【数据结构】—— 二叉树相关接口的实现

最新推荐文章于 2020-12-18 00:22:24 发布

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#二叉树 #动态增长 #C语言

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本文详细介绍了二叉树和队列数据结构的实现方法，包括公共头文件的定义，二叉树的创建、遍历、查找等操作，以及队列的初始化、销毁、入队、出队等功能。通过具体的代码示例，展示了如何使用这些数据结构进行高效的数据管理和处理。

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公共头文件common.h

#pragma once
#include<stdio.h>
#include<string.h>
#include<assert.h>
#include<stdlib.h>


typedef char BTDatatype;

typedef struct BinaryTreeNode
{
	BTDatatype _data;
	struct BinaryTreeNode* _left;
	struct BinaryTreeNode* _right;

}BTNode;

typedef BTNode* QDataType;
typedef struct QueueNode
{
	QDataType _data;
	struct QueueNode* _next;
}QueueNode;

typedef struct Queue
{
	QueueNode* _head;
	QueueNode* _tail;	
}Queue;

二叉树相关接口的介绍BTree.h

#ifndef __BTREE_H__
#define __BTREE_H__
#include"common.h"


//通过前序遍历的数组"ABD##E#H##CF##G##"构建二叉树
BTNode* BinaryTreeCreate(BTDatatype* array, int* pIndex);
void BinaryTreeDestory(BTNode** root);

int BinaryTreeSize(BTNode* root);
int BinaryTreeLeafSize(BTNode* root);
int BinaryTreeLevelSize(BTNode* root, int k);

BTNode* BinaryTreeFind(BTNode* root, BTDatatype x);

//遍历
void BinaryTreePrevOrder(BTNode* root);
void BinaryTreeInOrder(BTNode* root);
void BinaryTreePostOrder(BTNode* root);

//层序遍历
void  BinaryTreeLevelOrder(BTNode* root);
//判断二叉树是否为完全二叉树
int BinaryTreeComplete(BTNode* root);

void BTreeTest();

#endif //__BTREE_H__

队列头文件Queue.h(为实现二叉树的层序遍历)

#pragma once
#include"common.h"


void QueueInit(Queue* pq);
void QueueDestory(Queue* pq);
void QueuePush(Queue* pq,QDataType x);
void QueuePop(Queue* pq);

QDataType QueueFront(Queue* pq);

int QueueEmpty(Queue* pq);
int QueueSize(Queue* pq);
void QueuePrint(Queue* pq);

void QueueTest();

队列接口的实现Queue.c

#include"common.h"
#include"Queue.h"


//队列的初始化
void QueueInit(Queue* pq)
{
	assert(pq);
	pq->_head = (QueueNode*)malloc(sizeof(QueueNode));
	assert(pq->_head);
	pq->_tail = pq->_head;
	pq->_head->_next = NULL;

}
void QueueDestory(Queue* pq)
{
	assert(pq);
	QueueNode* cur = pq->_head;
	while (cur)
	{
		QueueNode* next = cur->_next;
		free(cur);
		cur = next;
	}
	
}
void QueuePush(Queue* pq, QDataType x)
{
	assert(pq);

	QueueNode* newnode = (QueueNode*)malloc(sizeof(QueueNode));
	assert(newnode);
	
	newnode->_data = x;
	newnode->_next = NULL;
	pq->_tail->_next = newnode;
	pq->_tail = newnode;
}

int QueueEmpty(Queue* pq)
{
	return pq->_head != pq->_tail;
}
int QueueSize(Queue* pq)
{
	int count = 0;
	if (QueueEmpty(pq) == 0)
		return 0;
	else
	{
		QueueNode* cur = pq->_head->_next;
		while (cur)
		{
			++count;
			cur = cur->_next;
		}
	}
	return count;
}
void QueuePop(Queue* pq)
{
	QueueNode*cur = NULL;

	assert(pq);
	if (QueueEmpty(pq) == 0)
		return;
	cur = pq->_head->_next;//保存队头的第一个元素
	if (pq->_tail == cur)//若队列中只有一个元素，让尾指针指向头指针
	{
		pq->_tail = pq->_head;
	}
	pq->_head->_next = cur->_next;//删除第一个元素
	free(cur);
}
QDataType QueueFront(Queue* pq)
{
	assert(pq);
	return pq->_head->_next->_data;
}

void QueuePrint(Queue* pq)
{
	assert(pq);
	QueueNode* cur = pq->_head->_next;
	while (cur)
	{
		printf("%d ", cur->_data);
		cur = cur->_next;
	}
	printf("\n");
}
void QueueTest()
{
	Queue q;
	//QueueInit(&q);
	//QueuePush(&q, 1);
	//QueuePush(&q, 2);
	//QueuePush(&q, 3);
	////printf("%d\n",QueueFront(&q));
	////QueuePop(&q);
	//printf("%d\n", QueueEmpty(&q));
	//printf("%d\n", QueueSize(&q));
	//QueuePrint(&q);
	QueueDestory(&q);
}

