二叉树的递归建立以及深度优先遍历

根据访问结点操作发生位置命名：　

① NLR：前序遍历(PreorderTraversal亦称（先序遍历））　　——访问根结点的操作发生在遍历其左右子树之前。　　

② LNR：中序遍历(InorderTraversal)　　——访问根结点的操作发生在遍历其左右子树之中（间）。　　

③ LRN：后序遍历(PostorderTraversal)　　——访问根结点的操作发生在遍历其左右子树之后。　　

注意：由于被访问的结点必是某子树的根，所以N(Node）、L(Left subtree）和R(Right subtree）又可解释为根、根的左子树和根的右子树。NLR、LNR和LRN分别又称为先根遍历、中根遍历和后根遍历。

前中后是指根结点的访问时机，在左右子树之前、中间或之后。

层序就是从根结点开始从上至下、从左到右地依次访问。

先上代码：

#include<stdio.h>
#include<stdlib.h>
#define Maxsize 100;

typedef int ElemType;
typedef struct BT
{
int data;
struct BT *lch, *rch;
} BT;

BT *CreatBT ();
void preorder (BT * T);
void inorder (BT * T);
void postorder (BT * T);
void leafnum (BT * T);
void ShowTree (BT * T);
void Nodenum (BT * T);
void printTree(BT *T,int n);
int main (void)
{
BT *T = NULL;
int choice;
do
{
printf ("\n");
printf (" 二叉树 \n");
printf (" ***************************\n");
printf (" * *\n");
printf (" * 主菜单 *\n");
printf (" * 1 建立二叉树 *\n");
printf (" * 2 先序遍历二叉树 *\n");
printf (" * 3 中序遍历二叉树 *\n");
printf (" * 4 后序遍历二叉树 *\n");
printf (" * 5 二叉树的叶子结点数 *\n");
printf (" * 6 显示二叉树 *\n");
printf (" * 7 二叉树的所有结点数 *\n");
printf (" * 8 退出程序运行 *\n");
printf (" ****************************\n");
printf (" 请输入您的选择（1，2，3，4，5，6，7，8): \n");
scanf ("%d", &choice);
if (choice == 1)
{
printf
("二叉树的建立，以输入“0”表示结束：！\n");
printf ("请输入根结点：\n");
T = CreatBT ();
printf ("二叉树成功建立");
}
else if (choice == 2)
{
printf ("先序遍历二叉树 :\n");
preorder (T);
}
else if (choice == 3)
{
printf ("中序遍历二叉树:\n");
inorder (T);
}
else if (choice == 4)
{
printf ("后序遍历二叉树 :\n ");
postorder (T);
}
else if (choice == 5)
{
printf (" 二叉树的叶子结点数为 : \n");
leafnum (T);
}
else if (choice == 6)
//  ShowTree (T);
printTree(T,1);
else if (choice == 7)
{
Nodenum (T);
}
else if (choice == 8)
exit (0);
}
while (choice <= 8);
}

BT *
CreatBT ()
{
BT *t;
int x;
scanf ("%d", &x);
if (x == 0)
{
t = NULL;
}
else
{
t = (BT *) malloc (sizeof (BT));
t->data = x;
printf ("\n请输入%d结点的左子结点:", t->data);
t->lch = CreatBT ();
printf ("\n请输入%d结点的右子结点:", t->data);
t->rch = CreatBT ();
}
return t;
}

void
preorder (BT * T)
{
if (T == NULL)
return;
else
{
printf ("%3d", T->data);
preorder (T->lch);
preorder (T->rch);
}
}

void
inorder (BT * T)
{
if (T == NULL)
return;
else
{
inorder (T->lch);
printf ("%3d", T->data);
inorder (T->rch);
}
}

void
postorder (BT * T)
{
if (T == NULL)
return;
else
{
postorder (T->lch);
postorder (T->rch);
printf ("%3d", T->data);
}
}
void
leafnum (BT * T)
{
static int count = 0;
if (T)
{
if (T->lch == NULL && T->rch == NULL)
{
count++;
printf("叶子是%4d\n",T->data);

}
leafnum (T->lch);
leafnum (T->rch);
printf ("叶子总数是%4d", count);
}
}

void
ShowTree (BT * T)
{
BT *stack[100];
BT *p;
int level[100][2];
int top, n, i;
int width = 4;
if (T != NULL)
{
printf ("\n二叉树的表示法f:\n");
top = 1;
stack[top] = T;
level[top][0] = width;
while (top > 0)
{
p = stack[top];
n = level[top][0];
for (i = 1; i <= n; i++)
printf (" ");
printf ("%d", p->data);
for (i = n + 1; i < 60; i += 2)
printf ("*");
printf ("\n\t\t");
top--;
if (p->rch != NULL)
{
top++;
stack[top] = p->rch;
level[top][0] = n + width;
level[top][1] = 2;
}
if (p->lch != NULL)
{
top++;
stack[top] = p->lch;
level[top][0] = n + width;
level[top][1] = 1;
}
}
}
}

void Nodenum (BT * T)
{
static int count = 0;
if (T)
{
count++;
Nodenum (T->lch);
Nodenum (T->rch);
}
else {
printf ("该二叉树总共有%d个结点。\n", count);
}
}
void printTree(BT *T,int n)
{
int i;
if(T == NULL)
return ;
else
{
printTree(T->lch,n+1);
for(i=0;i<n;i++)
printf("	");
printf("%d\n",T->data);

printTree(T->rch,n+1);
}
}

下面我用递归处理二叉树的前序、中序和后序遍历。

void visit(bt t,char *order)
{
if(t)
{
if(strcmp(order,"NLR")==0)  printf("%4d",t->data);
visit(t->lch,order);
if(strcmp(order,"LNR")==0)  printf("%4d",t->data);
visit(t->rch,order);
if(strcmp(order,"LRN")==0)  printf("%4d",t->data);
}
}