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。(更好的阅读体验，请移步我的个人博客)

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;
}

四、实验结果截图