二叉树的先序，中序，后序、层级的递归和非递归遍历和获取叶子节点和树的高度
代码中的二叉树的构造参考了
http://www.cnblogs.com/dolphin0520/archive/2011/08/25/2153720.html
代码的思想和图片的来源：好大学慕课浙江大学陈越、何钦铭的《数据结构》
话不多说，直接上代码
1 #include<stdio.h> 2 #include<stdlib.h> 3 #include<string.h> 4 #include <ctype.h> 5 6 //efine binary tree element type 7 typedef char elementType; 8 9 //define binary tree 10 typedef struct node{ 11 elementType element; 12 struct node *left; 13 struct node *right; 14 int flag;//为了进行非递归的后序遍历，设置入栈标志位，0表示第一次压栈、弹栈，1表示第二此压栈，弹栈 15 }bTree,*pBinTree; 16 17 18 //define the stack element type 19 typedef pBinTree dataType; 20 21 22 //define a stack to store binary tyoe 23 typedef struct node2{ 24 dataType element; 25 struct node2 *next; 26 }sta,*pStack; 27 28 29 /*=======================对树栈的操作==============================*/ 30 pStack createEmptyStack(){ 31 pStack stack = (pStack)malloc(sizeof(sta)); 32 if(stack){ 33 stack->next=NULL; 34 } 35 } 36 37 int isStackEmpty(pStack stack){ 38 return(stack->next==NULL); 39 } 40 41 void push(pStack stack,dataType element){ 42 pStack newNode = (pStack)malloc(sizeof(sta)); 43 newNode->element = element; 44 newNode->next = stack->next; 45 stack->next = newNode; 46 } 47 48 dataType pop(pStack stack){ 49 if(isStackEmpty(stack)){ 50 printf("the stack has been empty\n"); 51 return NULL; 52 } 53 pStack temp = stack->next; 54 stack->next = temp->next; 55 return temp->element; 56 } 57 58 int getStackSize(pStack stack){ 59 pStack p = stack->next; 60 int size=0; 61 while(p){ 62 size++; 63 p=p->next; 64 } 65 return size; 66 } 67 68 69 70 dataType getTop(pStack stack){ 71 if(isStackEmpty(stack)){ 72 printf("the stack has been empty\n"); 73 return NULL; 74 } 75 return (stack->next->element); 76 } 77 78 //定义一个字符型栈 79 typedef struct node3{ 80 elementType element; 81 struct node3 *next; 82 }charSta,*pCharStack; 83 84 /*====================================对字符栈的操作========================================*/ 85 pCharStack createEmptyCharStack(){ 86 pCharStack stack = (pCharStack)malloc(sizeof(charSta)); 87 if(stack){ 88 stack->next=NULL; 89 } 90 return stack; 91 } 92 93 int isCharStackEmpty(pCharStack stack){ 94 return(stack->next==NULL); 95 } 96 97 void pushCharStack(pCharStack stack,char ch){ 98 pCharStack newNode = (pCharStack)malloc(sizeof(charSta)); 99 newNode->element = ch; 100 newNode->next = stack->next; 101 stack->next=newNode; 102 } 103 104 105 elementType popCharStack(pCharStack stack){ 106 if(isCharStackEmpty(stack)){ 107 return; 108 } 109 pCharStack temp=stack->next; 110 stack->next=temp->next; 111 return temp->element; 112 } 113 114 /*============================为了对二叉树进行层次遍历，定义一个链式队列存放二叉树=================================*/ 115 116 //定义存放队列元素(二叉树)的链表 117 typedef struct node4{ 118 dataType element; 119 struct node4 *next; 120 }lis,*pList; 121 122 //定义队列的链式存储 123 typedef struct node5{ 124 struct node4 *font;//指向队列的头指针 125 struct node4 *rear;//指向队列尾的尾指针 126 }que,*pQueue; 127 128 pList createEmptyList(){ 129 pList list = (pList)malloc(sizeof(lis)); 130 if(list){ 131 list->next=NULL; 132 } 133 return list; 134 } 135 136 pQueue createEmptyQueue(){ 137 pQueue queue = (pQueue)malloc(sizeof(que)); 138 if(queue){ 139 queue->font=NULL; 140 queue->rear=NULL; 141 } 142 } 143 144 int isQueueEmpty(pQueue queue){ 145 return (queue->font==NULL); 146 } 147 148 