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// here all b tree nodes allocated in heap, not disk.
namespace CLRS
{
template <typename T, std::size_t D> class BTree;
template <typename T, std::size_t D> class BTreeNode;
template <typename T, std::size_t D>
std::pair<std::shared_ptr<BTreeNode<T, D>>, std::size_t>
b_tree_search(const std::shared_ptr<BTreeNode<T, D>> &x, T k);
template <typename T, std::size_t D>
void b_tree_create(BTree<T, D> *t);
template <typename T, std::size_t D>
void b_tree_split_child(const std::shared_ptr<BTreeNode<T, D>> &x,
std::size_t i);
template <typename T, std::size_t D>
void b_tree_insert(BTree<T, D> *t, T k);
template <typename T, std::size_t D>
void b_tree_insert_nonfull(const std::shared_ptr<BTreeNode<T, D>> &x,
T k);
template <typename T, std::size_t D>
void b_tree_delete(BTree<T, D> *t,
const std::shared_ptr<BTreeNode<T, D>> &x,
T k);
template <typename T, std::size_t D>
class BTree
{
std::shared_ptr<BTreeNode<T, D>> root;
public:
BTree() = default;
std::shared_ptr<BTreeNode<T, D>> get_root() {return root;}
void set_root(std::shared_ptr<BTreeNode<T, D>> r) {root = r;}
};
template <typename T, std::size_t D>
class BTreeNode
{
std::size_t n = 0;
// default minimum degree specified by template parameter D
std::size_t t = D;
bool leaf = true;
std::vector<T> keys;
std::vector<std::shared_ptr<BTreeNode>> childs;
public:
BTreeNode() = default;
// constructor only for unittest use
BTreeNode(const std::vector<T> &vk): n(vk.size()), keys(vk) {}
std::size_t get_n() const {return n;}
void set_n(std::size_t m) {n = m;}
// minimum D is set in constructor once and for all
std::size_t get_t() const {return t;}
bool get_leaf() const {return leaf;}
void set_leaf(bool l) {leaf = l;}
T get_key(std::size_t i) const {return keys[i];}
void push_back_key(T k) {keys.push_back(k);}
void insert_key(T k, std::size_t i)
{auto it = keys.begin() + i; keys.insert(it, k);}
void delete_key(std::size_t i)
{auto it = keys.begin() + i; keys.erase(it);}
void replace_key(T k, std::size_t i) {keys[i] = k;}
std::shared_ptr<BTreeNode> get_child(std::size_t i) const
{return childs[i];}
void push_back_child(std::shared_ptr<BTreeNode> n)
{childs.push_back(n);}
void insert_child(std::shared_ptr<BTreeNode> n, std::size_t i)
{auto it = childs.begin() + i; childs.insert(it, n);}
void delete_child(std::size_t i)
{auto it = childs.begin() + i; childs.erase(it);}
};
template <typename T, std::size_t D>
void b_tree_create(BTree<T, D> *t)
{
std::shared_ptr<BTreeNode<T, D>> x =
std::make_shared<BTreeNode<T, D>>();
t->set_root(x);
}
template <typename T, std::size_t D>
std::pair<std::shared_ptr<BTreeNode<T, D>>, std::size_t>
b_tree_search(const std::shared_ptr<BTreeNode<T, D>> &x, T k)
{
std::size_t i = 1;
while(i <= x->get_n() && k > x->get_key(i - 1))
++i;
if(i <= x->get_n() && k == x->get_key(i - 1))
return std::make_pair(x, i - 1);
else if(x->get_leaf())
return std::make_pair(nullptr, 0);
else
return b_tree_search(x->get_child(i - 1), k);
}
template <typename T, std::size_t D>
void b_tree_split_child(const std::shared_ptr<BTreeNode<T, D>> &x,
std::size_t i)
{
auto z = std::make_shared<BTreeNode<T, D>>();
auto y = x->get_child(i);
z->set_leaf(y->get_leaf());
z->set_n(D - 1);
for(std::size_t j = 1; j <= D - 1; ++j)
z->push_back_key(y->get_key(j + D - 1));
if(!y->get_leaf())
for(std::size_t j = 1; j <= D; ++j)
z->push_back_child(y->get_child(j + D - 1));
x->insert_child(z, i + 1);
x->insert_key(y->get_key(D - 1), i);
y->delete_key(D - 1);
y->set_n(D - 1);
x->set_n(x->get_n() + 1);
}
template <typename T, std::size_t D>
void b_tree_insert(BTree<T, D> *t, T k)
{
auto r = t->get_root();
if(r->get_n() == 2 * D - 1)
{
auto s = std::make_shared<BTreeNode<T, D>>();
t->set_root(s);
s->set_leaf(false);
