树和二叉树相关算法（一) c/c++

  1 //双亲储存结构
  2 typedef struct{
  3     ElemType data;
  4     int parent;
  5 }PTree[MaxSize];
  6  
  7 //孩子链储存结构
  8 const int MaxSons = 10;
  9 typedef struct node{
 10     ElemType data;
 11     struct node* sons[MaxSons];
 12 }TSonNode; 
 13 
 14 //孩子兄弟链储存结构
 15 typedef struct tnode{
 16     ElemType data;
 17     struct tnode* hp;
 18     struct tnode* vp;
 19 }TSBNode;
 20  
 21 //二叉树顺序储存结构
 22 typedef ElemType SqBinTree[MaxSize]; 
 23  
 24 //二叉树链式储存结构
 25 typedef struct bnode{
 26     ElemType data;
 27     struct bnode* lchild;
 28     struct bnode* rchild;
 29 }BTNode; 
 30  
 31 //二叉树三叉链表
 32 typedef struct btnode{
 33     ElemType data;
 34     struct btnode* lchild;
 35     struct btnode* parent;
 36     struct btnode* rchild;
 37 }BTTNode; 
 38 
 39 //孩子兄弟链求树的高度 
 40 int TreeHeight2(TSBNode *t)
 41 {
 42     TSBNode *p;
 43     int maxh = 0;
 44     int h = 0;
 45     if(t == NULL)
 46         return 0;
 47     else
 48     {
 49         p = t;
 50         while(p != NULL)
 51         {
 52             h = TreeHeight2(p->vp);
 53             if(h > maxh) maxh = h;
 54             p = p->hp;
 55         }
 56         return maxh+1;
 57     }
 58 }
 59 
 60 //用括号表达式创建二叉树 
 61 void CreateBTree(BTNode *&b,char *str)
 62 {
 63     BTNode *St[MaxSize];int top = -1;
 64     BTNode *p;
 65     int k = 1;
 66     
 67     b = NULL;
 68     while(*str != '\0')
 69     {
 70         switch(*str)
 71         {
 72             case '(':
 73                 k = 1;
 74                 St[++top] = p;
 75                 break;
 76             case ')':
 77                 top--;
 78                 break;
 79             case ',':
 80                 k = 2;
 81                 break;
 82             default:
 83                 p = (BTNode*)malloc(sizeof(BTNode));
 84                 p->data = *str;
 85                 p->lchild = NULL;
 86                 p->rchild = NULL;
 87                 if(b == NULL)
 88                 {
 89                     b = p;
 90                 }
 91                 else
 92                 {
 93                     if(k == 1)
 94                         St[top]->lchild = p;
 95                     else
 96                         St[top]->rchild = p;
 97                 }
 98         }
 99         str++;
100     }
101 }
102 //销毁二叉树 
103 void DestroyBTree(BTNode *b)
104 {
105     if(b != NULL)
106     {
107         DestroyBTree(b->lchild);
108         DestroyBTree(b->rchild);
109         free(b);
110     }
111 }
112 //查找结点(基于先序遍历) 
113 BTNode *FindNode(BTNode *b,ElemType e)
114 {
115     BTNode *p;
116     if(b == NULL)
117         return NULL;
118     else if(b->data == e)
119         return b;
120     else
121     {
122         p = FindNode(b->lchild,e);
123         if(p != NULL)
124             return p;
125         else
126             return FindNode(b->rchild,e);
127     }
128 } 
129 //找孩子结点
130 BTNode *LchildNode(BTNode *b)
131 {
132     return b->lchild;
133 } 
134 BTNode *RchildNode(BTNode *b)
135 {
136     return b->rchild;
137 } 
138 
139 //求二叉树的高度
140 int BTHeight(BTNode *b)
141 {
142     int lchildh,rchildh;
143     if(b == NULL)
144         return 0;
145     else
146     {
147         lchildh = BTHeight(b->lchild);
148         rchildh = BTHeight(b->rchild);
149         return lchildh>rchildh?:lchildh+1,rchildh+1;
150     }    
151 } 
152 
153 //输出二叉树
154 void DispBTree(BTNode *b)
155 {
156     if(b != NULL)
157     {
158         cout<<b->data;
