二叉树的遍历：前序，中序，后序，层序－－包括递归和非递归实现<转>
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created: 2005/12/30 created: 30:12:2005 10:39 filename: bintree.h author: Liu Qi purpose: 二叉树的3种遍历方式(包括非递归实现),前序，后序和中序，先访问根节点就是 前序(部分书籍称为先根遍历,个人觉得该说法更好^_^)，类似的，最后访问根节点就是后序
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#ifndef TREE_H#define TREE_H#include <stdio.h>#include <malloc.h>#include <stack>#include <queue>#include <assert.h>using namespace std;typedef int ElemType;typedef struct treeT{
ElemType key; struct treeT* left; struct treeT* right;}treeT, *pTreeT;/*===========================================================================* Function name: visit* Parameter: root:树根节点指针* Precondition: * Description: * Return value: * Author: Liu Qi, //-===========================================================================*/static void visit(pTreeT root){ if (NULL != root)
{
printf(" %d\n", root->key);
}}/*===========================================================================* Function name: BT_MakeNode * Parameter: target:元素值 * Precondition: None * Postcondition: NULL != pTreeT * Description: 构造一个tree节点，置左右指针为空，并且返回指向新节点的指针 * Return value: 指向新节点的指针 * Author: Liu Qi, [12/30/2005]===========================================================================*/static pTreeT BT_MakeNode(ElemType target){ pTreeT pNode = (pTreeT) malloc(sizeof(treeT)); assert( NULL != pNode ); pNode->key = target; pNode->left = NULL; pNode->right = NULL; return pNode;}/*===========================================================================* Function name: BT_Insert* Parameter: target:要插入的元素值, pNode:指向某一个节点的指针* Precondition: NULL != ppTree * Description: 插入target到pNode的后面* Return value: 指向新节点的指针* Author: Liu Qi, [12/29/2005]===========================================================================*/pTreeT BT_Insert(ElemType target, pTreeT* ppTree){ pTreeT Node; assert( NULL != ppTree ); Node = *ppTree; if (NULL == Node) { return *ppTree = BT_MakeNode(target); } if (Node->key == target) //不允许出现相同的元素 { return NULL; } else if (Node->key > target) //向左 { return BT_Insert(target, &Node->left); } else { return BT_Insert(target, &Node->right); }}/*===========================================================================* Function name: BT_PreOrder* Parameter: root:树根节点指针* Precondition: None* Description: 前序遍历* Return value: void* Author: Liu Qi, [12/29/2005]===========================================================================*/void BT_PreOrder(pTreeT root){ if (NULL != root) { visit(root); BT_PreOrder(root->left); BT_PreOrder(root->right); } }/*===========================================================================* Function name: BT_PreOrderNoRec* Parameter: root:树根节点指针* Precondition: Node* Description: 前序(先根)遍历非递归算法* Return value: void* Author: Liu Qi, [1/1/2006]===========================================================================*/void BT_PreOrderNoRec(pTreeT root){ stack<treeT *> s; while ((NULL != root) || !s.empty()) { if (NULL != root) { visit(root); s.push(root); root = root->left; } else { root = s.top(); s.pop(); root = root->right; } }}/*===========================================================================* Function name: BT_InOrder* Parameter: root:树根节点指针* Precondition: None* Description: 中序遍历* Return value: void* Author: Liu Qi, [12/30/2005]===========================================================================*/void BT_InOrder(pTreeT root){ if (NULL != root) { BT_InOrder(root->left); visit(root); BT_InOrder(root->right); }}/*===========================================================================* Function name: BT_InOrderNoRec* Parameter: root:树根节点指针* Precondition: None* Description: 中序遍历,非递归算法* Return value: void* Author: Liu Qi, [1/1/2006]===========================================================================*/void BT_InOrderNoRec(pTreeT root){ stack<treeT *> s; while ((NULL != root) || !s.empty()) { if (NULL != root) { s.push(root); root = root->left; } else { root = s.top(); visit(root); s.pop(); root = root->right; } }}/*===========================================================================* Function name: BT_PostOrder* Parameter: root:树根节点指针* Precondition: None* Description: 后序遍历* Return value: void* Author: Liu Qi, [12/30/2005]===========================================================================*/void BT_PostOrder(pTreeT root){ if (NULL != root) { BT_PostOrder(root->left); BT_PostOrder(root->right); visit(root); }}/*===========================================================================* Function name: BT_PostOrderNoRec* Parameter: root:树根节点指针* Precondition: None* Description: 后序遍历,非递归算法* Return value: void* Author: Liu Qi, // [1/1/2006]===========================================================================*/void BT_PostOrderNoRec(pTreeT root){//学习中，尚未明白}/*===========================================================================* Function name: BT_LevelOrder* Parameter: root:树根节点指针* Precondition: NULL != root* Description: 层序遍历* Return value: void* Author: Liu Qi, [1/1/2006]===========================================================================*/void BT_LevelOrder(pTreeT root){ queue<treeT *> q; treeT *treePtr; assert( NULL != root ); q.push(root); while (!q.empty()) { treePtr = q.front(); q.pop(); visit(treePtr); if (NULL != treePtr->left) { q.push(treePtr->left); } if (NULL != treePtr->right) { q.push(treePtr->right); } }}#endif
测试代码
#include <stdio.h>#include <stdlib.h>#include <time.h>#include "tree.h"#define MAX_CNT 5#define BASE 100int main(int argc, char *argv[]){ int i; pTreeT root = NULL; srand( (unsigned)time( NULL ) ); for (i=0; i<MAX_CNT; i++) { BT_Insert(rand() % BASE, &root); } //前序 printf("PreOrder:\n"); BT_PreOrder(root); printf("\n"); printf("PreOrder no recursion:\n"); BT_PreOrderNoRec(root); printf("\n"); //中序 printf("InOrder:\n"); BT_InOrder(root); printf("\n"); printf("InOrder no recursion:\n"); BT_InOrderNoRec(root); printf("\n"); //后序 printf("PostOrder:\n"); BT_PostOrder(root); printf("\n"); //层序 printf("LevelOrder:\n"); BT_LevelOrder(root); printf("\n"); return 0;}如果有兴趣不妨运行一下，看看效果^_^
另外请教怎样让二叉树漂亮的输出，即按照树的形状输出
思想是：
先找到最左边的叶子并把路上遇到的节点依次压栈，然后弹出栈顶的元素（该元素为最左边的叶子），并判断（1）它有没有右节点；（2）右节点是否被访问过。如果（1）为有右节点同时（2）为没有访问过，则先压入刚才弹出的元素，然后再压入它的右子树。否则，就访问该节点，并设置pre为改节点。
void BT_PostOrderNoRec(pTreeT root)
{
stack<pTreeT> s;
s.push(root);
while(root != 0 || !s.isEmpty()) {
//找到最左边的叶子
while((root = root->left) != 0) {
s.push(root);
}
pTree pre; //记录前一个访问的节点
root = s.pop(); //弹出栈顶元素
//如果右子树非空，并且右子树未访问过，
//则（在内层while循环中）把右子树压栈
if(root->right != 0 && pre != root->right) {
//要把上一句中弹出的元素重新压栈
s.push(root);
root = root->right;
s.push(root);
}
//否则
else {
弹出栈顶节点，访问它并设置pre为该节点
root = pre = s.pop();
visit(root);
//使root为0以免进入内层循环
root = 0;
}
}
* *
*
#
# #
{
stack<treeT *> s;
pTreeT pre=NULL;
while ((NULL != root) || !s.empty())
{
if (NULL != root)
{
s.push(root);
root = root->left;
}
else
{
root = s.top();
if (root->right!=NULL && pre!=root->right){
root=root->right;
}
else{
root=pre=s.top();
visit(root);
s.pop();
root=NULL;
}
}
}
}
现如下：
void BT_PostOrderNoRec(pTreeT root)
{
stack<treeT *> s;
pTreeT pre=NULL;
while ((NULL != root) || !s.empty())
{
if (NULL != root)
{
s.push(root);
root = root->left;
}
else
{
root = s.top();
if (root->right!=NULL && pre!=root->right){
root=root->right;
}
else{
root=pre=s.top();
visit(root);
s.pop();
root=NULL;
}
}
}
}
void BT_PostOrderNoRec(pTreeT root)
{
stack<treeT *> s;
pTreeT pre = NULL;
pTreeT top = NULL;
while ((NULL != root) || !s.empty())
{
if (NULL != root)
{
s.push(root);
root = root->right;
}
else
{
top = s.top();
if(top->left != NULL && top->left != pre)
root = top->left;
else
{
visit(top);
s.pop();
pre = top;
}
}
}
}
void BT_PostOrderNoRec(pTreeT root)
{
stack<treeT *> s;
pTreeT pre = NULL;
pTreeT top = NULL;
while ((NULL != root) || !s.empty())
{
if (NULL != root)
{
s.push(root);
root = root->left;
}
else
{
top = s.top();
if(top->right != NULL && top->right != pre)
root = top->right;
else
{
visit(top);
pre = top;
s.pop();
}
}
}
}