【数据结构周周练】012 利用队列和非递归算法实现二叉树的层次遍历

Dear 丶 2021-06-11 15:13 368阅读 0赞

# 一、前言 #

二叉树的遍历是比较多样化的遍历，有很多种遍历方式，先序遍历，中序遍历，后序遍历，层次遍历等等。本次给大家讲的是层次遍历，为了方便，我将题目中的数据改为编号，从左往右，从上往下依次遍历。方便大家看到结果。

# 二、题目 #

将下图用二叉树存入，并通过层次遍历方式，自上而下，从左往右对该树进行遍历。其中圆角矩形内为结点数据，旁边数字为结点编号，编号为0的结点为根节点，箭头指向的结点为箭尾的孩子结点。要求遍历每个结点时能够查询当前结点的数据以及编号，如果结点是根节点或者叶子结点，请说明。

实现功能后，将层次遍历变换为：自下而上，从右往左对该树进行遍历。并将结果输出。

![70][]

#  三、代码 #

#define MAXQUEUESIZE 10
    
    #include<iostream>
    #include<malloc.h>
    
    using namespace std;
    
    typedef struct BiTNode {
    	int data,number;
    	struct BiTNode *lChild, *rChild,*parent;
    
    }BiTNode,*BiTree;
    
    typedef struct {
    	BiTree *qBase;
    	int front;
    	int rear;
    }SqQueue;
    
    typedef struct LNode{
    	BiTree data;
    	struct LNode *next;
    }LNode,*LinkStack;
    
    int InitQueue(SqQueue &SQ) {
    	SQ.qBase = (BiTree*)malloc(MAXQUEUESIZE * sizeof(SqQueue));
    	if (!SQ.qBase)
    	{
    		cout << "空间分配失败（Allocate space failure）" << endl;
    		exit(OVERFLOW);
    	}
    	SQ.front = SQ.rear = 0;
    	return 1;
    }
    
    int EnQueue(SqQueue &SQ, BiTree e) {
    	if ((SQ.rear+1)% MAXQUEUESIZE == SQ.front)
    	{
    		cout << "队列已满(The queue is full)" << endl;
    		exit(OVERFLOW);
    	}
    	SQ.qBase[SQ.rear] = e;
    	SQ.rear = (SQ.rear + 1) % MAXQUEUESIZE;
    	return 1;
    }
    
    int DeQueue(SqQueue &SQ, BiTree &e) {
    	if (SQ.rear == SQ.front)
    	{
    		cout << "队列已空(The queue is null)" << endl;
    		return 0;
    	}
    	e = SQ.qBase[SQ.front];
    	SQ.front = (SQ.front + 1) % MAXQUEUESIZE;
    	return 1;
    }
    
    int InitStack(LinkStack &S) {
    	S = (LinkStack)malloc(sizeof(LNode));
    	if (!S)
    	{
    		cout << "空间分配失败（Allocate space failure）" << endl;
    		exit(OVERFLOW);
    	}
    	S->next = NULL;
    	return 1;
    }
    
    int Push(LinkStack &S, BiTree e) {
    	LinkStack p = (LinkStack)malloc(sizeof(LNode));
    	if (!p)
    	{
    		cout << "结点分配失败（Allocate node failure）" << endl;
    		exit(OVERFLOW);
    	}
    	S->data = e;
    	p->next = S;
    	S = p;
    	return 1;
    }
    int Pop(LinkStack &S, BiTree &e) {
    	LinkStack p = S->next;
    	if (!p)
    	{
    		cout << "栈空(The stack is null)" << endl;
    		exit(OVERFLOW);
    	}
    	e = p->data;
    	S->next = p->next;
    	free(p);
    	return 1;
    }
    
    int number = 0;
    int yon = 0;
    int yesOrNo[] = { 1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0 };
    int numData[] = { 1,2,4,3,5,7,8,6 };
    BiTree treeParent = NULL;
    
    int OperationBiTree(BiTree &BT) {
    	BT = (BiTree)malloc(sizeof(BiTNode));
    	if (!BT)
    	{
    		cout << "空间分配失败" << endl;
    		exit(OVERFLOW);
    	}
    	BT->number = number;
    	number++;
    	BT->data = numData[BT->number];
    	BT->lChild = NULL;
    	BT->rChild = NULL;
    	BT->parent = treeParent;
    	return 1;
    }
    
    void PreOrderCreatBiTree(BiTree &BT) {
    
    	OperationBiTree(BT);
    	treeParent = BT;
    	if (yesOrNo[yon++])
    		PreOrderCreatBiTree(BT->lChild);
    	treeParent = BT;
    	if (yesOrNo[yon++])
    		PreOrderCreatBiTree(BT->rChild);
    }
    
    void VisitBiTree(BiTree BT) {
    	cout << "当前结点的编号为：" << BT->number << ", ";
    	cout << "数据为：" << BT->data << ",";
    	if (!BT->parent)
    		cout << "当前结点为根节点。";
    	if (!BT->lChild && !BT->rChild)
    		cout << "当前结点为叶子结点。";
    	cout << endl;
    
    }
    
    void LevelOrderBiTree(BiTree BT, LinkStack &S) {
    	SqQueue SQ;
    	InitQueue(SQ);
    	InitStack(S);
    	BiTree t = BT;
    	EnQueue(SQ, t);
    	while (SQ.rear != SQ.front)
    	{
    		DeQueue(SQ, t);
    		Push(S, t);
    		VisitBiTree(t);
    		if (t->lChild)
    			EnQueue(SQ, t->lChild);
    		if (t->rChild)
    			EnQueue(SQ, t->rChild);
    	}
    }
    
    void main() {
    	BiTree BT,t;
    	LinkStack S;
    	PreOrderCreatBiTree(BT);
    
    	cout << "***********层次遍历——自上而下，从左往右***********\n\n";
    	LevelOrderBiTree(BT,S);
    
    	cout << "\n***********层次遍历——自下而上，从右往左***********\n\n";
    	while (S->next)
    	{
    		Pop(S, t);
    		VisitBiTree(t);
    	}
    	
    }

# 四、实现效果 #

![70 1][]

[70]: /images/20210516/85b6c8a8c9274c3fa13fb6111c218c8f.png
[70 1]: /images/20210516/3279f81212aa4203b123cb83d680383f.png