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遍历算法应用

遍历算法应用. 按先序序列建立二叉树的算法. Status CreateBiTree(BiTree &T){ // 按先序次序输入二叉树中的结点值 ( 一个字符 ) ， // 空格表示空树， // 构造二叉链表表示的二叉树 T scanf(&ch); if (ch ==‘ ’) T = NULL; else { if (!(T = (BiTNode *)malloc(sizeof(BiTNode)))) exit(OVERFLOW); T->data = ch;

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遍历算法应用

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  1. 遍历算法应用 • 按先序序列建立二叉树的算法 Status CreateBiTree(BiTree &T){ //按先序次序输入二叉树中的结点值(一个字符)， //空格表示空树， //构造二叉链表表示的二叉树T scanf(&ch); if (ch ==‘ ’) T = NULL; else { if (!(T = (BiTNode *)malloc(sizeof(BiTNode)))) exit(OVERFLOW); T->data = ch; CreateBiTree(T->lchild); CreateBiTree(T->rchild);} return OK; }

  2. F E D C B A G 按先序序列建立二叉树的算法 输入A B C _ _ D E _ G _ _ F _ _ _ 生成的二叉树及其存储结构为 T A B C D E F G

  3. 按先序序列建立二叉树的算法 • 若希望建立如下二叉树对应的存储结构，应输入的字符序列是 - + / a * e f b - 输入： - + a _ _ * b _ _ - c _ _ d _ _ / e _ _ f _ _ c d

  4. A B C D E F G 统计二叉树中叶子结点个数算法 #include <alloc.h> #include <stdio.h> typedef struct node { char data; struct node *lchild,*rchild; }JD; void countleaf(JD *bt,int *count) { if(bt!=NULL) { if((bt->lchild==NULL)&&(bt->rchild==NULL)) { (*count)++; return; } countleaf(bt->lchild,count); countleaf(bt->rchild,count); } }

  5. void main() { /* ABC00DE0G00F000 */ JD *head=NULL; int count=0; head=crt_bt_pre(head); countleaf(head,&count); printf("count of leaf node is %d\n",count);} JD *crt_bt_pre(JD *bt) { char ch; printf("ch="); scanf("%c",&ch); if(ch==' ') bt=NULL; else { bt=(JD *)malloc(sizeof(JD)); bt->data=ch; bt->lchild=crt_bt_pre(bt->lchild); bt->rchild=crt_bt_pre(bt->rchild);} return(bt); }

  6. 求二叉树深度算法 void treedepth(JD *bt,int *l,int *h) { int l1=0,l2=0,h1=0,h2=0; if(bt!=NULL) { (*l)++; if (*l>*h) *h=*l; treedepth(bt->lchild,&l1,&h1); treedepth(bt->rchild,&l2,&h2); if (h1>h2) *h=*h+h1; else *h=*h+h2; } } # include <alloc.h> #include <stdio.h> typedef struct node { char data; struct node *lchild,*rchild; }JD;

  7. JD *crt_bt_pre(JD *bt) { char ch; printf("ch="); scanf("%c",&ch); getchar(); if(ch==' ') bt=NULL; else { bt=(JD *)malloc(sizeof(JD)); bt->data=ch; bt->lchild=crt_bt_pre(bt->lchild); bt->rchild=crt_bt_pre(bt->rchild); } return(bt); } void main() { /* ABC00DE0G00F000 */ JD *head=NULL; int level=0,high=0; head=crt_bt_pre(head); treedepth(head,&level,&high); printf("depth of tree is %d\n",high); }

  8. 几个问答 • 具有n个结点的不同形态的二叉树有多少棵？ • 有 棵，如n=3时，有5种不同形态 • 已知结点先序序列和中序序列，是否可以唯一地确定一棵二叉树？ • 能，如先序序列ABCDEFG，中序序列CBEDAFG，对应的二叉树为 A A A B F B F BCDE C D FG G C DE G E Step1 Step2 Step3

  9. 几个问答 • 已知结点先序序列和后序序列，是否可以唯一地确定一棵二叉树？ • 不能， 如先序序列ABCK，后序序列BKCA • 已知结点中序序列和后序序列，是否可以唯一地确定一棵二叉树？ • 能，如中序序列BKCA，后序序列BKCA A A 或 BKC BKC A A C A C K BKC BK B Step1 Step2 Step3

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