数据结构-6.1二叉树的构建与遍历

1.二叉树的构建与遍历实现

代码如下（示例）：

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <malloc.h>

#define QUEUE_SIZE 5

typedef struct BTNode {
	char element;
	struct BTNode* left;
	struct 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;
	return 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 = %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;
	}
	paraQueuePtr->nodePtrs[paraQueuePtr->rear] = paraBTNodePtr;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
	printf("enqueue %c ends.\r\n", paraBTNodePtr->element);
}

BTNodePtr dequeue(QueuePtr paraQueuePtr) {
	if (isQueueEmpty(paraQueuePtr)) {
		printf("error, empty queue\r\n");
		return NULL;
	}

	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
	
	printf("dequeue %c ends.\r\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->left = NULL;
	resultPtr->right = 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] = '\0';

	printf("Levewise: %s\r\n", 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("\r\n");

	char* tempString = "acde#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;
}

2.结果输出

代码如下（示例）：

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.
Levewise: acdebf

总结

       首先写出构建结点和队列的数据结构，然后写出入队，出队的函数，出队返回值为队列的头指针地址，constructBTNode()将输入的字符串的字符给纳入结点element之中，然后StringToBTree()把队列中的元素用left，right指针连接起来构成二叉树，levelwise()函数对二叉树进行层次遍历，后面的preorder(),inorder(),postorder()是对前中后序输出。