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#ifndef _Binary_tree
#define _Binary_tree
#include <math.h>
#include <stddef.h> // NULL
#include <cassert>
template<class T> class Binary_tree {
protected:
T _content;
Binary_tree<T>* _left,*_right,*_super;
int number_node() const;
int search() const;
public:
inline virtual bool validator() const{ return true;} /* Fonction utile pour l'arbre AVL */
Binary_tree(const T&);
int h() const;
int H() const;
virtual bool isAVL() const;
virtual void push_left(Binary_tree<T>*);
virtual void push_right(Binary_tree<T>*);
inline Binary_tree<T>* root() {if(! _super) return this;return _super->root();};
inline Binary_tree<T>*& super() {return _super;};
virtual bool isComplete() const;
virtual bool isPerfect() const;
virtual bool remove_left();
virtual bool remove_right();
};
template<class T> Binary_tree<T>::Binary_tree(const T& t) : _content(t) {
_left = _right = _super = NULL;
}
template<class T> int Binary_tree<T>::h() const {
if(! _super) return 0;
return _super->h() + 1;
}
template<class T> int Binary_tree<T>::H() const {
int H_left,H_right;
_left ? H_left = _left->H() + 1 : H_left = 0;
_right ? H_right = _right->H() + 1 : H_right = 0;
return H_left < H_right ? H_right : H_left;
}
template<class T> bool Binary_tree<T>::isAVL() const {
if(! _left && ! _right) return true;
if(! _left) return _right->H() < 1; /* il faut enlever le = ? */
if(! _right) return _left->H() < 1;
return ::abs(_right->H() - _left->H()) <= 1;
}
template<class T> void Binary_tree<T>::push_left(Binary_tree<T>* left) {
bool add;
assert(left);
if(_left || left->_super) return;
left->_super = this;
_left = left;
add = root()->validator();
if(add == false){
left->_super = NULL;
_left = NULL;
}
}
template<class T> void Binary_tree<T>::push_right(Binary_tree<T>* right) {
bool add;
assert(right);
if(_right || right->_super) return;
right->_super = this;
_right = right;
add = root()->validator();
if(add == false){
right->_super = NULL;
_right = NULL;
}
}
template<class T> int Binary_tree<T>::number_node() const {
int nbNode=0;
if(_left != NULL) nbNode = nbNode + _left->number_node();
if(_right != NULL) nbNode = nbNode + _right->number_node();
return (1+nbNode);
}
template<class T> bool Binary_tree<T>::isComplete() const {
double height; /* nombre de noeuds théoriques selon la hauteur */
double nbNode;
height = pow(2,H()+1)-1;
nbNode = number_node();
if(height == nbNode)return true;
else return false;
}
template<class T> int Binary_tree<T>::search() const{
if(!_right && !_left) return 1;
if(!_left && _right) return 0;
if(_left && !_right) return 1;
if(_left->search() >= _right->search()) return 1;
else return 0;
}
template<class T> bool Binary_tree<T>::isPerfect() const {
double height; /* Nombre de noeuds théoriques minimum selon la hauteur */
double nbNode;
height = pow(2,H())-1;
nbNode = number_node();
if(nbNode <= height) return false;
else return search();
}
template<class T> bool Binary_tree<T>::remove_left() {
Binary_tree<T> *temp1,*temp2;
bool del = true; /* valide ou pas la suppression */
temp1 = _left;
temp2 = _left->_super;
_left->_super = NULL;
_left = NULL;
del = root()->validator();
if(del == false){
_left = temp1;
_left->_super = temp2;
}
return del;
}
template<class T> bool Binary_tree<T>::remove_right() {
Binary_tree<T> *temp1,*temp2;
bool del = true; /* valide ou pas la suppression */
temp1 = _right;
temp2 = _right->_super;
_right->_super = NULL;
_right = NULL;
del = root()->validator();
if(del == false){
_right = temp1;
_right->_super = temp2;
}
return del;
}
template<class T> class AVL_tree : public Binary_tree<T> {
protected:
virtual bool validator() const; /* Valide ou pas la modification de l'arbre AVL */
public:
AVL_tree(const T&);
virtual void push_left(Binary_tree<T>*);
virtual void push_right(Binary_tree<T>*);
inline bool isAVL() const { return true;}
};
template<class T> AVL_tree<T>::AVL_tree(const T& t) : Binary_tree<T>(t) {
}
template<class T> void AVL_tree<T>::push_left(Binary_tree<T>* left) {
bool add;
assert(left);
if(_left || left->super()) return;
if(! _right && left->H() > 1) return;
if(_right && ::abs(_right->H() - left->H()) > 1) return;
left->super() = this;
_left = left;
if(_right != NULL) return;
add = root()->validator();
if(add == false){
left->super() = NULL;
_left = NULL;
}
}
template<class T> void AVL_tree<T>::push_right(Binary_tree<T>* right) {
bool add;
assert(right);
if(_right || right->super()) return;
if(! _left && right->H() > 1) return;
if(_left && ::abs(_left->H() - right->H()) > 1) return;
right->super() = this;
_right = right;
if(_left != NULL) return;
add = root()->validator();
if(add == false){
right->super() = NULL;
_right = NULL;
}
}
template<class T>bool AVL_tree<T>::validator() const{
if(_super == NULL){
if(this->Binary_tree<T>::isAVL()) return true;
else return false;
}
}
#endif |
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