数据结构C语言版之二叉树操作

/*（1）采用下列方法之一建立二叉树的二叉链表：① 输入完全二叉树的先序序列，用#代表虚结点（空指针），如ABD###CE##F##，建立二叉树的二叉链表。② 已知二叉树的先序遍历序列和中序遍历序列，或者已知二叉树的中序遍历序列和后序遍历序列，建立二叉树的二叉链表。③ 将一棵二叉树的所有结点存储在一维数组中，虚结点用#表示，利用二叉树的性质5，建立二叉树的二叉链表。例如用数组a存储的二叉树的结点如下（0单元不用）： （2）写出对用二叉链表存储的二叉树进行先序、中序和后序遍历的递归和非递归算法。（3）写出对用二叉链表存储的二叉树进行层次遍历算法。（4）求二叉树的所有叶子及结点总数。*/#include<stdio.h>#include<stdlib.h>#define Stack_size 100#define Stackincreament 10#define MAXQ_size 100typedef struct Binode{char data;struct Binode *lchild,*rchild;}Binode,*Bitree;typedef struct{Bitree *base;int top;int stacksize;}sqstack;typedef struct{Bitree *base;int front;int rear;}sqQueue;int Qfull(sqQueue &Q){if((Q.rear+1)%MAXQ_size==Q.front)return 1;return 0;}void enQueue(sqQueue &Q,Bitree e){if(Qfull(Q))exit(0);Q.base[Q.rear]=e;Q.rear=(Q.rear+1)%MAXQ_size;}void initQueue(sqQueue &Q){Q.base=(Bitree*)malloc(MAXQ_size*sizeof(Binode));Q.front=Q.rear=0;}int Qempty(sqQueue &Q){if(Q.rear==Q.front)return 1;return 0;}void outQueue(sqQueue &Q,Bitree &e){if(Qempty(Q))exit(0);e=Q.base[Q.front];Q.front=(Q.front+1)%MAXQ_size;}void initstack(sqstack &s){s.base=(Bitree*)malloc(Stack_size*sizeof(Bitree));s.stacksize=Stack_size;if(!s.base)exit(0);s.top=0;}void push(sqstack &s,Bitree e){if(s.top>=s.stacksize){s.base=(Bitree*)realloc(s.base,(Stack_size+Stackincreament)*sizeof(Bitree));if(!s.base)   exit(0);s.stacksize+=Stackincreament;}s.base[s.top++]=e;}void pop(sqstack &s,Bitree &e){if(s.top==0)return ;e=s.base[--s.top];}void creatBiTree(Bitree &bt){char ch;ch=getchar();if(ch=='#')bt=NULL;else{bt=(Bitree)malloc(sizeof(Binode));bt->data=ch;creatBiTree(bt->lchild);creatBiTree(bt->rchild);}}int stackempty(sqstack &s){if(s.top==0)return 1;return 0;}Bitree Gettop(sqstack &s,Bitree &e){if(stackempty(s))exit(0);e=s.base[s.top-1];return e;}void preorderTraverse1(Bitree &bt){Bitree p;if(bt){sqstack s;initstack(s);push(s,bt);while(!stackempty(s)){while(Gettop(s,p)&&p){printf("%c",p->data);push(s,p->lchild);}pop(s,p);if(!stackempty(s)){pop(s,p);push(s,p->rchild);}}}printf("\n");}void preorderTraverse2(Bitree bt){if(bt){printf("%c",bt->data);preorderTraverse2(bt->lchild);preorderTraverse2(bt->rchild);}}/*void inorderTraverse1(Bitree &bt){if(bt){preorderTraverse1(bt->lchild);preorderTraverse1(bt->rchild);}printf("%c",bt->data);}*/void inorderTraverse2(Bitree &bt){Bitree p;sqstack s;if(bt){initstack(s);push(s,bt);while(!stackempty(s)){while(Gettop(s,p)&&p)push(s,p->lchild);pop(s,p);    if(!stackempty(s)){pop(s,p);printf("%c",p->data);push(s,p->rchild);}}}printf("\n");}void leafnum(Bitree bt,int &leaf){//用栈实现sqstack s;Bitree p;leaf=0;if(!bt)leaf=0;else{initstack(s);push(s,bt);while(!stackempty(s)){while(Gettop(s,p)&&p)push(s,p->lchild);pop(s,p);Gettop(s,p);push(s,p->rchild);if(!Gettop(s,p)){pop(s,p);leaf++;pop(s,p);printf("第%d个叶子结点为:%c\n",leaf,p->data);}if(!stackempty(s)){Gettop(s,p);pop(s,p);push(s,p->rchild);}}}printf("该树的叶子数为:%d\n,总结点数为:%d\n",leaf,2*leaf-1);}void leveltraverse(Bitree bt){sqQueue Q;Bitree p;if(bt){initQueue(Q);enQueue(Q,bt);while(!Qempty(Q)){outQueue(Q,p);printf("%c",p->data);if(p->lchild)enQueue(Q,p->lchild);if(p->rchild)enQueue(Q,p->rchild);}}printf("\n");}void Depth(Bitree bt,int &depth){//树高Bitree p;sqQueue Q;int hp,tp,lc;initQueue(Q);if(bt){hp=tp=depth=0;Q.base[tp++]=bt;lc=tp;while(hp<tp){p=Q.base[hp++];if(p->lchild)Q.base[tp++]=p->lchild;if(p->rchild)Q.base[tp++]=p->rchild;if(lc==hp){depth++;lc=tp;}}}printf("该树的高度为:%d\n",depth);}int judge(Bitree bt){//判断是否为完全二叉树int flag=0;Bitree p;sqQueue Q;if(!bt)return 1;initQueue(Q);enQueue(Q,bt);while(!Qempty(Q)){outQueue(Q,p);if(p->lchild&&!flag)enQueue(Q,p->lchild);else if(p->lchild)return 0;else flag=1;if(p->rchild&&!flag)enQueue(Q,p->rchild);else if(p->rchild)return 0;else flag=1;}return 1;}void storage(Bitree bt){//将二叉树结点存入一维数组char a[100];int i=1,k=1;int Q1[100],front=0,rear=0;Bitree p;sqQueue Q;for(i=1;i<=100;i++)a[i]='#';if(!bt)return;else{initQueue(Q);enQueue(Q,bt);Q1[rear++]=k;while(!Qempty(Q)){outQueue(Q,p);k=Q1[front++];a[k]=p->data;if(p->lchild){enQueue(Q,p->lchild); Q1[rear++]=2*k;}if(p->rchild){enQueue(Q,p->rchild); Q1[rear++]=2*k+1;}}}for(int j=1;j<=front;j++)printf("%5c",a[j]);printf("\n");}int main(){int leaf,depth;Bitree bt;creatBiTree(bt);    preorderTraverse1(bt);preorderTraverse2(bt);printf("\n");inorderTraverse2(bt);leveltraverse(bt);leafnum(bt,leaf);Depth(bt,depth);if(judge(bt))printf("该树为完全二叉树.\n");else    printf("该树不是完全二叉树.\n");storage(bt);return 0;}