149 void addQueue(pQueue queue,dataType element){ 150 if(isQueueEmpty(queue)){ 151 pList list = createEmptyList(); 152 list->element=element; 153 queue->font=list; 154 queue->rear=list; 155 }else{ 156 pList list = (pList)malloc(sizeof(lis)); 157 list->element=element; 158 list->next = queue->rear->next; 159 queue->rear->next=list; 160 queue->rear=list; 161 } 162 } 163 164 dataType deleteQueue(pQueue queue){ 165 if(isQueueEmpty(queue)){ 166 return; 167 } 168 dataType element = queue->font->element; 169 if(queue->font==queue->rear){ 170 queue->font=queue->rear=NULL; 171 }else{ 172 queue->font = queue->font->next; 173 } 174 return element; 175 } 176 177 178 /*==========================二叉树的构造和遍历==================================*/ 179 /* 180 构造一棵二叉树， 181 s为存储二叉树的元素的字符数组，s为形如A(B,C(D,E))形式的字符串 182 tree为二叉树创建好的根节点，但是元素为空 183 */ 184 pBinTree createBinTree(char *s){ 185 int i,isRight; 186 pStack treeStack = createEmptyStack();//存放节点 187 pCharStack charStack = createEmptyCharStack();//存放分隔符 188 pBinTree root = (pBinTree)malloc(sizeof(bTree)); 189 pBinTree temp,p; 190 root->element=s[0]; 191 root->left=NULL; 192 root->right=NULL; 193 push(treeStack,root); 194 i=1; 195 while(i<strlen(s)){ 196 if(s[i]=='('){ 197 pushCharStack(charStack,s[i]); 198 isRight=0; 199 }else if(s[i]==','){ 200 isRight=1; 201 }else if(s[i]==')'){ 202 pop(treeStack); 203 popCharStack(charStack); 204 }else if(isalpha(s[i])){ 205 p=(pBinTree)malloc(sizeof(bTree)); 206 p->element=s[i]; 207 p->left=NULL; 208 p->right=NULL; 209 temp=getTop(treeStack); 210 //printf("%c %c\n",s[i],s[i+1]); 211 if(isRight==1){ 212 temp->right=p; 213 }else{ 214 temp->left=p; 215 } 216 217 if(s[i+1]=='('){ 218 push(treeStack,p); 219 } 220 } 221 i++; 222 } 223 return root; 224 } 225 226 //先序遍历 227 void preOrderTraversal(pBinTree tree){ 228 if(tree){ 229 printf("%c ",tree->element); 230 preOrderTraversal(tree->left); 231 preOrderTraversal(tree->right); 232 } 233 } 234 235 //先序遍历的非递归方法 236 void preOrderTraversalStack(pBinTree tree){ 237 pBinTree t = tree; 238 pStack stack = createEmptyStack(); 239 while(t || !isStackEmpty(stack)){ 240 while(t){ 241 printf("%c ",t->element); 242 push(stack,t); 243 t = t->left; 244 } 245 246 if(!isStackEmpty(stack)){ 247 t = pop(stack); 248 t = t->right; 249 } 250 251 } 252 253 } 254 //中序遍历 255 void middlerOrderTraversal(pBinTree tree){ 256 if(tree){ 257 middlerOrderTraversal(tree->left); 258 printf("%c ",tree->element); 259 middlerOrderTraversal(tree->right); 260 } 261 } 262 263 //中序遍历的非递归方法 264 void middlerOrderTraversalStack(pBinTree tree){ 265 pStack stack = createEmptyStack(); 266 pBinTree t =tree;; 267 while(!isStackEmpty(stack) || t){ 268 while(t){ 269 push(stack,t); 270 t=t->left; 271 } 272 if(!isStackEmpty(stack)){ 273 t = pop(stack); 274 printf("%c ",t->element); 275 t = t->right; 276 } 277 } 278 279 } 280 281 //后序遍历 282 void postOrderTraversal(pBinTree tree){ 283 if(tree){ 284 postOrderTraversal(tree->left); 285 postOrderTraversal(tree->right); 286 printf("%c ",tree->element); 287 } 288 } 289 290 //后序遍历的非递归方法 291 void postOrderTraversalStack(pBinTree tree){ 292 pBinTree t = tree; 293 pStack stack = createEmptyStack(); 294 while(t || !isStackEmpty(stack)){ 295 while(t){ 296 t->flag=0; 297 push(stack,t); 298 t=t->left; 299 } 300 if(!isStackEmpty(stack)){ 