引言
树是一种比较重要的数据结构,尤其是二叉树。在这里简单介绍二叉树。
二叉树是一种特殊的树,在二叉树中每个节点最多有两个子节点,一般称为左子节点和右子节点(或左孩子和右孩子),并且二叉树的子树有左右之分,其次序不能任意颠倒。
1. 二叉树的定义
二叉树是n(n>=0)个结点的有限集合,该集合或者为空集(称为空二叉树),或者由一个根结点和两棵互不相交的、分别称为根结点的左子树和右子树组成。
2. 二叉树的遍历
二叉树的存储分为顺序存储和链式存储 。顺序存储在右斜树这种极端情况下,会十分浪费存储空间,顺序存储结构一般适用于完全二叉树。因此二叉树的存储一般会使用链式存储,在这里只介绍链式存储:
二叉树的链式存储结构,将节点的数据结构定义为一个数据域和两个指针域,如下图所示:
一、结构体的定义
typedef struct BTNode{
char element;
BTNode* left;
BTNode* right;
}BTNode, *BTNodePtr;
/**
* A queue with a number of pointer;
*/
typedef struct BTNodePtrQueue{
BTNodePtr* nodePtrs;
int front;
int rear;
}BTNodePtrQueue, *QueuePtr;
二、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
三、判断是否为空
bool isQueueEmpty(QueuePtr paraQueuePtr){
if((paraQueuePtr->front + 1)% QUEUE_SIZE == paraQueuePtr->rear){
return true;
}// Of if
return false;
}// Of isQueueEmpty
四、入队
void enqueue(QueuePtr paraQueuePtr, BTNodePtr paraBTNodePtr){
printf("front = %d, rear = %d.\r\n",paraQueuePtr->front, paraQueuePtr->rear);
if((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE){
printf("Error, trying to enqueue %c.queue full.\r\n",paraBTNodePtr->element);
return;
}// Of if
paraQueuePtr->nodePtrs[paraQueuePtr->rear] = paraBTNodePtr;
paraQueuePtr->rear = (paraQueuePtr->rear +1)% QUEUE_SIZE;
printf("enqueue %c ends.\r\n",paraBTNodePtr->element);
}// Of enqueue
五、出队
BTNodePtr dequeue(QueuePtr paraQueuePtr){
if(isQueueEmpty(paraQueuePtr)) {
printf("Error, empty queue\r\n");
return NULL;
}// Of if
paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
// BTNodePtr tempPtr = paraQueuePtr->nodePtrs[paraQueuePtr->front +1 ];
printf("dequeue %c ends.\r\n",paraQueuePtr->nodePtrs[paraQueuePtr->front]->element);
return paraQueuePtr->nodePtrs[paraQueuePtr->front];
}// Of dequeue
六、构造一个结点
BTNodePtr constructBTNode(char paraChar){
BTNodePtr resultPtr = (BTNodePtr)malloc(sizeof(BTNode));
resultPtr->element = paraChar;
resultPtr->left = NULL;
resultPtr->right = NULL;
return resultPtr;
}// Of constructBTNode
七、将字符串转化成函数
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;
八、层序遍历
void levelwise(BTNodePtr paraTreePtr){
// Use a queue to mange the pointer.
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] = '\0';
printf("Levelwise: %s\r\n",tempString);
}// Of levelwise
九、先序
void preorder(BTNodePtr tempPtr){
if(tempPtr == NULL){
return;
}// Of if
printf("%c,tempPtr->element");
preorder(tempPtr->left);
preorder(tempPtr->right);
}// Of preorder
十、中序
void inorder(BTNodePtr tempPtr){
if(tempPtr == NULL){
return;
}// Of if
inorder(tempPtr->left);
printf("%c", tempPtr->element);
inorder(tempPtr->right);
}// Of inorder
十一、后序
void postorder(BTNodePtr tempPtr){
if(tempPtr == NULL){
return;
}// Of if
postorder(tempPtr->left);
postorder(tempPtr->right);
printf("%c",tempPtr->element);
}// Of postorder.
十二、完整代码
#include <stdio.h>
#include <malloc.h>
#define QUEUE_SIZE 5
/**
* Binary tree node
*/
typedef struct BTNode{
char element;
BTNode* left;
BTNode* right;
}BTNode, *BTNodePtr;
/**
* A queue with a number of pointer;
*/
typedef struct BTNodePtrQueue{
BTNodePtr* nodePtrs;
int front;
int rear;
}BTNodePtrQueue, *QueuePtr;
/**
* Initialize the queue.