159         if(b->lchild != NULL||b->rchild != NULL)
160         {
161             cout<<"(";
162             DispBTree(b->lchild);
163             if(b->rchild != NULL)cout<<",";
164             DispBTree(b->rchild);
165             cout<<")";
166         }
167     }    
168 } 
169 
170 //递归算法遍历二叉树
171 void PreOrder(BTNode *b)
172 {
173     if( b!= NULL)
174     {
175         cout<<b->data;
176         PreOrder(b->lchild);
177         PreOrder(b->rchild);
178     }
179 } 
180 
181 void InOrder(BTNode *b)
182 {
183     if(b != NULL)
184     {
185         InOrder(b->lchild);
186         cout<<b->data;
187         InOrder(b->rchild);
188     }
189 }
190 
191 void PostOrder(BTNode *b)
192 {
193     if(b != NULL)
194     {
195         PostOrder(b->lchild);
196         PostOrder(b->rchild);
197         cout<<b->data;
198     }
199 }
200 
201 //求给定二叉树结点个数
202 
203 int Nodes(BTNode *b)
204 {
205     int num = 0;
206     if(b == NULL)
207         return 0;
208     else
209         return Nodes(b->lchild) + Nodes(b->rchild) + 1;    
210 } 
211 
212 //输出所有叶子结点
213 void DispLeaf(BTNode *b)
214 {
215     if(b != NULL)
216     {
217         if(b->lchild == NULL && b->rchild == NULL)
218             cout<<b->data;
219         else
220         {
221             DispLeaf(b->lchild);
222             DispLeaf(b->rchild);
223         }
224     }    
225 } 
226 
227 //返回结点值为x的结点的深度
228 int Level(BTNode *b,ElemType e,int h)
229 {
230     int l;
231     if(b == NULL)
232         return 0;
233     else if(b->data == e)
234         return h;
235     else
236     {
237         l = Level(b->lchild,e,h+1);
238         if( l == 0)
239             return Level(b->rchild,e,h+1);
240         else
241             return l;    
242     }    
243 } 
244 
245 //求第k层结点个数
246 int Lnodenum(BTNode *b,int k,int h)
247 {
248     int num = 0;
249     if(b == NULL)
250         return 0;
251     if(h == k)
252         num++;
253     else if(h < k)
254     {
255         num += Lnodenum(b->lchild,k,h+1);
256         num += Lnodenum(b->rchild,k,h+1);
257     }
258     return num;
259 } 
260 
261 //判断两棵树是否相似
262 bool Like(BTNode *b1,BTNode *b2)
263 {
264     bool like1,like2;
265     if(b1 == NULL && b2 == NULL)
266         return true;
267     else if(b1 == NULL || b2 == NULL)
268         return false;
269     else
270     {
271         like1 = Like(b1->lchild,b2->lchild);
272         like2 = Like(b1->rchild,b2->rchild);
273         return like1 && like2;    
274     }    
275 } 
276 
277 //输出值为x的结点的所有祖先
278 bool ancestor(BTNode *b,ElemType e)
279 {
280     if(b == NULL)
281         return false;
282     else if(b->lchild != NULL && b->lchild->data == e 
283         || b->rchild != NULL && b->rchild->data == e)
284     {
285             cout<<b->data;
286             return true;        
287     }
288     else if(ancestor(b->lchild,e) || ancestor(b->rchild,e))
289     {
290         cout<<b->data;
291         return true;    
292     }    
293     else
294         return false;
295 } 
296 
297 //非递归算法遍历二叉树  算法一 
298 void PreOrder1(BTNode *b)
299 {
300     BTNode *St[MaxSize];int top=-1;            //创建栈并初始化 
301     BTNode *p;                                //结点p为当前处理的结点 
302     if(b != NULL)                            //b不为空时 
303     {
304         p = b;                                //p指向b 
305         St[++top] = p;                        //p入栈 
306         while(top!=-1)                        //栈不空时，说明有正在处理的结点 
307         {
308             p = St[top];                    //把当前处理的结点拿出来，避免丢失 
