• 二叉樹

• 概念

一棵二叉樹是結點的一個有限集合，該集合或者為空，或者是由一個根節點加上兩棵別稱為左子樹和右子樹的二又樹組成。 二叉樹的特點: 1.每個結點最多有兩棵子樹，即二叉樹不存在度大於2的結點。2.二又樹的子樹有左右之分，其子樹的次序不能顛倒  

• 特殊的二叉樹

      1.滿二叉樹:一個二叉樹，如果每一個層的結點數都達到最大值，則這個二又樹就是滿二叉樹。也就是說，如果一個二叉樹的層數為K，且結點總數是(2^k)-1，則它就是滿二叉樹。       2.完全二叉樹:完全二又樹是效率很高的資料結構，完全- -又樹是由滿二又樹而引出來的。對於深度為K的，有n個結點的二叉樹，當且僅當其每一個結點都與深度為K的滿二又樹中編號從1至n的結點一對應時稱之為完全二又樹。要注意的是滿二叉樹是-種特殊的完全二叉樹。  

具體實現程式碼如下：

• BinaryTree.h

#pragma once
#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
#include <assert.h>
#include "Queue.h"
#include "Stack.h"


typedef char BTDataType ;
typedef struct BTNode
{
	struct BTNode* _left;
	struct BTNode* _right;
	BTDataType _data;
}BTNode;

// 通過前序遍歷的陣列"ABD##E#H##CF##G##"構建二叉樹
BTNode* BinaryTreeCreate(BTDataType* a, int* pi);
void BinaryTreeDestory(BTNode** root);
int BinaryTreeSize(BTNode* root);
int BinaryTreeLeafSize(BTNode* root);
int BinaryTreeLevelKSize(BTNode* root, int k);
BTNode* BinaryTreeFind(BTNode* root, BTDataType x);
// 遍歷 遞迴
void BinaryTreePrevOrder(BTNode* root);//前序遍歷
void BinaryTreeInOrder(BTNode* root);//中序遍歷
void BinaryTreePostOrder(BTNode* root);//後序遍歷
void BinaryTreeLevelOrder(BTNode* root);//層序遍歷

// 遍歷 非遞迴
void BinaryTreePrevOrderNonR(BTNode* root);//前序遍歷的非遞迴
void BinaryTreeInOrderNonR(BTNode* root);//中序遍歷的非遞迴
void BinaryTreePostOrderNonR(BTNode* root);//後序遍歷的非遞迴
void TestBinaryTree();


 

• BinaryTree.c

#include "BinaryTree.h"
#include "Queue.h"
#include "Stack.h"



BTNode* BuyBTNode(BTDataType x)
{
	BTNode* node = (BTNode*)malloc(sizeof(BTNode));
	node->_data= x;
	node->_left =NULL;
	node->_right = NULL;
	return node;
}


BTNode* BinaryTreeCreate(BTDataType* a,int* pi)
{
	if (a[*pi] != '#')
	{
		BTNode* root = BuyBTNode(a[*pi]);
		(*pi)++;
		root->_left = BinaryTreeCreate(a, pi);
		(*pi)++;
		root->_right = BinaryTreeCreate(a, pi);

		return root;
	}
	else
	{
		return NULL;
	}
}

int BinaryTreeSize(BTNode* root)
{
	if (root == NULL)
	{
		return 0;
	}
	else
	{
		           
		return BinaryTreeSize(root->_left) + BinaryTreeSize(root->_right) + 1;
	}
}

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 BinaryTreeLevelKSize(BTNode* root, int k)
{
	if (root == NULL)
	{
		return 0;
	}
	if (k == 1)
	{
		return 1;
	}
	return BinaryTreeLevelKSize(root->_left, k - 1) +
		BinaryTreeLevelKSize(root->_right, k - 1);
}

