1.1前言
二叉树：就是每个节点都只能有两个子节点的树结构。
二叉树遍历：所谓遍历是指沿着某条搜索路线，依次对树中每个结点均做一次且仅做一次访问。访问结点所做的操作依赖于具体的应用问题。 遍历是二叉树上最重要的运算之一，是二叉树上进行其它运算之基础。
遍历分类：前序遍历(Preorder Traversal 亦称（先序遍历））——访问根结点的操作发生在遍历其左右子树之前。
中序遍历(Inorder Traversal)——访问根结点的操作发生在遍历其左右子树之中（间）。
后序遍历(Postorder Traversal)——访问根结点的操作发生在遍历其左右子树之后。
层序遍历——自上而下，自左至右逐层访问树的结点的过程就是层序遍历。2.具体实现
2.1定义结构体
typedef struct BTNode{
char element;
BTNode* left;
BTNode* right;
}BTNode, *BTNodePtr;
typedef struct BTNodePtrQueue{
BTNodePtr* nodePtrs;
int front;
int rear;
}BTNodePtrQueue, *QueuePtr;
2.2初始化
QueuePtr initQueue(){
QueuePtr resultQueuePtr = (QueuePtr)malloc(sizeof(struct BTNodePtrQueue));
resultQueuePtr->nodePtrs = (BTNodePtr*)malloc(QUEUE_SIZE * sizeof(BTNodePtr));
resultQueuePtr->front = 0;
resultQueuePtr->rear = 1;
return resultQueuePtr;
}//Of initQueue
2.3判断队列是否为空
bool isQueueEmpty(QueuePtr paraQueuePtr){
if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
return true;
}//Of if
return false;
}//Of isQueueEmpty
2.4节点入列，删除队列第一个节点并且返回该节点。
void enqueue(QueuePtr paraQueuePtr, BTNodePtr paraBTNodePtr){
printf("front = %d, rear = %d.rn", paraQueuePtr->front, paraQueuePtr->rear);
if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
printf("Error, trying to enqueue %c. queue full.rn", paraBTNodePtr->element);
return;
}//Of if
paraQueuePtr->nodePtrs[paraQueuePtr->rear] = paraBTNodePtr;
paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
printf("enqueue %c ends.rn", paraBTNodePtr->element);
}//Of enqueue
BTNodePtr dequeue(QueuePtr paraQueuePtr){
if (isQueueEmpty(paraQueuePtr)) {
printf("Error, empty queuern");
return NULL;
}//Of if
paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
//BTNodePtr tempPtr = paraQueuePtr->nodePtrs[paraQueuePtr->front + 1];
printf("dequeue %c ends.rn", paraQueuePtr->nodePtrs[paraQueuePtr->front]->element);
return paraQueuePtr->nodePtrs[paraQueuePtr->front];
}//Of dequeue
2.5构造一节点
BTNodePtr constructBTNode(char paraChar){
BTNodePtr resultPtr = (BTNodePtr)malloc(sizeof(BTNode));
resultPtr->element = paraChar;
resultPtr->left = NULL;
resultPtr->right = NULL;
return resultPtr;
}//Of constructBTNode
2.6将一个字符串转化为二叉树
BTNodePtr stringToBTree(char* paraString){
int i;
char ch;
//Use a queue to manage the pointers
QueuePtr tempQueuePtr = initQueue();
BTNodePtr resultHeader;
BTNodePtr tempParent, tempLeftChild, tempRightChild;
i = 0;
ch = paraString[i];
resultHeader = constructBTNode(ch);
enqueue(tempQueuePtr, resultHeader);
while(!isQueueEmpty(tempQueuePtr)) {
tempParent = dequeue(tempQueuePtr);
//The left child
i ++;
ch = paraString[i];
if (ch == '#') {
tempParent->left = NULL;
} else {
tempLeftChild = constructBTNode(ch);
enqueue(tempQueuePtr, tempLeftChild);
tempParent->left = tempLeftChild;
}//Of if
//The right child
i ++;
ch = paraString[i];
if (ch == '#') {
tempParent->right = NULL;
} else {
tempRightChild = constructBTNode(ch);
enqueue(tempQueuePtr, tempRightChild);
tempParent->right = tempRightChild;
}//Of if
}//Of while
return resultHeader;
}//Of stringToBTree
2.7遍历方式（依次层序遍历，前序遍历，中序遍历，后序遍历）
void levelwise(BTNodePtr paraTreePtr){
//Use a queue to manage the pointers
char tempString[100];
int i = 0;
QueuePtr tempQueuePtr = initQueue();
BTNodePtr tempNodePtr;
enqueue(tempQueuePtr, paraTreePtr);
while(!isQueueEmpty(tempQueuePtr)) {
tempNodePtr = dequeue(tempQueuePtr);
//For output.
tempString[i] = tempNodePtr->element;
i ++;
if (tempNodePtr->left != NULL){
enqueue(tempQueuePtr, tempNodePtr->left);
}//Of if
if (tempNodePtr->right != NULL){
enqueue(tempQueuePtr, tempNodePtr->right);
}//Of if
}//Of while
tempString[i] = ' ';
printf("Levelwise: %srn", tempString);
}//Of levelwise
void preorder(BTNodePtr tempPtr){
if (tempPtr == NULL){
return;
}//Of if
printf("%c", tempPtr->element);
preorder(tempPtr->left);
preorder(tempPtr->right);
}//Of preorder
void inorder(BTNodePtr tempPtr){
if (tempPtr == NULL) {
return;
}//Of if
inorder(tempPtr->left);
printf("%c", tempPtr->element);
inorder(tempPtr->right);
}//Of inorder
void postorder(BTNodePtr tempPtr){
if (tempPtr == NULL) {
return;
}//Of if
postorder(tempPtr->left);
postorder(tempPtr->right);
printf("%c", tempPtr->element);
}//Of postorder
2.8测试
void BTNodeTest(){
BTNodePtr tempHeader;
tempHeader = constructBTNode('c');
printf("There is only one node. Preorder visit: ");
preorder(tempHeader);
printf("rn");
char* tempString = "acde#bf######";
tempHeader = stringToBTree(tempString);
printf("Preorder: ");
preorder(tempHeader);
printf("rn");
printf("Inorder: ");
inorder(tempHeader);
printf("rn");
printf("Postorder: ");
postorder(tempHeader);
printf("rn");
printf("Levelwise: ");
levelwise(tempHeader);
printf("rn");
}//Of test
int main(){
BTNodeTest();
return 0;
}
2.9运行结果
There is only one node. Preorder visit: c front = 0, rear = 1. enqueue a ends. dequeue a ends. front = 1, rear = 2. enqueue c ends. front = 1, rear = 3. enqueue d ends. dequeue c ends. front = 2, rear = 4. enqueue e ends. dequeue d ends. front = 3, rear = 0. enqueue b ends. front = 3, rear = 1. enqueue f ends. dequeue e ends. dequeue b ends. dequeue f ends. Preorder: acedbf Inorder: ecabdf Postorder: ecbfda Levelwise: front = 0, rear = 1. enqueue a ends. dequeue a ends. front = 1, rear = 2. enqueue c ends. front = 1, rear = 3. enqueue d ends. dequeue c ends. front = 2, rear = 4. enqueue e ends. dequeue d ends. front = 3, rear = 0. enqueue b ends. front = 3, rear = 1. enqueue f ends. dequeue e ends. dequeue b ends. dequeue f ends. Levelwise: acdebf -------------------------------- Process exited after 0.1319 seconds with return value 0 请按任意键继续. . .
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