309             cout<<St[top]->data;            //访问结点并且出栈 
310             top--;
311             if(p->rchild != NULL)            //栈后进先出，所以先让右结点进栈 
312                 St[++top] = p->rchild;        
313             if(p->lchild != NULL)            //左结点进栈 
314                 St[++top] = p->lchild;
315         }
316     }
317 }
318 
319 //非递归算法遍历二叉树  算法二 
320 void PreOrder2(BTNode *b)
321 {
322     BTNode *St[MaxSize];int top = -1;        //定义一个栈保存访问过的结点 
323     BTNode *p;                                //p为当前处理的树的根节点指针 
324         
325     p = b;                                    //p指向b 
326     while(top != -1 || p != NULL)            //栈不空或者p不为空 
327     {
328         while(p != NULL)                    //p不为空，访问p结点和其所有左下结点并进栈 
329         {
330             cout<<p->data;                    //访问结点p 
331             St[++top] = p;                    //p结点入栈 
332             p = p->lchild;                    //移动到左孩子 
333         }
334         if(top != -1)                        //处理完左下结点之后转向右节点 
335         {
336             p = St[top--]->rchild;            //转向栈顶结点的右孩子并且栈顶出栈（ 因为栈顶结点处理完毕，不出栈会死循环) 
337         }
338     }
339 }
340 
341 //非递归算法中序遍历二叉树
342 void InOrder1(BTNode *b)
343 {
344     BTNode *St[MaxSize],*p;int top = -1;
345     
346     p = b;
347     while(top != -1 || p != NULL)
348     {
349         while(p != NULL)
350         {
351             St[++top] = p;    
352             p = p->lchild;
353         }    
354         if(top != -1)
355         {
356             cout<<St[top]->data;
357             p = St[top--]->rchild;
358         }
359     }
360     
361 } 
362 
363 //非递归算法后序遍历二叉树
364 void PostOrder1(BTNode *b)
365 {
366     BTNode *St[MaxSize];BTNode *p;int top = -1;
367     BTNode *r;
368     bool flag;
369     
370     p = b;
371     do
372     {
373         while(p != NULL)
374         {
375             St[++top] = p;
376             p = p->lchild;    
377         }
378         r = NULL;
379         flag = true;
380         while(top != -1 && flag)
381         {
382             p = St[top];
383             if(p->rchild == r)
384             {
385                 cout<<p->data;
386                 r = p;
387                 top--;
388             }
389             else
390             {
391                 p = p->rchild;
392                 flag = false; 
393             }
394         }
395     }while(top != -1);
396 } 
397 
398 //输出从根节点到每个叶子结点的路径逆序列(非递归算法)
399 void AllPath1(BTNode *b)
400 {
401     BTNode *Path[MaxSize];BTNode *p;int top = -1;
402     BTNode *pre;
403     bool flag;
404     
405     p = b;
406     do
407     {
408         while(p != NULL)
409         {
410             Path[++top] = p;
411             p = p->lchild;
412         }
413         pre = NULL;
414         flag = true;
415         while(top != -1 && flag)
416         {
417             p = Path[top];
418             if(p -> rchild == pre)
419             {
420                 if(p -> lchild == NULL && p->rchild == NULL)
421                 {
422                     cout<< p->data <<" : ";
423                     for(int i = 0;i <= top;i++)
424                         cout<<Path[i]->data;
425                     cout<<endl;
426                 }
427                 pre = p;
428                 top--;
429             }
430             else
431             {
432                 p = p->rchild;
433                 flag = false;
434             }
435         }
436     }while(top != -1);
437 } 
438