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

 void _BinaryTreePrevOrder(BTNode* root, int* a, int* pi)
{
	if (root == NULL)
	{
		return ;
	}
	printf("%c ", root->_data);
	(*pi)++;
	_BinaryTreePrevOrder(root->_left, a, pi);
	_BinaryTreePrevOrder(root->_right, a, pi);

}
void BinaryTreePrevOrder(BTNode* root)//前序遍歷
{
	if (root == NULL)
		return ;
	int treeSize = BinaryTreeSize(root);
	int* arr = (int*)malloc(sizeof(int)*treeSize);
	int i = 0;
	_BinaryTreePrevOrder(root, arr, &i);

}

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

void BinaryTreeInOrder(BTNode* root)//中序遍歷
{
	if (root == NULL)
		return;
	int treeSize = BinaryTreeSize(root);
	int* arr = (int*)malloc(sizeof(int)*treeSize);
	int i = 0;
	_BinaryTreeInOrder(root, arr, &i);

}

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

void BinaryTreePostOrder(BTNode* root)//後序遍歷
{
	if (root == NULL)
	{
		return;
	}
	int treeSize = BinaryTreeSize(root);
	int* arr = (int*)malloc(sizeof(int)*treeSize);
	int i = 0;
	_BinaryTreePostOrder(root, arr, &i);
	
}

void BinaryTreeLevelOrder(BTNode* root)//層序遍歷
{
	Queue q;
	QueueInit(&q);
	if (root != NULL)
	{
		QueuePush(&q, root);
		while (QueueEmpty(&q) != 0)
		{
			BTNode* front = QueueFront(&q);
			QueuePop(&q);
			printf("%c ", front->_data);
			if (front->_left)
			{
				QueuePush(&q, front->_left);
			}
			if (front->_right)
			{
				QueuePush(&q, front->_right);
			}
		}
	}
	printf("\n");
}

void BinaryTreePrevOrderNonR(BTNode* root)//前序遍歷的非遞迴
{
	Stack st;
	StackInit(&st,10);
	BTNode* cur = root;
	while (cur || StackEmpty(&st) != 0)
	{
		//開始訪問一棵樹
		//1.先訪問樹的左路節點
		while (cur)
		{
			printf("%c ", cur->_data);
			StackPush(&st, cur);
			cur = cur->_left;
		}
		BTNode* top = StackTop(&st);
		StackPop(&st);
		//2.訪問左路節點的右子樹
		cur = top->_right;		
	}
	printf("\n");
}

void BinaryTreeInOrderNonR(BTNode* root)//中序遍歷的非遞迴
{
	Stack st;
	StackInit(&st, 10);
	BTNode* cur = root;
	while (cur || StackEmpty(&st) != 0)
	{
		while (cur)
		{
			StackPush(&st, cur);
			cur = cur->_left;
		}
		BTNode* top = StackTop(&st);
		printf("%c ", top->_data);
		StackPop(&st);
		cur = top->_right;
	}
	printf("\n");
}
 

• test.c

# include "BinaryTree.h"
#include "Queue.h"
#include "Stack.h"

void BinaryTreeTest()
{
	char* array = "ABD##E#H##CF##G##";
	int i = 0;
	BTNode* tree = BinaryTreeCreate(array, &i);
	printf("%d\n", BinaryTreeSize(tree));
	printf("%d\n", BinaryTreeLeafSize(tree));
	BinaryTreePrevOrder(tree); //遞迴的前序遍歷
	printf("\n");
	printf("\n");
	BinaryTreeInOrder(tree);//遞迴的中序序遍歷
	printf("\n");
	printf("\n");
	BinaryTreePostOrder(tree);//遞迴的後序遍歷
	printf("\n");
	printf("\n");
    BinaryTreeLevelOrder(tree);//層序遍歷
	printf("\n");
	printf("\n");
	BinaryTreePrevOrderNonR(tree);//非遞迴的前序遍歷
	printf("\n");
	BinaryTreeInOrderNonR(tree);//中序遍歷的非遞迴
	
}

int main()
{
	BinaryTreeTest();
	system("pause");
	return 0;

}