/*
*Copyright(c) 2015,煙臺大學計算機學院
*All rights reserved.
*文件名稱:test.cpp
*作者:林莉
*完成日期:2015年9月11日
*版本:v1.0
*
*問題描述:假設二叉樹採用二叉鏈存儲結構存儲,分別實現以下算法,並在程序中完成測試。
*輸入描述:無
*程序輸出:所得結果。
*/
1.頭文件:btree.h定義數據結構並聲明用於完成基本運算的函數。
#ifndef BTREE_H_INCLUDED
#define BTREE_H_INCLUDED
#define MaxSize 100
typedef char ElemType;
typedef struct node
{
ElemType data; //數據元素
struct node *lchild; //指向左孩子
struct node *rchild; //指向右孩子
} BTNode;
void CreateBTNode(BTNode *&b,char *str); //由str串創建二叉鏈
BTNode *FindNode(BTNode *b,ElemType x); //返回data域爲x的節點指針
BTNode *LchildNode(BTNode *p); //返回*p節點的左孩子節點指針
BTNode *RchildNode(BTNode *p); //返回*p節點的右孩子節點指針
int BTNodeDepth(BTNode *b); //求二叉樹b的深度
void DispBTNode(BTNode *b); //以括號表示法輸出二叉樹
void DestroyBTNode(BTNode *&b); //銷燬二叉樹
#endif // BTREE_H_INCLUDED
2.源文件:btree.cpp實現各個函數
#include <stdio.h>
#include <malloc.h>
#include "btree.h"
void CreateBTNode(BTNode *&b,char *str) //由str串創建二叉鏈
{
BTNode *St[MaxSize],*p=NULL;
int top=-1,k,j=0;
char ch;
b=NULL; //建立的二叉樹初始時爲空
ch=str[j];
while (ch!='\0') //str未掃描完時循環
{
switch(ch)
{
case '(':
top++;
St[top]=p;
k=1;
break; //爲左節點
case ')':
top--;
break;
case ',':
k=2;
break; //爲右節點
default:
p=(BTNode *)malloc(sizeof(BTNode));
p->data=ch;
p->lchild=p->rchild=NULL;
if (b==NULL) //p指向二叉樹的根節點
b=p;
else //已建立二叉樹根節點
{
switch(k)
{
case 1:
St[top]->lchild=p;
break;
case 2:
St[top]->rchild=p;
break;
}
}
}
j++;
ch=str[j];
}
}
BTNode *FindNode(BTNode *b,ElemType x) //返回data域爲x的節點指針
{
BTNode *p;
if (b==NULL)
return NULL;
else if (b->data==x)
return b;
else
{
p=FindNode(b->lchild,x);
if (p!=NULL)
return p;
else
return FindNode(b->rchild,x);
}
}
BTNode *LchildNode(BTNode *p) //返回*p節點的左孩子節點指針
{
return p->lchild;
}
BTNode *RchildNode(BTNode *p) //返回*p節點的右孩子節點指針
{
return p->rchild;
}
int BTNodeDepth(BTNode *b) //求二叉樹b的深度
{
int lchilddep,rchilddep;
if (b==NULL)
return(0); //空樹的高度爲0
else
{
lchilddep=BTNodeDepth(b->lchild); //求左子樹的高度爲lchilddep
rchilddep=BTNodeDepth(b->rchild); //求右子樹的高度爲rchilddep
return (lchilddep>rchilddep)? (lchilddep+1):(rchilddep+1);
}
}
void DispBTNode(BTNode *b) //以括號表示法輸出二叉樹
{
if (b!=NULL)
{
printf("%c",b->data);
if (b->lchild!=NULL || b->rchild!=NULL)
{
printf("(");
DispBTNode(b->lchild);
if (b->rchild!=NULL) printf(",");
DispBTNode(b->rchild);
printf(")");
}
}
}
void DestroyBTNode(BTNode *&b) //銷燬二叉樹
{
if (b!=NULL)
{
DestroyBTNode(b->lchild);
DestroyBTNode(b->rchild);
free(b);
}
}
3.測試函數:main.cpp,完成相關測試工作。
(1)計算二叉樹節點個數;
<code class="hljs perl has-numbering"><span class="hljs-comment">#include <stdio.h></span> <span class="hljs-comment">#include "btree.h"</span> <span class="hljs-keyword">int</span> Nodes(BTNode <span class="hljs-variable">*b</span>) { <span class="hljs-keyword">if</span> (b==NULL) <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; <span class="hljs-keyword">else</span> <span class="hljs-keyword">return</span> Nodes(b->lchild)+Nodes(b->rchild)+<span class="hljs-number">1</span>; } <span class="hljs-keyword">int</span> main() { BTNode <span class="hljs-variable">*b</span>; CreateBTNode(b,<span class="hljs-string">"A(B(D,E(H(J,K(L,M(,N))))),C(F,G(,I)))"</span>); <span class="hljs-keyword">printf</span>(<span class="hljs-string">"二叉樹節點個數: <span class="hljs-variable">%d</span>\n"</span>, Nodes(b)); DestroyBTNode(b); <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; }</code>
運行結果:
(2)輸出所有葉子節點;
<code class="hljs lasso has-numbering"><span class="hljs-variable">#include</span> <span class="hljs-subst"><</span>stdio<span class="hljs-built_in">.</span>h<span class="hljs-subst">></span> <span class="hljs-variable">#include</span> <span class="hljs-string">"btree.h"</span> <span class="hljs-literal">void</span> DispLeaf(BTNode <span class="hljs-subst">*</span>b) { <span class="hljs-keyword">if</span> (b<span class="hljs-subst">!=</span><span class="hljs-built_in">NULL</span>) { <span class="hljs-keyword">if</span> (b<span class="hljs-subst">-></span>lchild<span class="hljs-subst">==</span><span class="hljs-built_in">NULL</span> <span class="hljs-subst">&&</span> b<span class="hljs-subst">-></span>rchild<span class="hljs-subst">==</span><span class="hljs-built_in">NULL</span>) printf(<span class="hljs-string">"%c "</span>,b<span class="hljs-subst">-></span><span class="hljs-built_in">data</span>); <span class="hljs-keyword">else</span> { DispLeaf(b<span class="hljs-subst">-></span>lchild); DispLeaf(b<span class="hljs-subst">-></span>rchild); } } } int main() { BTNode <span class="hljs-subst">*</span>b; CreateBTNode(b,<span class="hljs-string">"A(B(D,E(H(J,K(L,M(,N))))),C(F,G(,I)))"</span>); printf(<span class="hljs-string">"二叉樹中所有的葉子節點是: "</span>); DispLeaf(b); printf(<span class="hljs-string">"\n"</span>); DestroyBTNode(b); <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; } </code>
