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namespace CLRS
{
template <typename T>
class FibHeap;
template <typename T>
class FibHeapTreeNode;
template <typename T>
FibHeap<T> make_fib_heap();
template <typename T>
void fib_heap_insert(const FibHeap<T> &,
const std::shared_ptr<FibHeapTreeNode<T>> &);
template <typename T>
std::shared_ptr<FibHeapTreeNode<T>>
fib_heap_minimum(const FibHeap<T> &);
template <typename T>
FibHeap<T> fib_heap_union(const FibHeap<T> &, const FibHeap<T> &);
template <typename T>
std::shared_ptr<FibHeapTreeNode<T>> fib_heap_extract_min(FibHeap<T> &);
template <typename T>
void consolidate(FibHeap<T> &);
template <typename T>
void fib_heap_link(const FibHeap<T> &,
const std::shared_ptr<FibHeapTreeNode<T>> &,
const std::shared_ptr<FibHeapTreeNode<T>> &);
template <typename T>
void fib_heap_decrease_key(FibHeap<T> &,
const std::shared_ptr<FibHeapTreeNode<T>> &,
T);
template <typename T>
void cut(const FibHeap<T> &,
const std::shared_ptr<FibHeapTreeNode<T>> &,
const std::shared_ptr<FibHeapTreeNode<T>> &);
template <typename T>
void cascading_cut(const FibHeap<T> &,
const std::shared_ptr<FibHeapTreeNode<T>> &);
template <typename T>
void fib_heap_delete(FibHeap<T> &,
const std::shared_ptr<FibHeapTreeNode<T>> &);
/*
* doubly linked circular list helper functions
*/
// just assign itself to the left and right of node.
template <typename T>
void fib_heap_list_make(const std::shared_ptr<FibHeapTreeNode<T>> &x)
{
x->set_left(x);
x->set_right(x);
}
// just link first to the second and the left of second
template <typename T>
void fib_heap_list_insert(const std::shared_ptr<FibHeapTreeNode<T>> &x,
const std::shared_ptr<FibHeapTreeNode<T>> &y)
{
x->set_right(y);
x->set_left(y->get_left());
y->get_left()->set_right(x);
y->set_left(x);
}
// just need the removing node as parameter, link its left and right
template <typename T>
void fib_heap_list_remove(const std::shared_ptr<FibHeapTreeNode<T>> &x)
{
x->get_left()->set_right(x->get_right());
x->get_right()->set_left(x->get_left());
}
// make the first a child of the second, increase second's degree
template <typename T>
void fib_heap_list_add_child(
const std::shared_ptr<FibHeapTreeNode<T>> &x,
const std::shared_ptr<FibHeapTreeNode<T>> &y)
{
if(y->get_child() != nullptr)
{
fib_heap_list_insert(x, y->get_child());
x->set_p(y);
}
else
{
fib_heap_list_make(x);
y->set_child(x);
x->set_p(y);
}
y->incr_degree();
}
// make the first not a child of the second, decrease second's degree
template <typename T>
void fib_heap_list_remove_child(
const std::shared_ptr<FibHeapTreeNode<T>> &x,
const std::shared_ptr<FibHeapTreeNode<T>> &y)
{
fib_heap_list_remove(x);
if(x->get_right() == x)
y->set_child(nullptr);
else
y->set_child(x->get_right());
y->decr_degree();
}
/*
* calculate maxmum degreee based on amount of nodes
*/
std::size_t fib_maximum_degree(std::size_t n)
{
// loga(b) = log2(b) / log2(a)
double gold = (1 + std::sqrt(2)) / 2;
double below = std::log2(gold);
double top = std::log2(n);
return top / below;
}
template <typename T>
class FibHeap
{
public:
using FibNodeSHPTR = std::shared_ptr<FibHeapTreeNode<T>>;
FibHeap() = default;
std::size_t get_n() const {return n;}
FibNodeSHPTR get_min() const {return min;}
void incr_n() {++n;}
void decr_n() {--n;}
void set_n(std::size_t m) {n = m;}
void set_min(FibNodeSHPTR m) {min = m;}
private:
std::size_t n = 0;
FibNodeSHPTR min = nullptr;
};
template <typename T>
class FibHeapTreeNode
{
public:
using FibNodeSHPTR = std::shared_ptr<FibHeapTreeNode>;
FibHeapTreeNode() = default;
FibHeapTreeNode(T k): key(k) {}
T get_key() const {return key;}
void set_key(T k) {key = k;}
bool get_mark() const {return mark;}
void set_mark() {mark = true;}
void clear_mark() {mark = false;}
std::size_t get_degree() const {return degree;}
void incr_degree() {++degree;}
void decr_degree() {--degree;}
FibNodeSHPTR get_p() const {return p;}
void set_p(const FibNodeSHPTR &parent) {p = parent;}
FibNodeSHPTR get_child() const {return child;}
void set_child(const FibNodeSHPTR &c) {child = c;}
FibNodeSHPTR get_left() const {return left;}
void set_left(const FibNodeSHPTR &l) {left = l;}
FibNodeSHPTR get_right() const {return right;}
void set_right(const FibNodeSHPTR &r) {right = r;}
