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#include<iostream>
using namespace std;
template<class H> class MultiBST {
virtual MultiBST<H>* ins(H x) = 0;
virtual int multiplicity(H x) = 0;
virtual void inorder() = 0;
};
template<class H>
class node {
public:
node(H val) : _key{val}, _parent{nullptr}, _left{nullptr}, _right{nullptr}, _rk{1} {}
H& key() { return _key; }
const H& key() const { return _key; }
node<H>*& parent() { return _parent; }
const node<H>*& parent() const { return _parent; }
node<H>*& left() { return _left; }
const node<H>*& left() const { return _left; }
node<H>*& right() { return _right; }
const node<H>*& right() const { return _right; }
int& rk() { return _rk; }
const int& rk() const { return _rk; }
private:
H _key;
node<H>* _parent;
node<H>* _left;
node<H>* _right;
int _rk;
};
template<class H>
class MyMultiBST : public MultiBST<H> {
public:
MyMultiBST() : _root{nullptr} {}
node<H>*& root() { return _root; }
const node<H>*& root() const { return _root; }
int multiplicity(H x) {
auto elem = _search(x);
if(elem)
return elem->rk();
return 0;
}
MyMultiBST<H>* ins(H x) {
auto iter = _search(x);
if(iter) {
iter->rk() = iter->rk()+1;
} else {
iter = _root;
node<H>* y{nullptr};
while(iter) {
y = iter;
if(iter->key() > x)
iter = iter->left();
else
iter = iter->right();
}
node<H>* nodus = new node<H>{x};
nodus->parent() = y;
if(!y) {
_root = nodus;
} else if(y->key() > x) {
y->left() = nodus;
} else {
y->right() = nodus;
}
}
return this;
}
void inorder() {
_inorder(_root);
}
MyMultiBST<H>* del(H x) {
node<H>* y;
node<H>* z = _search(x);
if(!z) return this;
if(z->rk() > 1) {
z->rk() = z->rk()-1;
} else {
if(!z->left()) {
_transplant(z, z->right());
} else if(!z->right()) {
_transplant(z, z->left());
} else {
y = _min(z->right());
if(y->parent() != z) {
_transplant(y, y->right());
y->right() = z->right();
y->right()->parent() = y;
}
_transplant(z, y);
y->left() = z->left();
y->left()->parent() = y;
delete z;
}
}
return this;
}
node<H>* predecessor(H x) {
auto iter = _search(x);
if(!iter) return nullptr;
if(iter->left())
return _max(iter->left());
auto y = iter->parent();
while(y && iter == y->left()) {
iter = y;
y = y->parent();
}
return y;
}
int rank(H x) {
auto iter = predecessor(x);
int sum{1};
while(iter) {
sum+=iter->rk();
iter = predecessor(iter->key());
}
return sum;
}
private:
void _transplant(node<H>* u, node<H>* v) {
if(!u->parent()) _root = v;
else if(u == u->parent()->left())
u->parent()->left() = v;
else
u->parent()->right() = v;
if(v)
v->parent() = u->parent();
}
node<H>* _max(node<H>* x) {
if(!x) return nullptr;
auto iter = x;
while(iter->right()) {
iter = iter->right();
}
return iter;
}
node<H>* _min(node<H>* x) {
if(!x) return nullptr;
auto iter = x;
while(iter->left()) {
iter = iter->left();
}
return iter;
}
void _inorder(node<H>* p) {
if(p) {
_inorder(p->left());
for(int i = 0; i < p->rk(); ++i) {
cout << p->key() << ' ';
}
_inorder(p->right());
}
}
node<H>* _search(H val) {
auto iter = _root;
while(iter && iter->key() != val) {
if(iter->key() > val)
iter = iter->left();
else
iter = iter->right();
}
return iter;
}
node<H>* _root;
};
int main() {
MyMultiBST<int>* t = new MyMultiBST<int>{};
for(auto const& i : {10, 7, 7, 23, 30, 4, 1, 5, 9, 5, 1, 7, 1, 9})
t->ins(i);
t->inorder();
cout << '\n';
for(auto const& i : {5, 7, 17})
cout << i << ": " << t->multiplicity(i) << endl;
for(auto const& i : {7, 4, 23, 7, 7})
t->del(i);
t->inorder();
cout << '\n';
for(auto const& i: {5, 9, 30})
cout << t->rank(i) << ' ';
delete t;
return 0;
}
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