二叉树相关接口的实现BTree.h

#define _CRT_SECURE_NO_WARNINGS
#include"common.h"
#include"BTree.h"
#include"Queue.h"

//通过前序遍历的数组"ABD##E#H##CF##G##"构建二叉树
BTNode* BinaryTreeCreate(BTDatatype* array, int* pIndex)
{
	if (array[(*pIndex)] == '#')
	{
		(*pIndex)++;
		return NULL;
	}

		BTNode* root = (BTNode*)malloc(sizeof(BTNode));
		root->_left = NULL;
		root->_right = NULL;
		root->_data = array[(*pIndex)];

		(*pIndex)++;
		root->_left = BinaryTreeCreate(array, pIndex);
		root->_right = BinaryTreeCreate(array, pIndex);

		return root;
	

}
void BinaryTreeDestory(BTNode** root)
{

}

int BinaryTreeSize(BTNode* root)
{
	if (root == NULL)
		return 0;
	return BinaryTreeSize(root->_left) + BinaryTreeSize(root->_right) + 1;
}
//int BinaryTreeLeafSize(BTNode* root)
//{
//	if (root == NULL)
//		return 0;
//	int LeftLeaf = 0;
//	int RightLeaf = 0;
//
//	if (root->_left == NULL && root->_right == NULL)
//		return 1;
//	LeftLeaf = BinaryTreeLeafSize(root->_left);
//	RightLeaf = BinaryTreeLeafSize(root->_right);
//
//	return LeftLeaf + RightLeaf;
//}
int BinaryTreeLeafSize(BTNode* root)
{
	if (root == NULL)
		return 0;
	if (root->_left == NULL && root->_right == NULL)
		return 1;
	return BinaryTreeLeafSize(root->_left) + BinaryTreeLeafSize(root->_right);
}
int BinaryTreeLevelSize(BTNode* root, int k)
{
	if (root == NULL)
		return 0;
	if (k == 1)
		return 1;
	return BinaryTreeLevelSize(root->_left, k - 1) 
		+ BinaryTreeLevelSize(root->_right, k - 1);
}

BTNode* BinaryTreeFind(BTNode* root, BTDatatype x)
{
	BTNode* ret = NULL;
	if (root == NULL)
		return NULL;
	if (root->_data == x)
		return root;
	ret = BinaryTreeFind(root->_left, x);
	if (ret)
		return ret;
	ret = BinaryTreeFind(root->_right, x);
	if (ret)
		return ret;

	return NULL;
}

//遍历
void BinaryTreePrevOrder(BTNode* root)
{
	if (root == NULL)
		return;
	printf("%c ", root->_data);

	BinaryTreePrevOrder(root->_left);
	BinaryTreePrevOrder(root->_right);
}
void BinaryTreeInOrder(BTNode* root)
{
	if (root == NULL)
		return;
	
	BinaryTreeInOrder(root->_left);
	printf("%c ", root->_data);
	BinaryTreeInOrder(root->_right);

}
void BinaryTreePostOrder(BTNode* root)
{
	if (root == NULL)
		return;
	BinaryTreePostOrder(root->_left);
	BinaryTreePostOrder(root->_right);
	printf("%c ", root->_data);
	
}

//层序遍历
void  BinaryTreeLevelOrder(BTNode* root)
{
	Queue q;
	QueueInit(&q);
	if (root != NULL)
	{
		QueuePush(&q, root);
		while (QueueEmpty(&q) != 0)
		{
			BTNode* front = QueueFront(&q);
			printf("%c ", front->_data);
			QueuePop(&q);
			if (front->_left)
				QueuePush(&q, front->_left);
			if (front->_right)
				QueuePush(&q, front->_right);
		}
		printf("\n");
	}
}
//判断二叉树是否为完全二叉树
int BinaryTreeComplete(BTNode* root)
{
	Queue q;
	QueueInit(&q);
	if (root != NULL)
	{
		QueuePush(&q, root);
		while (QueueEmpty(&q) != 0)
		{
			BTNode* front = QueueFront(&q);
			QueuePop(&q);

			if (front == NULL)
				break;

			QueuePush(&q, front->_left);
			QueuePush(&q, front->_right);
		}
		while (QueueEmpty(&q) != 0)
		{
			BTNode* front = QueueFront(&q);
			if (front != NULL)
			{
				QueueDestory(&q);
				return 0;
			}
			QueuePop(&q);
		}
	}
	return 1;
}


void BTreeTest()
{
	char array[100] = "ABD##E#H##CF##G##";
	//构造二叉树
	int Index = 0;
	BTNode* tree = BinaryTreeCreate(array, &Index);
	
	printf("%d\n", BinaryTreeSize(tree));
	printf("%d\n", BinaryTreeLevelSize(tree,3));
	printf("%d\n", BinaryTreeLeafSize(tree));
	BinaryTreePrevOrder(tree);
	printf("\n");
	BinaryTreeInOrder(tree);
	printf("\n");
	BinaryTreePostOrder(tree);
	printf("\n");
	BinaryTreeLevelOrder(tree);

	printf("%d\n", BinaryTreeComplete(tree));
}