it
//If it does have a left or right node, set the child to the parent
//If it has both left and right, we need to work some magic. First we find
//the smallest value and set the node we want to delete to that value (removing it)
void erase(int item, Node*& n) {
if (n != nullptr) {
if (item == n->data) {
if (n->right == nullptr && n->left == nullptr) {
delete n;
n = nullptr;
} else if (n->right == nullptr) {
Node* temp = n;
n = n->left;
delete n;
} else if (n->left == nullptr){
Node* temp = n;
n = n->right;
delete n;
} else {
Node *temp = findMin(n->right);
n->data = temp->data;
erase(item, n->right);
}
} else if (item < n->data) {
erase(item, n->left);
} else {
erase(item, n->right);
}
}
}

//look through all the nodes
//insert the node on the correct node, it will be added to the left if the value is less
//added to the right if the value is greater
void insert(int item, Node*& n) {
if (n != nullptr) {
if (item < n->data) {
insert(item, n->left);
} else {
insert(item, n->right);
}
} else {
n = new Node(item);
}
}
};
```

Let me know if you have any improvements or comments!

### The typical Node structure in C++

The next couple of posts are going to require the use of a node object. I’ve seen people make the node way more complicating then it should be as a class. The point of a node is to hold data and be aware of it’s neighbors. All you really need is a simple struct.

In the instance of a stack or list, a node just really needs to know who’s next after them. Note in the code below, to create a node, I need some data passed in, that’s it. It’s up to the coder to set the next pointer in their code that is utilizing the node.

```struct Node
{
int data;
Node* next;

Node(int d){
data = d;
next = nullptr;
}
};```

When we start looking at linked lists and binary search trees, we might consider a struct that is aware of the nodes on both sides of it. Again, it is up to the code using the node structure to set the left and right pointers to the right node neighbors.

```struct Node
{
int data;
Node* left;
Node* right;

Node(int d){
data = d;
left = nullptr;
right = nullptr;
}
};```

Pretty dang simple!