1. The Binary Search Tree Data Structure
Mugurel Ionuț Andreica
Spring 2012

2. The Properties of a Binary Search Tree
A binary search tree is a binary tree with some extra properties
This implies that it maintains the same information as a binary tree (left son, right son, parent, pointer to some useful information)
Extra properties:
The elements (useful information) stored in the tree nodes are comparable
The elements stored in the left sub-tree of a node p are ≤ the element stored by p
The elements stored in the right sub-tree of a node p are > the element stored by p
Faster search
More complicated removal (because the property of the BST must be maintained)

3. Binary Search Tree - example

4. Binary Search Tree – C++ code
template<typename T> class BSTNode {
public:
BSTNode<T> *root, *left_son, *right_son, *parent;
T *pinfo;
BSTNode() {
left_son = right_son = NULL;
root = this;
pinfo = NULL; }
void setInfo(T info) {
pinfo = new T;
*pinfo = info;
void insertInfo(T x) {
if (pinfo == NULL)
setInfo(x);
else
insert_rec(x);
void insert_rec(T x) {
int next_son;
if (x <= (*pinfo))
next_son = 0;
else
next_son = 1;
if (next_son == 0) { // left son
if (left_son == NULL) {
left_son = new BSTNode<T>;
left_son->pinfo = new T;
*(left_son->pinfo) = x;
left_son->left_son = left_son->right_son = NULL;
left_son->parent = this;
left_son->root = root;
} else
left_son->insert_rec(x);
} else { // right son
if (right_son == NULL) {
right_son = new BSTNode<T>;
right_son->pinfo = new T;
*(right_son->pinfo) = x;
right_son->left_son = right_son->right_son = NULL;
right_son->parent = this;
right_son->root = root;
right_son->insert_rec(x); }

5. Binary Search Tree – C++ code (cont.)
BSTNode<T>* findInfo(T x) {
BSTNode<T> *rez;
if (pinfo == NULL)
return NULL;
if ((*pinfo) == x)
return this;
if (x <= (*pinfo)) {
if (left_son != NULL)
return left_son->findInfo(x);
else
} else {
if (right_son != NULL)
return right_son->findInfo(x); }
void removeInfo(T x) {
BSTNode<T> *t = findInfo(x);
if (t != NULL)
t->remove();
void remove() {
BSTNode<T> *p;
T *paux;
if (left_son == NULL && right_son == NULL) {
if (parent == NULL) { // this == root
delete this->pinfo;
root->pinfo = NULL;
} else {
if (parent->left_son == this)
parent->left_son = NULL;
else
parent->right_son = NULL;
delete this; }
if (left_son != NULL) {
p = left_son;
while (p->right_son != NULL)
p = p->right_son;
} else { // right_son != NULL
p = right_son;
while (p->left_son != NULL)
p = p->left_son;

6. Binary Search Tree – C++ code (cont.)
paux = p->pinfo;
p->pinfo = this->pinfo;
this->pinfo = paux;
p->remove(); }
void inOrderTraversal() {
if (left_son != NULL)
left_son->inOrderTraversal();
printf("%d\n", *pinfo); // we should use the correct format
// for printing type T values
if (right_son != NULL)
right_son->inOrderTraversal(); };
int main() {
srand(7290);
BSTNode<int> *r = new BSTNode<int>;
r->insertInfo(6);
r->insertInfo(8);
r->insertInfo(1);
r->insertInfo(9);
r->insertInfo(10);
r->insertInfo(4);
r->insertInfo(13);
r->insertInfo(1);
r->insertInfo(12);
r->inOrderTraversal();
printf("%d\n", r->findInfo(100));
printf("%d\n", r->findInfo(1));
printf("%d\n", r->findInfo(12));
printf("%d\n", r->findInfo(8));
printf("%d\n", r->findInfo(10));
printf("%d\n", r->findInfo(4));
(r->findInfo(6))->remove();
r->removeInfo(9);
return 0; }