二项堆

Posted 2020-08-19

算法来自算法导论第19章

设计类：二项堆这个东西的逻辑是这样的：节点-二项树-二项堆，so刚开始时想设计三个类，BNode BTree BHeap

后来发现BTree是完全没有必要的。。BTree的功能完全可以写在BNode里（Link），所以最后就只设计了两个类。

拖这么久是因为有个指针没指对。。算导里关于Union的部分少了修改next_x->Sibling->Parent的部分，就是这部分坑了我两星期。。反复的debug，最后终于发现是Parent出错了，然后，，就没有然后了。。如此简单的bug

顺便把难看的代码附上

  1 //Binomial Heap
  2 #include <iostream>
  3 #include <vector>
  4 #include <string>
  5 #include <my.cpp>
  6 
  7 class BNode:public my::total_ordering<BNode>{
  8     friend std::ostream& operator<<(std::ostream&,const BNode*);
  9     friend class BHeap;
 10     
 11     public:
 12         explicit BNode(int key,BNode *parent=nullptr,BNode *child=nullptr,BNode *sibling=nullptr,int degree=0):
 13         Key(key),Parent(parent),Child(child),Sibling(sibling),Degree(degree) {}
 14         virtual bool operator==(const BNode& n) const override{
 15             return Key == n.Key;
 16         }
 17         virtual bool operator<(const BNode& n) const override{
 18             return Key < n.Key;
 19         }
 20         static void exchange(BNode *n1,BNode *n2){
 21             std::swap(n1->Key,n2->Key);
 22         }
 23                 
 24     protected:
 25         static BNode* Link(BNode *left,BNode *right){
 26             left->Parent = right;
 27             left->Sibling = right->Child;
 28             right->Child = left;
 29             ++right->Degree;
 30             return right;
 31         }
 32     private:
 33         int Key;
 34         BNode *Parent,*Child,*Sibling;
 35         int Degree;
 36         
 37 };
 38 inline std::ostream& operator<<(std::ostream& os,const BNode *n){
 39     if (not n) os << "NULLPTR";
 40     else os << n->Key;
 41     return os;
 42 }
 43 
 44 class KeyGreaterError{
 45     friend std::ostream& operator<<(std::ostream&,const KeyGreaterError&);
 46     
 47     public:
 48         explicit KeyGreaterError(const std::string& str):msg(str) {}
 49         explicit KeyGreaterError(const char* str):msg(std::string(str)) {}
 50     private:
 51         std::string msg;
 52 };
 53 inline std::ostream& operator<<(std::ostream& os,const KeyGreaterError& err){
 54     os << err.msg;
 55     return os;
 56 }
 57 
 58 class BHeap{
 59     friend std::ostream& operator<<(std::ostream&,const BHeap*);
 60     
 61     public:
 62         explicit BHeap(BNode *head=nullptr):Head(head) {}
 63         explicit operator bool() const{
 64             if (Head) return true;
 65             else return false;
 66         }
 67         BNode* Find_Minimum() const{
 68             BNode *root(Head),*MIN(root);
 69             while (root){
 70                 if (root < MIN) MIN = root;
 71                 root = root->Sibling;
 72             }
 73             return MIN;
 74         }
 75         void Insert(int x){
 76             BNode *n(new BNode (x));
 77             Insert(n);
 78         }
 79         BNode* Extract_Min(){
 80             BNode* MIN(Find_Minimum());
 81             if (not MIN) return nullptr;
 82             if ((not MIN->Parent) and (not MIN->Sibling)){
 83                 Head = nullptr;
 84             }else if (not MIN->Parent){
 85                 Head = MIN->Sibling;
 86                 MIN->Sibling->Parent = nullptr;
 87             }else if (MIN->Sibling){
 88                 MIN->Parent->Sibling = MIN->Sibling;
 89                 MIN->Sibling->Parent = MIN->Parent;
 90             }else{
 91                 MIN->Parent->Sibling = nullptr;
 92             }
 93             BHeap *heap1(new BHeap (this->Head));
 94             BNode *child(MIN->Child);
 95             if (child){
 96                 BNode *next(child->Sibling),*next_tmp(nullptr);
 97                 child->Sibling = nullptr;
 98                 child->Parent = nullptr;
 99                 while (next){
100                     child->Parent = next;
101                     next_tmp = next->Sibling; 
102                     next->Sibling = child;
103                     child = next;
104                     next = next_tmp;
105                 }
106             }
107             if (child) child->Parent = nullptr;
108             BHeap *heap2(new BHeap (child));
109             BHeap *union_heap(Union(heap1,heap2));
110             Head = union_heap->Head;
111             delete union_heap;
112             return MIN;
113         }
114         void Delete(BNode *n){
115             Decrease_Key(n,-1);
116             delete Extract_Min();
117         }
118         void Collect_Nodes(){
119             BNode *MIN = Extract_Min();
120             while (MIN){
121                 delete MIN;
122                 MIN = Extract_Min();
123             }
124         }
125         
126     protected:
127         BNode *Head;
128         
129         static BNode* Merge(BHeap *H1,BHeap *H2){
130             BNode *head1(H1->Head),*head2(H2->Head),*head(nullptr),*now(nullptr);
131             if (head1 and head2){
132                 if (head1->Degree > head2->Degree){
133                     head = head2;
134                     head2 = head2->Sibling;
135                 }else{
136                     head = head1;
137                     head1 = head1->Sibling;
138                 }
139             }else if (head1){
140                 head = head1;
141                 head1 = head1->Sibling;
142             }else if (head2){
143                 head = head2;
144                 head2 = head2->Sibling;
145             }else return nullptr;
146             now = head;
147             while (head1 and head2){
148                 if (head1->Degree > head2->Degree){
149                     now->Sibling = head2;
150                     head2->Parent = now;
151                     now = head2;
152                     head2 = head2->Sibling;
153                 }else{
154                     now->Sibling = head1;
155                     head1->Parent = now;
156                     now = head1;
157                     head1 = head1->Sibling;
158                 }
159             }
160             while (head1){
161                 now->Sibling = head1;
162                 head1->Parent = now;
163                 now = head1;
164                 head1 = head1->Sibling;
165             }
166             while (head2){
167                 now->Sibling = head2;
168                 head2->Parent = now;
169                 now = head2;
170                 head2 = head2->Sibling;
171             }
172             return head;
173         }
174         static BHeap* Union(BHeap *H1,BHeap *H2){
175             BHeap *heap(new BHeap (Merge(H1,H2)));
176             delete H1;
177             delete H2;
178             if (not heap->Head) return heap;
179             BNode *x(heap->Head),*next_x(x->Sibling),*prev_x(nullptr);
180             while (next_x){
181                 if ((x->Degree != next_x->Degree) or ((next_x->Sibling) and (next_x->Sibling->Degree == x->Degree))){
182                     prev_x = x;
183                     x = next_x;
184                 }else if (x->Key <= next_x->Key){
185                     x->Sibling = next_x->Sibling;
186                     if (x->Sibling) x->Sibling->Parent = x;
187                     BNode::Link(next_x,x);
188                 }else{
189                     if (not prev_x) heap->Head = next_x;
190                     else prev_x->Sibling = next_x;
191                     next_x->Parent = prev_x;
192                     BNode::Link(x,next_x);
193                     x = next_x;
194                 }
195                 next_x = x->Sibling;
196             }
197             return heap;
198         }
199         void Insert(BNode *x){
200             BHeap *heap_orig(new BHeap (this->Head)),*heap_node(new BHeap (x));
201             BHeap *union_heap (Union(heap_orig,heap_node));
202             Head = union_heap->Head;
203             delete union_heap;
204         }
205         void Decrease_Key(BNode *node,int key){
206             if (key > node->Key) throw KeyGreaterError("orig key is "+std::to_string(node->Key)+" but "+std::to_string(key)+" given.");
207             node->Key = key;
208             BNode *node_this(node),*node_parent(node->Parent);
209             while ((node_parent) and (node_this->Key < node_parent->Key) and (node_this->Degree < node_parent->Degree)){
210                 BNode::exchange(node_this,node_parent);
211                 node_this = node_parent;
212                 node_parent = node_parent->Parent;
213             } 
214         }
215 };
216 inline std::ostream& operator<<(std::ostream& os,const BHeap *h){
217     os << h->Head;
218     return os;
219 }
220 
221 int main(){
222     BHeap H;
223     for (int i=1;i<=10;++i) H.Insert(i);
224     std::cout << &H;
225     H.Collect_Nodes();
226     std::cout << " " << &H;
227 }

