一、介紹
二叉樹是一種重要的數(shù)據(jù)結(jié)構(gòu)，在很多方面都有重要的應(yīng)用，此文主要記錄了二叉樹的基礎(chǔ)知識(shí)，包括二叉樹的建立、前中后序遍歷方式、層次遍歷方式、求解二叉樹的深度、求解二叉樹的節(jié)點(diǎn)總數(shù)、求解二叉樹每層的節(jié)點(diǎn)數(shù)目等。(更好的閱讀體驗(yàn)，請(qǐng)移步我的個(gè)人博客)
二、實(shí)現(xiàn)思路
主要借助棧和隊(duì)列方式實(shí)現(xiàn)二叉樹的非遞歸訪問等操作，二叉樹的建立采用遞歸方式。層次遍歷時(shí)，借助隊(duì)列數(shù)據(jù)結(jié)構(gòu)，將根節(jié)點(diǎn)入隊(duì)，當(dāng)隊(duì)列不為空時(shí)，退出隊(duì)列的一個(gè)節(jié)點(diǎn)，判斷此節(jié)點(diǎn)是否有左孩子，如有則訪問，并將此孩子入隊(duì)列，然后判斷此節(jié)點(diǎn)是否有右孩子，如有則訪問，并將有孩子入隊(duì)列；重復(fù)此過程即可。
三、實(shí)現(xiàn)代碼
#include<stdio.h>
#include<malloc.h>
#define MAXSIZE 100
typedef char dataType;
//二叉樹結(jié)構(gòu)
typedef struct bnode{
dataType data;
struct bnode *lChild,*rChild;
}Bnode,*BTree;
//隊(duì)列結(jié)構(gòu)
typedef struct {
BTree data[MAXSIZE];
int front,rear;
}SeqQueue,*PSeqQueue;
//棧的結(jié)構(gòu)
typedef struct {
BTree data[MAXSIZE];
int top;
}SeqStack,*PSeqStack;
//隊(duì)列的初始化
PSeqQueue initSeqQueue(){
PSeqQueue queue;
queue = (PSeqQueue)malloc(sizeof(SeqQueue));
if(queue){
queue->front = queue->rear = 0;
}
return queue;
}
//判斷隊(duì)列是否為空
int emptyQueue(PSeqQueue queue){
if(queue && queue->front==queue->rear){
return 1;
}else{
return 0;
}
}
//入隊(duì)列
int pushQueue(PSeqQueue queue,Bnode *node){
if((queue->rear+1)%MAXSIZE == queue->front){//判斷隊(duì)列是否滿了
return -1;
}else{
queue->rear = (queue->rear+1)%MAXSIZE;//位置為0的地址空間不用，方便判斷是否為空
queue->data[queue->rear] = node;
return 1;
}
}
//出隊(duì)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;
}
}
//讀取隊(duì)頭元素
int frontQueue(PSeqQueue queue,BTree *node){
if(queue->rear == queue->front){
return -1;
}else{
*node = queue->data[(queue->front+1)%MAXSIZE];
return 1;
}
}
//銷毀隊(duì)列
void destroyQueue(PSeqQueue *queue){
if(*queue){
free(*queue);
*queue = NULL;
}
}
//棧的初始化
PSeqStack initStack(){
PSeqStack stack;
stack = (PSeqStack)malloc(sizeof(SeqStack));
if(stack){
stack->top = -1;
}
return stack;
}
//判斷棧是否為空 1,空;0,非空
int emptyStack(PSeqStack stack){
if(stack->top == -1){
return 1;
}else{
return 0;
}
}
//入棧
int pushStack(PSeqStack stack,Bnode *node){
if(stack->top == MAXSIZE-1){
return 0;
}else{
stack->top ++;
stack->data[stack->top] = node;
return 1;
}
}
//出棧
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);
}
//二叉樹的建立
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;
}
//先序遍歷二叉樹
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;
}
}
}
//中序遍歷此二叉樹
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;
}
}
}
//后序遍歷打印元素
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);
}
}
//層次遍歷二叉樹
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);
}
}
}
}
//求二叉樹的高度
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;
}
}
}
//求解二叉樹每層節(jié)點(diǎn)的個(gè)數(shù)
void levelCount(BTree tree,int l,int num[]){
if(tree){
num[l]++;
levelCount(tree->lChild,l+1,num);
levelCount(tree->rChild,l+1,num);
}
}
//求解二叉樹節(jié)點(diǎn)總數(shù)
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;//記錄每層的節(jié)點(diǎn)數(shù),l從1開始,樹的深度
treeHeight = height(tree);
printf("\n此二叉樹的深度為: %d\n",treeHeight);
treeCount = countTree(tree);
printf("此二叉樹的節(jié)點(diǎn)總數(shù)為: %d\n",treeCount);
levelCount(tree,l,countNum);
printf("此二叉樹各層的節(jié)點(diǎn)數(shù)為: ");
for(i=1;i<=treeHeight;i++){
printf("第%d層數(shù)目: %d, ",i,countNum[i]);
}
printf("\n\n");
printf("先序遍歷此二叉樹: ");
perOrder(tree);
printf("\n");
printf("中序遍歷此二叉樹: ");
inOrder(tree);
printf("\n");
printf("后序遍歷此二叉樹: ");
postOrder(tree);
printf("\n");
printf("層次遍歷此二叉樹: ");
levelOrder(tree);
printf("\n");
return 0;
}
四、實(shí)驗(yàn)結(jié)果截圖
實(shí)驗(yàn)結(jié)果截圖.png
