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

2. The Elements of a Binary Tree
composed of nodes
one special node: the root => rooted trees
unrooted trees also exist (but they are not studied in this course)
each node has:
one left son (possibly NULL)
one right son (possibly NULL)
one parent (NULL, in case of the root)
a pointer to some useful information

3. Binary Tree - example

4. Binary Tree – C++ code void setRoot(BinaryTreeNode<T> *r) {
root = r; }
void insert(T x) {
if (pinfo == NULL)
setInfo(x);
else
insert_rec(x);
void insert_rec(T x) {
int next_son = rand() % 2;
if (next_son == 0) // left son {
if (left_son == NULL) {
left_son = new BinaryTreeNode<T>;
left_son->pinfo = new T;
*(left_son->pinfo) = x;
left_son->left_son = left_son->right_son
= NULL;
#include <stdio.h>
#include <stdlib.h>
char chstack[1000]; // will be used later
template <typename T> class BinaryTreeNode {
public:
T *pinfo;
BinaryTreeNode<T> *left_son, *right_son, *parent, *root;
BinaryTreeNode() {
pinfo = NULL;
left_son = right_son = parent = NULL;
root = this; }
void setInfo(T info)
pinfo = new T;
*pinfo = info;

5. Binary Tree – C++ code (cont.)
left_son->parent = this;
left_son->root = root; }
else
left_son->insert_rec(x);
else // right son {
if (right_son == NULL) {
right_son = new BinaryTreeNode<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);
BinaryTreeNode<T>* find(T x) {
BinaryTree<T> *rez;
if (pinfo == NULL)
return NULL;
// Use an equality testing function instead
if ((*pinfo) == x)
return this;
if (left_son != NULL)
rez = left_son->find(x);
else
rez = NULL;
if (rez != NULL)
return rez;
else if (right_son != NULL)
return right_son->find(x);

6. Binary Tree – C++ code (cont.)
else
return NULL; }
void remove() {
BinaryTreeNode<T> *leaf;
// find a leaf in this node's subtree
leaf = findLeaf();
if (this == leaf) {
if (parent == NULL) // this == root {
if (this->pinfo != NULL) delete this->pinfo;
root->pinfo = NULL; }
else {
if (parent->left_son == this)
parent->left_son = NULL;
parent->right_son = NULL;
delete this->pinfo;
delete this; }}
else {
if (leaf->parent->left_son == leaf)
leaf->parent->left_son = NULL;
else
leaf->parent->right_son = NULL;
leaf->parent = parent;
leaf->left_son = left_son;
leaf->right_son = right_son;
delete this->pinfo;
this->pinfo = leaf->pinfo;
delete leaf; }
void removeInfo(T x) {
BinaryTreeNode<T> *t = find(x);
if (t != NULL) t->remove();
BinaryTreeNode<T>* findLeaf() {
if (left_son == NULL && right_son == NULL)
return this;

7. Binary Tree – C++ code (cont.)
else
if (left_son != NULL)
return left_son->findLeaf();
return right_son->findLeaf(); }
void preOrderTraversal() {
printf("%d\n", *pinfo); /* we should use the correct format for printing type T values */
left_son->preOrderTraversal();
if (right_son != NULL)
right_son->preOrderTraversal();
void postOrderTraversal() {
left_son->postOrderTraversal();
right_son->postOrderTraversal();
printf("%d\n", *pinfo); /* we should use the correct format for printing type T values */ }
void inOrderTraversal() {
if (left_son != NULL)
left_son->inOrderTraversal();
if (right_son != NULL)
right_son->inOrderTraversal();
void preOrderTraversal2(int level) {
int i;
for (i = 0; i < level; i++)
printf("-");

8. Binary Tree – C++ code (cont.)
int main() {
srand(7290);
BinaryTreeNode<int> *r = new BinaryTreeNode<int>;
// r->setRoot(r);
r->insert(6);
r->insert(8);
r->insert(1);
r->insert(9);
r->insert(10);
r->insert(4);
r->insert(13);
r->insert(12);
r->preOrderTraversal();
printf("___\n");
r->preOrderTraversal2(0);
if (left_son != NULL)
left_son->preOrderTraversal2(level + 1);
if (right_son != NULL)
right_son->preOrderTraversal2(level + 1); }
void preOrderTraversal3(int level) {
int i;
for (i = 1; i <= level; i++)
printf("%c", chstack[i]);
printf("* %d\n", (*pinfo)); /* use the correct format */
chstack[level + 1] = 'L';
left_son->preOrderTraversal3(level + 1);
chstack[level + 1] = 'R';
right_son->preOrderTraversal3(level + 1); };

9. Binary Tree – C++ code (cont.)
r->preOrderTraversal3(0);
printf("___\n");
r->postOrderTraversal();
r->inOrderTraversal();
printf("%d\n", r->find(100));
printf("%d\n", r->find(1));
printf("%d\n", r->find(12));
printf("%d\n", r->find(8));
printf("%d\n", r->find(10));
printf("%d\n", r->find(20));
(r->find(10))->remove();
printf("_______\n%d\n", r->find(1));
return 0; }