Binomial Heap

 

 1 #include <iostream>
 2 #include <vector>
 3 
 4 namespace my{
 5     template<typename T>
 6     class total_ordering{
 7     public:
 8         virtual bool operator==(const T&) const =0;
 9         virtual bool operator<(const T&) const =0;
10         virtual bool operator!=(const T& obj) const{
11             return not (*this == obj);
12         }
13         virtual bool operator<=(const T& obj) const{
14             return ((*this == obj) or (*this < obj));
15         }
16         virtual bool operator>(const T& obj) const{
17             return not (*this <= obj);
18         }
19         virtual bool operator>=(const T& obj) const{
20             return not (*this < obj);
21         }
22         virtual ~total_ordering() {};
23     };
24     
25     template <typename P>
26     class QSort{
27     //typedef double P;
28     typedef std::vector<P> PVec;
29     
30     public:
31         QSort(const PVec& x):orig(x) {sort();}
32         PVec getans(){
33             return orig;
34         }
35         
36     private:
37         PVec orig;
38         void sort(){
39             subsort(this->orig.begin(),this->orig.end());
40         }
41         void subsort(typename PVec::iterator begin_iter,typename PVec::iterator end_iter){
42             if (end_iter - begin_iter <= 1) return;
43             P key = *begin_iter;
44             typename PVec::iterator beg=begin_iter,end=end_iter;
45             while (begin_iter != end_iter){
46                 while (begin_iter != end_iter){
47                     if (*--end_iter >= key) continue;
48                     swap(begin_iter,end_iter);
49                     break;
50                 }
51                 while (begin_iter != end_iter){
52                     if (*++begin_iter <= key) continue;
53                     swap(begin_iter,end_iter);
54                     break;
55                 }
56             }
57             subsort(beg,begin_iter);
58             subsort(begin_iter+1,end);
59         }
60         static void swap(typename PVec::iterator &a,typename PVec::iterator &b){
61             if (*a == *b) return;
62             std::swap(*a,*b);
63         }
64     };
65     
66 } 

namespace my