数据结构 二叉树与遍历

1.概述

二叉树的遍历是一个很常见的问题。二叉树的遍历方式主要有：先序遍历、中序遍历、后序遍历、层次遍历。先序、中序、后序其实指的是父节点被访问的次序。若在遍历过程中，父节点先于它的子节点被访问，就是先序遍历；父节点被访问的次序位于左右孩子节点之间，就是中序遍历；访问完左右孩子节点之后再访问父节点，就是后序遍历。不论是先序遍历、中序遍历还是后序遍历，左右孩子节点的相对访问次序是不变的，总是先访问左孩子节点，再访问右孩子节点。而层次遍历，就是按照从上到下、从左向右的顺序访问二叉树的每个节点。

四种主要的遍历思想为：

前序遍历：根结点 ---> 左子树 ---> 右子树

中序遍历：左子树---> 根结点 ---> 右子树

后序遍历：左子树 ---> 右子树 ---> 根结点

层次遍历：只需按层次遍历即可

例如，求下面二叉树的各种遍历

前序遍历： A B D E J H C F I

中序遍历： D B J E H A F C I

后序遍历： D J H E B F I C A

层次遍历：A B C D E F I J H

2.上代码

#include
#include

#define QUEUE_SIZE 5

typedef struct BTNode {
	char element;
	BTNode* left;
	BTNode* right;
}BTNode,*BTNodePtr;

typedef struct BTNodePtrQueue {
	BTNodePtr* nodePtrs;
	int front;
	int rear;
}BTNodePtrQueue, *QueuePtr;

QueuePtr initQueue() {
	QueuePtr resultQueuePtr = (QueuePtr)malloc(sizeof(struct BTNodePtrQueue));
	resultQueuePtr->nodePtrs = (BTNodePtr*)malloc(QUEUE_SIZE * sizeof(BTNodePtr));
	resultQueuePtr->front = 0;
	resultQueuePtr->rear = 1;
	resultQueuePtr; 
}

bool isQueueEmpty(QueuePtr paraQueuePtr) {
	if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
		return true;
	}
	return false;
}


void enqueue(QueuePtr paraQueuePtr, BTNodePtr paraBTNodePtr) {
	printf("front = %d, rear = %dn",paraQueuePtr->front,paraQueuePtr->rear);
	if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
		printf("Error, trying to enqueue %c. queue full.n",paraBTNodePtr->element);
		return;
	}
	paraQueuePtr->nodePtrs[paraQueuePtr->rear] = paraBTNodePtr;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
	printf("enqueue %c ends.n",paraBTNodePtr->element);
}

BTNodePtr dequeue(QueuePtr paraQueuePtr) {
	if (isQueueEmpty(paraQueuePtr)) {
		printf("Error, empty queuen");
		return NULL;
	}
	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
	
	printf("dequeue %c ends.n",paraQueuePtr->nodePtrs[paraQueuePtr->front]->element);
	return paraQueuePtr->nodePtrs[paraQueuePtr->front];
}

BTNodePtr constructBTNode(char paraChar) {
	BTNodePtr resultPtr = (BTNodePtr)malloc(sizeof(BTNode));
	resultPtr->element = paraChar;
	resultPtr->right = NULL;
	resultPtr->left = NULL;
	return resultPtr; 
}

BTNodePtr stringToBTree(char* paraString) {
	int i;
	char ch;
	
	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);
		
		i++;
		ch = paraString[i];
		if (ch == '#') {
			tempParent->left = NULL;
		}
		else {
			tempLeftChild = constructBTNode(ch);
			enqueue(tempQueuePtr, tempLeftChild);
			tempParent->left = tempLeftChild; 
		}
		
		i++;
		ch = paraString[i];
		if (ch == '#') {
			tempParent->right = NULL;
		}
		else {
			tempRightChild = constructBTNode(ch);
			enqueue(tempQueuePtr, tempRightChild);
			tempParent->right = tempRightChild;
		}
	}
	
	return resultHeader; 
}

void levelWise(BTNodePtr paraTreePtr) {
	char tempString[100];
	int i = 0;
	QueuePtr tempQueuePtr = initQueue();
	BTNodePtr tempNodePtr;
	enqueue(tempQueuePtr, paraTreePtr);
	while (!isQueueEmpty(tempQueuePtr)) {
		tempNodePtr = dequeue(tempQueuePtr);
		
		tempString[i] = tempNodePtr->element;
		i++;
		
		if (tempNodePtr->left != NULL) {
			enqueue(tempQueuePtr, tempNodePtr->left);
		}  
		if (tempNodePtr->right != NULL) {
			enqueue(tempQueuePtr, tempNodePtr->right);
		}
	}
	
	tempString[i] = ' ';
	
	printf("LevelWise:-> %sn",tempString);
}

void preorder(BTNodePtr tempPtr) {
	if (tempPtr == NULL) {
		return;
	}
	
	printf("%c",tempPtr->element);
	preorder(tempPtr->left);
	preorder(tempPtr->right);
}

void inorder(BTNodePtr tempPtr) {
	if (tempPtr == NULL) {
		return;
	}
	
	inorder(tempPtr->left);
	printf("%c",tempPtr->element);
	inorder(tempPtr->right);
}

void postorder(BTNodePtr tempPtr) {
	if (tempPtr == NULL) {
		return;
	}
	
	postorder(tempPtr->left);
	postorder(tempPtr->right);
	printf("%c",tempPtr->element);
}

int main() {
	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: n");
	levelWise(tempHeader);
	printf("rn");
	
	return 1;
}

 3.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