二叉树作为数据结构其实是一个挺有意思的结构,可以有多种应用
我们直接来看一下二叉树的代码:
#include<stdlib.h> #include<stdio.h> #include<malloc.h> #include<string.h> #
define maxsize 100 //二叉树的基本操作:建立,前序,中序,后序,层次,求叶子数,求层数,求结点树 //二叉树的数据结构
//创建数据域和左右指针域 typedef struct Tree { char data; struct tree* lchild; struct tree*
rchild; }tree; //建立二叉数初始化 void inittree(tree* root) { root->data = ""; root->
rchild= NULL; root->lchild = NULL; } //二叉数的创建 tree* create(tree* root) { char
value; scanf_s("%c", &value); if (value == '#') { root = NULL; } else { root = (
tree*)malloc(sizeof(tree)); root->data = value; root->lchild = create(root->
lchild); root->rchild = create(root->rchild); } return root; }
//创建二叉树的结点(二级指针写法) void createnode(tree** node) { char p_data; scanf_s("%c", &
p_data); if (p_data == '#') { *node = NULL; } else { *node = (tree*)malloc(
sizeof(tree)); (*node)->data = p_data; createnode(&((*node)->lchild));
createnode(&((*node)->rchild)); } } //判断二叉树是否为空 int tempty(tree* root) { if (
root->data == "") { printf("二叉树为空\n"); return 0; } else { printf("二叉树不为空\n");
return 1; } } //先序遍历(递归) void porder(tree* root) { if (root != NULL) { printf(
"%c\t", root->data); porder(root->lchild); porder(root->rchild); } } //中序遍历(递归)
void morder(tree* root) { if (root != NULL) { morder(root->lchild); printf(
"%c\t", root->data); morder(root->rchild); } } //后序遍历(递归) void torder(tree* root
) { if (root != NULL) { torder(root->lchild); torder(root->rchild); printf(
"%c\t", root->data); } } //先序遍历非递归 //访问左子树的结点存入栈中(继续深入)直到无法访问再让其出栈回退访问右子树 void
p_order(tree* root) { if (root == NULL) { return; } tree* box[10];
//创建栈存储每次打印结点的位置 int box_top = -1;//栈顶的标记,为和数组下标保持一致 tree* move = root;
//从根节点开始打印 while (box_top != -1 || move) { while (move) { //把路径入栈并且打印结点 printf(
"%c\t", move->data); box[++box_top] = move;//把结点存入数组中 move = move->lchild;
//移动到存入结点的左子树 } if (box_top != -1)//判断如果访问完左子树 { move = box[box_top];//获取栈顶元素
box_top--;//回溯 move = move->rchild;//移动访问右子树 } } } //中序遍历非递归
//持续深入左子树并且存储结点直到无法深入然后回溯并且打印,出栈再访问右子树 void m_order(tree* root) { tree* box[10];
//创建栈,用于存放结点的位置 int box_top = -1;//定义栈顶的标记 tree* move = root;//定义移动的指针 while (
box_top!= -1 || move) { //深入访问左子树 while (move) { box[++box_top] = move; move =
move->lchild; } if (box_top != -1) { move = box[box_top--];//获取栈顶元素且回溯 printf(
"%c\t", move->data); move = move->rchild;//移动到右子树 } } } //后序遍历非递归
//先访问左子树一直深入直到无法访问,打印结点然后回溯,再访问右子树,在打印回溯,会出现两个树根 //定义访问标记如果访问过就不再打印来解决回溯后多次打印的问题
void t_order(tree* root) { if (root == NULL) { return; } tree* box[10]; int
box_top= -1; tree* move = root; tree* visit = NULL;//访问标记 while (move) { box[++
box_top] = move; move = move->lchild; } while (box_top != -1) { move = box[
box_top--]; if (move->rchild == NULL || move->rchild == visit)//判断当前结点的右子树是否被访问
{ printf("%c\t", move->data); visit = move;//改变标记的位置就是回溯到上一层的树根 } else { box[++
box_top] = move; move = move->rchild; while (move) { box[++box_top] = move; move
= move->lchild; } } } } //二叉树求叶子数 int leaves(tree* root) { if (root == NULL) {
return 0; } else if (root->lchild == NULL && root->rchild == NULL) { return 1; }
else { return leaves(root->lchild) + leaves(root->rchild); } } //求树深度的递归算法 int
deep(tree* root) { int lnum, rnum; if (root == NULL) { return 0; } else { lnum =
deep(root->lchild); rnum = deep(root->rchild); return (lnum > rnum ? lnum : rnum
) + 1; } } //求二叉树中以某值为根的子树深度(递归) void x_deep(tree* root , char x) { int lnum = 0
, rnum = 0; if (root == NULL) { printf("空树深度为0\n"); } if (root->data == x) {
printf("%d\n", deep(root)); } else { if (root->lchild) { x_deep(root->lchild, x)
; } if (root->rchild) { x_deep(root->rchild, x); } } } //二叉树求指定结点的层数 int floor(
tree* root, char x) { int lnum, rnum, fnum; if (root == NULL) { fnum = 0; } else
if (root->data == x) { fnum = 1; } else { lnum = floor(root->lchild, x); rnum =
