C前序遍历二叉树Morris Traversal算法

　　首先来递归算法，简单易懂：

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>

typedef struct TreeNode{
    char data;
    struct TreeNode *lchild, *rchild;
}TreeNode;

void PreOrderTraverse(TreeNode *t){
    if( NULL == t ) return;
    printf("%c",t->data);
    PreOrderTraverse(t->lchild);
    PreOrderTraverse(t->rchild);
}

　　然后是栈模拟递归：

typedef struct StackNode{
    TreeNode *pdata;
    struct StackNode *next;
}StackNode;
typedef struct Stack{
    StackNode *top;
}Stack;

Stack *init_s(){
    Stack *pnew = (Stack *)malloc(sizeof(Stack));
    pnew->top = NULL;
    return pnew;
}
void push(Stack *s,TreeNode *p){
    StackNode *pnew = (StackNode *)malloc(sizeof(StackNode));
    pnew->pdata = p;
    pnew->next = s->top;
    s->top = pnew;
}
bool empty_stack(Stack *s){
    return NULL == s->top;
}
TreeNode *pop(Stack *s){
    TreeNode *p = NULL;
    StackNode *pn = NULL;
    if( ! empty_stack(s) ){
        pn = s->top;
        p = pn->pdata;
        s->top = pn->next;
        free(pn);    
    }
    return p;
}
void PreOrderTraverse(TreeNode *t){
    if( NULL == t ) return;
    TreeNode *p = NULL;
    Stack *s = init_s();
    push(s,t);
    while( ! empty_stack(s) ){
        p = pop(s);
        if( NULL == p ){
            continue;
        }
        printf("%c",p->data);
        push(s,p->rchild);
        push(s,p->lchild);
    }
}

　　Morris Traversal算法：空间复杂度O(1)：

　　用线索二叉树（threaded binary tree）的概念，利用叶子的左右闲指针指向遍历的前驱或者后继节点。

　　算法如下：

　　1、初始化当前节点为root
　　2、若当前节点不为空
　　　　a) 若当前节点没有左孩子
　　　　　　访问当前节点，并将当前节点移向右孩子
　　　　b) 若当前节点有左孩子
　　　　　　找到左子树的最右边那个节点
　　　　　　若它的右指针为空，访问当前节点,把它的右指针指向cur,并移动到当前节点到左孩子
　　　　　　若它的右指针为当前节点，则把它的右指针重新设为空（恢复树），并移动到当前节点的右孩子
　　3、重复第2步

void PreOrderTraverse(TreeNode *t){
    if( NULL == t ) return;
    TreeNode *pcur = t, *pre = NULL;
    while( pcur ){
        if( pcur->lchild ){
            pre = pcur->lchild;
            while( pcur != pre->rchild && NULL != pre->rchild ){
                pre = pre->rchild;
            }
            if( pre->rchild == pcur ){
                pre->rchild = NULL;                
                pcur = pcur->rchild;
            }
            else{
                printf("%c",pcur->data);
                pre->rchild = pcur;                
                pcur = pcur->lchild;
            }
        }
        else{
            printf("%c",pcur->data);
            pcur = pcur->rchild;
        }
    } 
}

　　main函数：

int main(){
    TreeNode *t = (TreeNode *)malloc(sizeof(TreeNode));
    TreeNode *pnew = (TreeNode *)malloc(sizeof(TreeNode));
    t->data = 'A';
    t->lchild = pnew;
    t->lchild->data = 'B';

    t->lchild->lchild = NULL;
    pnew = (TreeNode *)malloc(sizeof(TreeNode));
    t->lchild->rchild = pnew;
    t->lchild->rchild->data = 'D';
    t->lchild->rchild->lchild = NULL;
    t->lchild->rchild->rchild = NULL;
    
    pnew = (TreeNode *)malloc(sizeof(TreeNode));
    t->rchild = pnew;
    t->rchild->data = 'C';
    t->rchild->lchild = NULL;
    t->rchild->rchild = NULL;
    PreOrderTraverse(t);    
    printf("\n");
}