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namespace CLRS
{
// recursive version of search
template <typename T>
TreeNode<T> *tree_search(TreeNode<T> *x, T k)
{
if(x == nullptr || k == x->get_value())
return x;
if(k < x->get_value())
return tree_search(x->get_left(), k);
else
return tree_search(x->get_right(), k);
}
// iterative version of serach
template <typename T>
TreeNode<T> *iterative_tree_search(TreeNode<T> *x, T k)
{
while(x != nullptr && k != x->get_value())
{
if(k < x->get_value())
x = x->get_left();
else
x = x->get_right();
}
return x;
}
template <typename T>
TreeNode<T> *tree_minimum(TreeNode<T> *x)
{
while(x->get_left() != nullptr)
x = x->get_left();
return x;
}
template <typename T>
TreeNode<T> *tree_maximum(TreeNode<T> *x)
{
while(x->get_right() != nullptr)
x = x->get_right();
return x;
}
template <typename T>
TreeNode<T> *tree_successor(TreeNode<T> *x)
{
if(x->get_right() != nullptr)
return tree_minimum(x->get_right());
TreeNode<T> *y = x->get_parent();
while(y != nullptr && x == y->get_right())
{
x = y;
y = y->get_parent();
}
return y;
}
template <typename T>
TreeNode<T> *tree_predecessor(TreeNode<T> *x)
{
if(x->get_left() != nullptr)
return tree_maximum(x->get_left());
TreeNode<T> *y = x->get_parent();
while(y != nullptr && x == y->get_left())
{
x = y;
y = y->get_parent();
}
return y;
}
template <typename T>
void tree_insert(Tree<T> *t, TreeNode<T> *z)
{
TreeNode<T> *y = nullptr;
TreeNode<T> *x = t->get_root();
while(x != nullptr)
{
y = x;
if(z->get_value() < x->get_value())
x = x->get_left();
else
x = x->get_right();
}
z->set_parent(y);
if(y == nullptr)
t->set_root(z);
else if(z->get_value() < y->get_value())
y->set_left(z);
else
y->set_right(z);
}
// update of left and right of v is caller's duty.
template <typename T>
void transplant(Tree<T> *t, TreeNode<T> *u, TreeNode<T> *v)
{
if(u->get_parent() == nullptr)
t->set_root(v);
else if(u == u->get_parent()->get_left())
u->get_parent()->set_left(v);
else
u->get_parent()->set_right(v);
if(v != nullptr)
v->set_parent(u->get_parent());
}
template <typename T>
void tree_delete(Tree<T> *t, TreeNode<T> *z)
{
if(z->get_left() == nullptr)
transplant(t, z, z->get_right());
else if(z->get_right() == nullptr)
transplant(t, z, z->get_left());
else
{
TreeNode<T> *y = tree_minimum(z->get_right());
if(y->get_parent() != z)
{
transplant(t, y, y->get_right());
y->set_right(z->get_right());
y->get_right()->set_parent(y);
}
transplant(t, z, y);
y->set_left(z->get_left());
y->get_left()->set_parent(y);
}
}
}
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