private:
T key;
bool mark = false;
std::size_t degree = 0;
FibNodeSHPTR p = nullptr;
FibNodeSHPTR child = nullptr;
FibNodeSHPTR left = nullptr;
FibNodeSHPTR right = nullptr;
};
template <typename T>
FibHeap<T> make_fib_heap()
{
return FibHeap<T>();
}
template <typename T>
void fib_heap_insert(FibHeap<T> &h,
const std::shared_ptr<FibHeapTreeNode<T>> &x)
{
if(h.get_min() == nullptr)
{
fib_heap_list_make(x);
h.set_min(x);
}
else
{
fib_heap_list_insert(x, h.get_min());
if(x->get_key() < h.get_min()->get_key())
h.set_min(x);
}
h.incr_n();
}
template <typename T>
std::shared_ptr<FibHeapTreeNode<T>>
fib_heap_minimum(const FibHeap<T> &h)
{
return h.get_min();
}
template <typename T>
FibHeap<T> fib_heap_union(const FibHeap<T> &h1, const FibHeap<T> &h2)
{
FibHeap<T> h;
h.set_min(h1.get_min());
auto h_min = h.get_min();
auto h2_n = h2.get_min();
// concatenate
if(h_min == nullptr)
h.set_min(h2_n);
else if(h2_n != nullptr)
do
{
auto temp = h2_n;
h2_n = h2_n->get_right();
fib_heap_list_insert(temp, h_min);
}
while(h2_n != h2.get_min());
if(h2.get_min() != nullptr && h1.get_min() != nullptr &&
h2.get_min()->get_key() < h1.get_min()->get_key())
h.set_min(h2.get_min());
h.set_n(h1.get_n() + h2.get_n());
return h;
}
template <typename T>
std::shared_ptr<FibHeapTreeNode<T>> fib_heap_extract_min(FibHeap<T> &h)
{
auto z = h.get_min();
if(z != nullptr)
{
auto n = z->get_child();
for(std::size_t d = 1; d <= z->get_degree(); ++d)
{
auto temp = n->get_right();
fib_heap_list_insert(n, z);
n->set_p(nullptr);
n = temp;
}
fib_heap_list_remove(z);
if(z->get_right() == z)
h.set_min(nullptr);
else
{
h.set_min(z->get_right());
consolidate(h);
}
h.decr_n();
}
return z;
}
template <typename T>
void consolidate(FibHeap<T> &h)
{
std::size_t max_degree = fib_maximum_degree(h.get_n());
std::shared_ptr<FibHeapTreeNode<T>> a[max_degree + 1];
auto w = h.get_min();
/*
* the reason why the former commit of code below causes a bug:
* the min of fib heap may be removed from the root list
* and then the former while loop is infinite.
* Fix: compute the length of root list and take it as the while contition
* TODO: data root list length better stored in class FibHeap
*/
std::size_t root_list_len = 0;
do
{
++root_list_len;
w = w->get_right();
}
while(w != h.get_min());
// handle each node of root list
while(root_list_len != 0)
{
auto x = w;
w = w->get_right();
std::size_t d = x->get_degree();
while(a[d] != nullptr)
{
auto y = a[d];
if(y->get_key() < x->get_key())
{
auto temp = x;
x = y;
y = temp;
}
fib_heap_link(h, y, x);
a[d] = nullptr;
++d;
}
a[d] = x;
--root_list_len;
}
// now the root list must be reconstructed
h.set_min(nullptr);
for(std::size_t i = 0; i <= max_degree; ++i)
{
if(a[i] != nullptr)
{
if(h.get_min() == nullptr)
{
fib_heap_list_make(a[i]);
h.set_min(a[i]);
}
else
{
fib_heap_list_insert(a[i], h.get_min());
if(a[i]->get_key() < h.get_min()->get_key())
h.set_min(a[i]);
}
}
}
}
template <typename T>
void fib_heap_link(const FibHeap<T> &h,
const std::shared_ptr<FibHeapTreeNode<T>> &y,
const std::shared_ptr<FibHeapTreeNode<T>> &x)
{
fib_heap_list_remove(y);
fib_heap_list_add_child(y, x);
y->clear_mark();
}
template <typename T>
void fib_heap_decrease_key(FibHeap<T> &h,
const std::shared_ptr<FibHeapTreeNode<T>> &x,
T k)
{
if(x->get_key() < k)
throw std::logic_error("new key is greater than current key");
x->set_key(k);
auto y = x->get_p();
if(y != nullptr && x->get_key() < y->get_key())
{
cut(h, x, y);
cascading_cut(h, y);
}
if(x->get_key() < h.get_min()->get_key())
h.set_min(x);
}
template <typename T>
void cut(const FibHeap<T> &h,
const std::shared_ptr<FibHeapTreeNode<T>> &x,
const std::shared_ptr<FibHeapTreeNode<T>> &y)
{
fib_heap_list_remove_child(x, y);
fib_heap_list_insert(x, h.get_min());
x->set_p(nullptr);
x->clear_mark();
}
template <typename T>
void cascading_cut(const FibHeap<T> &h,
const std::shared_ptr<FibHeapTreeNode<T>> &y)
{
auto z = y->get_p();
if(z != nullptr)
{
if(!y->get_mark())
y->set_mark();
else
{
cut(h, y, z);
cascading_cut(h, z);
}
}
}
template <typename T>
void fib_heap_delete(FibHeap<T> &h,
const std::shared_ptr<FibHeapTreeNode<T>> &x,
T k)
{
fib_heap_decrease_key(h, x, k);
fib_heap_extract_min(h);
}
}
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