301 t = pop(stack); 302 if(t->flag==0){ 303 t->flag=1; 304 push(stack,t); 305 t=t->right; 306 }else{ 307 printf("%c ",t->element); 308 t=NULL; 309 } 310 } 311 } 312 } 313 314 /*二叉树的层次遍历*/ 315 void levelOrderTraversal(pBinTree tree){ 316 pQueue queue = createEmptyQueue(); 317 pBinTree tr = tree; 318 if(!tree){ 319 return; 320 } 321 addQueue(queue,tr); 322 while(!isQueueEmpty(queue)){ 323 tr = deleteQueue(queue); 324 printf("%c ",tr->element); 325 if(tr->left){ 326 addQueue(queue,tr->left); 327 } 328 if(tr->right){ 329 addQueue(queue,tr->right); 330 } 331 } 332 } 333 334 /*Application of binary tree teaversal*/ 335 336 //get the mount of leaf node,we just need add condition at preOrderTraversal 337 int getMountOfLeaves(pBinTree tree){ 338 pStack stack = createEmptyStack(); 339 pBinTree tr =tree; 340 int mount=0; 341 while(tr || !isStackEmpty(stack)){ 342 while(tr){ 343 if(tr->left==NULL && tr->right==NULL){ 344 mount++; 345 } 346 push(stack,tr); 347 tr=tr->left; 348 } 349 if(!isStackEmpty(stack)){ 350 tr = pop(stack); 351 tr=tr->right; 352 } 353 } 354 return mount; 355 } 356 357 /*get the height of binary tree, the hight of binary is max(subLeftTree,subRightTree)*/ 358 int getHeigthOfBinaryTree(pBinTree tree){ 359 int hl,hr,maxH; 360 if(tree){ 361 hl=getHeigthOfBinaryTree(tree->left); 362 hr=getHeigthOfBinaryTree(tree->right); 363 maxH=(hl>hr)?hl:hr; 364 return maxH+1; 365 } 366 return 0; 367 } 368 369 //非递归的方法获取二叉树的高度，其实二叉树的高度就是栈中元素的最大值 370 int getHeigthOfBinaryTreeStack(pBinTree tree){ 371 pBinTree t = tree; 372 int hMax=0,stackSize; 373 pStack stack = createEmptyStack(); 374 while(t || !isStackEmpty(stack)){ 375 while(t){ 376 t->flag=0; 377 push(stack,t); 378 t=t->left; 379 } 380 if(!isStackEmpty(stack)){ 381 t = pop(stack); 382 if(t->flag==0){ 383 t->flag=1; 384 push(stack,t); 385 t=t->right; 386 }else{ 387 /*这里已经弹栈一个元素，因此栈的容量应为 getSize+1*/ 388 stackSize=getStackSize(stack)+1; 389 //printf("stackSize %d",stackSize); 390 if(stackSize>hMax){ 391 hMax=stackSize; 392 } 393 t=NULL; 394 } 395 } 396 } 397 return hMax; 398 } 399 400 401 402 void main(){ 403 char s[]="A(B(D,F(E)),C(G(,H),I))"; 404 //char s[]="A(B,C)"; 405 pBinTree root =createBinTree(s); 406 printf("preOrderTraversal\n"); 407 preOrderTraversal(root); 408 printf("\nPreOrderTraversalStack\n"); 409 preOrderTraversalStack(root); 410 411 printf("\n\n================================\n"); 412 413 printf("\nmiddleOrderTraversal\n"); 414 middlerOrderTraversal(root); 415 printf("\nmiddleOrderTraversalStack\n"); 416 middlerOrderTraversalStack(root); 417 418 printf("\n\n================================\n"); 419 420 printf("\npostOrderTraversal\n"); 421 postOrderTraversal(root); 422 printf("\npostOrderTraversalStack\n"); 423 postOrderTraversalStack(root); 424 425 printf("\n\n================================\n"); 426 427 428 printf("\nThe level order traversal\n"); 429 levelOrderTraversal(root); 430 431 printf("\n\n=========the application of binary tree traversal===========\n"); 432 int leavesMount = getMountOfLeaves(root); 433 printf("\nnumber one:get the leaves mount:%d\n",leavesMount); 434 435 int maxHeight = getHeigthOfBinaryTreeStack(root); 436 printf("\nnuber two:get height of the binary tree:%d",maxHeight); 437 438 }
下面是代码中使用二叉树“A(B(D,F(E)),C(G(,H),I))”的图解，方便大家理解
代码的运行结果：
