C语言实现二叉树的各种遍历及求解深度
一、介绍
二叉树是一种重要的数据结构，在很多方面都有重要的应用，此文主要记录了二叉树的基础知识，包括二叉树的建立、前中后序遍历方式、层次遍历方式、求解二叉树的深度、求解二叉树的节点总数、求解二叉树每层的节点数目等。
二、实现思路
主要借助栈和队列方式实现二叉树的非递归访问等操作，二叉树的建立采用递归方式。层次遍历时，借助队列数据结构，将根节点入队，当队列不为空时，退出队列的一个节点，判断此节点是否有左孩子，如有则访问，并将此孩子入队列，然后判断此节点是否有右孩子，如有则访问，并将有孩子入队列；重复此过程即可。
三、实现代码
#include<stdio.h>
#include<malloc.h>
#define MAXSIZE 100
typedef char dataType;
//二叉树结构
typedef struct bnode{
dataType data;
struct bnode *lChild,*rChild;
}Bnode,*BTree;
//队列结构
typedef struct {
BTree data[MAXSIZE];
int front,rear;
}SeqQueue,*PSeqQueue;
//栈的结构
typedef struct {
BTree data[MAXSIZE];
int top;
}SeqStack,*PSeqStack;
//队列的初始化
PSeqQueue initSeqQueue(){
PSeqQueue queue;
queue = (PSeqQueue)malloc(sizeof(SeqQueue));
if(queue){
queue->front = queue->rear = 0;
}
return queue;
}
//判断队列是否为空
int emptyQueue(PSeqQueue queue){
if(queue && queue->front==queue->rear){
return 1;
}else{
return 0;
}
}
//入队列
int pushQueue(PSeqQueue queue,Bnode *node){
if((queue->rear+1)%MAXSIZE == queue->front){//判断队列是否满了
return -1;
}else{
queue->rear = (queue->rear+1)%MAXSIZE;//位置为0的地址空间不用，方便判断是否为空
queue->data[queue->rear] = node;
return 1;
}
}
//出队列
int popQueue(PSeqQueue queue,BTree *node){
if(emptyQueue(queue)){
return -1;
}else{
queue->front = (queue->front +1)%MAXSIZE;
*node = queue->data[queue->front];
return 1;
}
}
//读取队头元素
int frontQueue(PSeqQueue queue,BTree *node){
if(queue->rear == queue->front){
return -1;
}else{
*node = queue->data[(queue->front+1)%MAXSIZE];
return 1;
}
}
//销毁队列
void destroyQueue(PSeqQueue *queue){
if(*queue){
free(*queue);
*queue = NULL;
}
}
//栈的初始化
PSeqStack initStack(){
PSeqStack stack;
stack = (PSeqStack)malloc(sizeof(SeqStack));
if(stack){
stack->top = -1;
}
return stack;
}
//判断栈是否为空 1,空;0,非空
int emptyStack(PSeqStack stack){
if(stack->top == -1){
return 1;
}else{
return 0;
}
}
//入栈
int pushStack(PSeqStack stack,Bnode *node){
if(stack->top == MAXSIZE-1){
return 0;
}else{
stack->top ++;
stack->data[stack->top] = node;
return 1;
}
}
//出栈
int popStack(PSeqStack stack,BTree *node){
if(emptyStack(stack) == 1){
return 0;
}else{
*node = stack->data[stack->top];
stack->top --;
return 1;
}
}
//打印元素
void visit(char ch){
printf("%c \t",ch);
}
//二叉树的建立
BTree createTree(){
BTree tree;
dataType str;
str = getchar();
if(str == '#'){
tree = NULL;
}else{
tree = (BTree)malloc(sizeof(Bnode));
tree->data = str;
tree->lChild = createTree();
tree->rChild = createTree();
}
return tree;
}
//先序遍历二叉树
void perOrder(BTree tree){
PSeqStack stack;
BTree p = tree;
stack = initStack();
while(p || ! emptyStack(stack)){
if(p){
visit(p->data);
pushStack(stack,p);
p = p->lChild;
}else{
popStack(stack,&p);
p = p->rChild;
}
}
}
//中序遍历此二叉树
void inOrder(BTree tree){
PSeqStack stack;
BTree p = tree;
stack = initStack();
while(p || !emptyStack(stack)){
if(p){
pushStack(stack,p);
p = p->lChild;
}else{
popStack(stack,&p);
visit(p->data);
p = p->rChild;
}
}
}
//后序遍历打印元素
void postOrder(BTree tree){
PSeqStack s1,s2;
BTree p = tree;
s1 = initStack();
s2 = initStack();
while(p || !emptyStack(s2)){
if(p){
pushStack(s1,p);
pushStack(s2,p);
p = p->rChild;
}else{
popStack(s2,&p);
p = p->lChild;
}
}
while(!emptyStack(s1)){
popStack(s1,&p);
visit(p->data);
}
}
//层次遍历二叉树
void levelOrder(BTree tree ){
BTree p = tree;
PSeqQueue queue = initSeqQueue();
if(p){
pushQueue(queue,p);
while(!emptyQueue(queue)){
popQueue(queue,&p);
visit(p->data);
if(p->lChild){
pushQueue(queue,p->lChild);
}
if(p->rChild){
pushQueue(queue,p->rChild);
}
}
}
}
//求二叉树的高度
int height(BTree tree){
int h1,h2;
if(tree == NULL){
return 0;
}else{
h1 = height(tree->lChild);
h2 = height(tree->rChild);
if(h1>h2){
return h1+1;
}else{
return h2+1;
}
}
}
//求解二叉树每层节点的个数
void levelCount(BTree tree,int l,int num[]){
if(tree){
num[l]++;
levelCount(tree->lChild,l+1,num);
levelCount(tree->rChild,l+1,num);
}
}
//求解二叉树节点总数
int countTree(BTree tree){
int lCount,rCount;
if(tree == NULL){
return 0;
}
lCount = countTree(tree->lChild);
rCount = countTree(tree->rChild);
return lCount + rCount +1;
}
int main(){
BTree tree = createTree();
int i=0;
int countNum[10]={0,0,0,0,0,0,0,0,0,0},l=1,treeHeight,treeCount;//记录每层的节点数,l从1开始,树的深度
treeHeight = height(tree);
printf("\n此二叉树的深度为: %d\n",treeHeight);
treeCount = countTree(tree);
printf("此二叉树的节点总数为: %d\n",treeCount);
levelCount(tree,l,countNum);
printf("此二叉树各层的节点数为: ");
for(i=1;i<=treeHeight;i++){
printf("第%d层数目: %d, ",i,countNum[i]);
}
printf("\n\n");
printf("先序遍历此二叉树: ");
perOrder(tree);
printf("\n");
printf("中序遍历此二叉树: ");
inOrder(tree);
printf("\n");
printf("后序遍历此二叉树: ");
postOrder(tree);
printf("\n");
printf("层次遍历此二叉树: ");
levelOrder(tree);
printf("\n");
return 0;
}