s->push_back_child(r);
b_tree_split_child(s, 0);
b_tree_insert_nonfull(s, k);
}
else
b_tree_insert_nonfull(r, k);
}
template <typename T, std::size_t D>
void b_tree_insert_nonfull(const std::shared_ptr<BTreeNode<T, D>> &x, T k)
{
std::size_t i = x->get_n();
if(x->get_leaf())
{
while(i >= 0 && k < x->get_key(i - 1))
--i;
x->insert_key(k, i);
x->set_n(x->get_n() + 1);
}
else
{
while(i >= 0 && k < x->get_key(i - 1))
--i;
if(x->get_child(i)->get_n() == 2 * D - 1)
{
b_tree_split_child(x, i);
if(k > x->get_key(i))
++i;
}
b_tree_insert_nonfull(x->get_child(i), k);
}
}
template <typename T, std::size_t D>
void b_tree_delete(BTree<T, D> *t, const std::shared_ptr<BTreeNode<T, D>> &x, T k)
{
std::size_t i = 1;
while(i <= x->get_n() && k > x->get_key(i - 1))
++i;
if(i <= x->get_n() && k == x->get_key(i - 1))
{
// case 1: leaf node
if(x->get_leaf())
{
x->delete_key(i - 1);
x->set_n(x->get_n() - 1);
}
else
{
// case 2a
if(x->get_child(i - 1)->get_n() >= D)
{
auto y = x->get_child(i - 1);
T j = y->get_key(y->get_n() - 1);
b_tree_delete(t, y, j);
x->replace_key(j, i - 1);
}
// case 2b which is opposite to 2a
else if(x->get_child(i)->get_n() >= D)
{
auto z = x->get_child(i);
T j = z->get_key(0);
b_tree_delete(t, z, j);
x->replace_key(j, i - 1);
}
// case 2c
else
{
auto y = x->get_child(i - 1);
auto z = x->get_child(i);
y->push_back_key(k);
y->set_n(y->get_n() + 1);
x->delete_key(i - 1);
x->delete_child(i);
x->set_n(x->get_n() - 1);
for(std::size_t n = 0; n < z->get_n(); ++n)
y->push_back_key(z->get_key(n));
y->set_n(z->get_n() + y->get_n());
if(!y->get_leaf())
for(std::size_t n = 0; n <= z->get_n(); ++n)
y->push_back_child(z->get_child(n));
b_tree_delete(t, y, k);
}
}
}
else
{
auto self = x->get_child(i - 1);
std::shared_ptr<BTreeNode<T, D>> brother;
// case 3a
if(self->get_n() == D - 1)
{
if(i - 1 > 0 && x->get_child(i - 2)->get_n() >= D)
{
brother = x->get_child(i - 2);
std::size_t bl = brother->get_n();
T down = x->get_key(i - 2);
T up = brother->get_key(bl - 1);
self->insert_key(down, 0);
self->set_n(self->get_n() + 1);
x->replace_key(up, i - 2);
if(!brother->get_leaf())
{
self->insert_child(brother->get_child(bl), 0);
brother->delete_child(bl);
}
brother->delete_key(bl - 1);
brother->set_n(bl - 1);
}
else if(i <= x->get_n() && x->get_child(i)->get_n() >= D)
{
brother = x->get_child(i);
std::size_t bl = brother->get_n();
T down = x->get_key(i - 1);
T up = brother->get_key(0);
self->push_back_key(down);
self->set_n(x->get_n() + 1);
x->replace_key(up, i - 1);
if(!brother->get_leaf())
{
self->push_back_child(brother->get_child(0));
brother->delete_child(0);
}
brother->delete_key(0);
brother->set_n(bl - 1);
}
// case 3b
else
{
if(i - 1 == 0)
{
brother = x->get_child(i);
T down = x->get_key(i - 1);
self->push_back_key(down);
self->set_n(self->get_n() + 1);
for(std::size_t i = 0; i < brother->get_n(); ++i)
self->push_back_key(brother->get_key(i));
if(!self->get_leaf())
for(std::size_t i = 0; i <= brother->get_n(); ++i)
self->push_back_child(brother->get_child(i));
self->set_n(self->get_n() + brother->get_n());
x->delete_key(i - 1);
x->delete_child(i);
x->set_n(x->get_n() - 1);
if(x->get_n() == 0)
t->set_root(self);
}
else
{
brother = x->get_child(i - 2);
T down = x->get_key(i - 2);
brother->push_back_key(down);
brother->set_n(brother->get_n() + 1);
for(std::size_t i = 0; i < self->get_n(); ++i)
brother->push_back_key(self->get_key(i));
if(!brother->get_leaf())
for(std::size_t i = 0; i <= self->get_n(); ++i)
brother->push_back_child(self->get_child(i));
brother->set_n(self->get_n() + brother->get_n());
x->delete_key(i - 2);
x->delete_child(i - 1);
x->set_n(x->get_n() - 1);
if(x->get_n() == 0)
t->set_root(brother);
self = brother;
}
}
}
b_tree_delete(t, self, k);
}
}
}
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