floor(root->rchild, x); if (lnum == 0 && rnum == 0)//查找失败 {
/*printf("查找结束\n");*/ fnum = 0; } else { fnum = ((lnum > rnum) ? lnum : rnum) +
1; } } return fnum; } //统计数中结点个数 int nodenum(tree* root) { if (root == NULL) {
return 0; } else { return(nodenum(root->lchild) + nodenum(root->rchild)) + 1; }
} //层序遍历BFS //准备工作:构造队列 typedef struct queue { tree* qdata[maxsize]; int front;
int rear; }q; //对队列进行初始化 void initqueue(q* node) { node->front = node->rear = 0;
} //判断队列是否为空 void empty(q* node) { if (node->front == node->rear) { printf(
"队列为空"); } } //入队 void push(q* node, tree* root) { node->qdata[node->rear] =
root; node->rear++; } //出队 tree* pop(q* node, tree* root) { return node->qdata[(
++node->front) - 1]; } //二叉树层次遍历BFS void BFS(tree* root) { q* node; node = (q*)
malloc(sizeof(q)); initqueue(node); if (root != NULL) { push(node, root); }
while (node->front != node->rear) { tree* root1 = (tree*)malloc(sizeof(tree));
root1= pop(node, root1); printf("%c\t", root1->data); if (root1->lchild != NULL)
{ push(node, root1->lchild); } if (root1->rchild != NULL) { push(node, root1->
rchild); } } } int main() { //测试:12#46###3#5##,ABC##DE#G##F### tree* root = (
tree*)malloc(sizeof(tree)); inittree(root); printf("请按先序遍历的次序输入二叉树:\n"); root =
create(root); int temp; while (1) { printf(
"*****************************二叉树综合实验****************************\n"); printf(
"*****************************1.二叉树先序遍历**************************\n"); printf(
"*****************************2.二叉树中序遍历**************************\n"); printf(
"*****************************3.二叉树后序遍历**************************\n"); printf(
"*****************************4.二叉树先序遍历(非递归)****************\n"); printf(
"*****************************5.二叉树先序遍历(非递归)****************\n"); printf(
"*****************************6.二叉树先序遍历(非递归)****************\n"); printf(
"*****************************7.二叉树层次遍历(BFS)*******************\n"); printf(
"*****************************8.求二叉树深度(递归)********************\n"); printf(
"*****************************9.二叉树求叶子数**************************\n"); printf(
"*****************************10.二叉树求结点数*************************\n"); printf(
"*****************************11.二叉树求指定结点所在的层数*************\n"); printf(
"*****************************12.判断二叉树是否为空树*******************\n"); printf(
"*****************************13.求二叉树中以某值为根的子树深度(递归)*\n"); printf(
"*****************************14.退出exit*******************************\n");
printf(
"***********************************************************************\n");
printf("输入你的选项:"); scanf_s("%d", &temp); if (temp == 14) { printf("程序退出》》》");
break; } switch (temp) { case 1: printf("二叉树前序遍历(递归)为:\n"); porder(root); printf
("\n"); break; case 2: printf("二叉树中序遍历(递归)为:\n"); morder(root); printf("\n");
break; case 3: printf("二叉树后序遍历(递归)为:\n"); torder(root); printf("\n"); break;
case 4: printf("二叉树前序遍历为:\n"); p_order(root); printf("\n"); break; case 5:
printf("二叉树中序遍历为:\n"); m_order(root); printf("\n"); break; case 6: printf(
"二叉树后序遍历为:\n"); t_order(root); printf("\n"); break; case 7: printf(
"BFS层序遍历二叉树:\n"); BFS(root); printf("\n"); break; case 8: printf("二叉树的深度为%d层\n",
deep(root)); break; case 9: printf("二叉树中含有%d个叶子结点\n", leaves(root)); break; case
10: printf("二叉树共有%d个结点\n", nodenum(root)); break; case 11: { char x; printf(
"请输入你要查找的结点:"); scanf_s(" %c", &x);//注意:一定要在%c前加个blank,让缓冲区置空! printf(
"当前结点所在的层数为:%d\n", floor(root, x)); } break; case 12: tempty(root); printf("\n")
; break; case 13: { char x2; printf("请输入你要查找的结点:"); scanf_s(" %c", &x2); printf(
"以%c为子树的深度为:",x2); x_deep(root, x2); printf("\n"); } break; default: printf(
"error"); break; } } return 0; }
程序执行结果:

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