*/
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
/**
* Is the queue empty?
*/
bool isQueueEmpty(QueuePtr paraQueuePtr){
if((paraQueuePtr->front + 1)% QUEUE_SIZE == paraQueuePtr->rear){
return true;
}// Of if
return false;
}// Of isQueueEmpty
/**
* Add a pointer to the queue.
*/
void enqueue(QueuePtr paraQueuePtr, BTNodePtr paraBTNodePtr){
printf("front = %d, rear = %d.\r\n",paraQueuePtr->front, paraQueuePtr->rear);
if((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE){
printf("Error, trying to enqueue %c.queue full.\r\n",paraBTNodePtr->element);
return;
}// Of if
paraQueuePtr->nodePtrs[paraQueuePtr->rear] = paraBTNodePtr;
paraQueuePtr->rear = (paraQueuePtr->rear +1)% QUEUE_SIZE;
printf("enqueue %c ends.\r\n",paraBTNodePtr->element);
}// Of enqueue
/**
* Remove an element from the queue and return.
*/
BTNodePtr dequeue(QueuePtr paraQueuePtr){
if(isQueueEmpty(paraQueuePtr)) {
printf("Error, empty queue\r\n");
return NULL;
}// Of if
paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
// BTNodePtr tempPtr = paraQueuePtr->nodePtrs[paraQueuePtr->front +1 ];
printf("dequeue %c ends.\r\n",paraQueuePtr->nodePtrs[paraQueuePtr->front]->element);
return paraQueuePtr->nodePtrs[paraQueuePtr->front];
}// Of dequeue
/**
* Construct a BTNode using the given char.
*/
BTNodePtr constructBTNode(char paraChar){
BTNodePtr resultPtr = (BTNodePtr)malloc(sizeof(BTNode));
resultPtr->element = paraChar;
resultPtr->left = NULL;
resultPtr->right = NULL;
return resultPtr;
}// Of constructBTNode
/**
* Construct a binary tree using the given string.
*/
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;
/**
* Levelwise.
*/
void levelwise(BTNodePtr paraTreePtr){
// Use a queue to mange the pointer.
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] = '\0';
printf("Levelwise: %s\r\n",tempString);
}// Of levelwise
/**
* Preorder.
*/
void preorder(BTNodePtr tempPtr){
if(tempPtr == NULL){
return;
}// Of if
printf("%c,tempPtr->element");
preorder(tempPtr->left);
preorder(tempPtr->right);
}// Of preorder
/**
* Inorder.
*/
void inorder(BTNodePtr tempPtr){
if(tempPtr == NULL){
return;
}// Of if
inorder(tempPtr->left);
printf("%c", tempPtr->element);
inorder(tempPtr->right);
}// Of inorder
/**
* Post order.
*/
void postorder(BTNodePtr tempPtr){
if(tempPtr == NULL){
return;
}// Of if
postorder(tempPtr->left);
postorder(tempPtr->right);
printf("%c",tempPtr->element);
}// Of postorder.
/**
* The entrance.
*/
int main(){
BTNodePtr tempHeader;
tempHeader = constructBTNode('c');
printf("There is only one node. Preorder visit: ");
preorder(tempHeader);
printf("\r\n");
char* tempString = "abde#bf######";
tempHeader = stringToBTree(tempString);
printf("Preorder: ");
preorder(tempHeader);
printf("\r\n");
printf("Inorder: ");
inorder(tempHeader);
printf("\r\n");
printf("Postorder: ");
postorder(tempHeader);
printf("\r\n");
printf("Levelwise: ");
levelwise(tempHeader);
printf("\r\n");
return 1;
}// Of main
十三、运行代码
There is only one node. Preorder visit: 0,tempPtr->element
front = 0, rear = 1.
enqueue a ends.
dequeue a ends.
front = 1, rear = 2.
enqueue d ends.
dequeue d ends.
Preorder: 0,tempPtr->element0,tempPtr->element
Inorder: ad
Postorder: da
Levelwise: front = 0, rear = 1.
enqueue a ends.
dequeue a ends.
front = 1, rear = 2.
enqueue d ends.
dequeue d ends.
Levelwise: ad