運行結果:
(3)求二叉樹b的葉子節點個數
<code class="hljs lasso has-numbering"><span class="hljs-variable">#include</span> <span class="hljs-subst"><</span>stdio<span class="hljs-built_in">.</span>h<span class="hljs-subst">></span> <span class="hljs-variable">#include</span> <span class="hljs-string">"btree.h"</span> int LeafNodes(BTNode <span class="hljs-subst">*</span>b) <span class="hljs-comment">//求二叉樹b的葉子節點個數</span> { int num1,num2; <span class="hljs-keyword">if</span> (b<span class="hljs-subst">==</span><span class="hljs-built_in">NULL</span>) <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (b<span class="hljs-subst">-></span>lchild<span class="hljs-subst">==</span><span class="hljs-built_in">NULL</span> <span class="hljs-subst">&&</span> b<span class="hljs-subst">-></span>rchild<span class="hljs-subst">==</span><span class="hljs-built_in">NULL</span>) <span class="hljs-keyword">return</span> <span class="hljs-number">1</span>; <span class="hljs-keyword">else</span> { num1<span class="hljs-subst">=</span>LeafNodes(b<span class="hljs-subst">-></span>lchild); num2<span class="hljs-subst">=</span>LeafNodes(b<span class="hljs-subst">-></span>rchild); <span class="hljs-keyword">return</span> (num1<span class="hljs-subst">+</span>num2); } } int main() { BTNode <span class="hljs-subst">*</span>b; CreateBTNode(b,<span class="hljs-string">"A(B(D,E(H(J,K(L,M(,N))))),C(F,G(,I)))"</span>); printf(<span class="hljs-string">"二叉樹b的葉子節點個數: %d\n"</span>,LeafNodes(b)); DestroyBTNode(b); <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; }</code>
運行結果:
(4)設計一個算法Level(b,x,h),返回二叉鏈b中data值爲x的節點的層數。
<code class="hljs perl has-numbering"><span class="hljs-comment">#include <stdio.h></span> <span class="hljs-comment">#include "btree.h"</span> <span class="hljs-keyword">int</span> Level(BTNode <span class="hljs-variable">*b</span>,ElemType <span class="hljs-keyword">x</span>,<span class="hljs-keyword">int</span> h) { <span class="hljs-keyword">int</span> l; <span class="hljs-keyword">if</span> (b==NULL) <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (b->data==<span class="hljs-keyword">x</span>) <span class="hljs-keyword">return</span> h; <span class="hljs-keyword">else</span> { l=Level(b->lchild,<span class="hljs-keyword">x</span>,h+<span class="hljs-number">1</span>); <span class="hljs-keyword">if</span> (l==<span class="hljs-number">0</span>) <span class="hljs-keyword">return</span> Level(b->rchild,<span class="hljs-keyword">x</span>,h+<span class="hljs-number">1</span>); <span class="hljs-keyword">else</span> <span class="hljs-keyword">return</span> l; } } <span class="hljs-keyword">int</span> main() { BTNode <span class="hljs-variable">*b</span>; CreateBTNode(b,<span class="hljs-string">"A(B(D,E(H(J,K(L,M(,N))))),C(F,G(,I)))"</span>); <span class="hljs-keyword">printf</span>(<span class="hljs-string">"值爲\'K\'的節點在二叉樹中出現在第 <span class="hljs-variable">%d</span> 層上n"</span>,Level(b,<span class="hljs-string">'K'</span>,<span class="hljs-number">1</span>)); DestroyBTNode(b); <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; } </code>
運行結果:
(5)判斷二叉樹是否相似(關於二叉樹t1和t2相似的判斷:①t1和t2都是空的二叉樹,相似;②t1和t2之一爲空,另一不爲空,則不相似;③t1的左子樹和t2的左子樹是相似的,且t1的右子樹與t2的右子樹是相似的,則t1和t2相似。)
<code class="hljs perl has-numbering"><span class="hljs-comment">#include <stdio.h></span> <span class="hljs-comment">#include "btree.h"</span> <span class="hljs-keyword">int</span> Like(BTNode <span class="hljs-variable">*b1</span>,BTNode <span class="hljs-variable">*b2</span>) { <span class="hljs-keyword">int</span> like1,like2; <span class="hljs-keyword">if</span> (b1==NULL && b2==NULL) <span class="hljs-keyword">return</span> <span class="hljs-number">1</span>; <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (b1==NULL || b2==NULL) <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; <span class="hljs-keyword">else</span> { like1=Like(b1->lchild,b2->lchild); like2=Like(b1->rchild,b2->rchild); <span class="hljs-keyword">return</span> (like1 & like2); } } <span class="hljs-keyword">int</span> main() { BTNode <span class="hljs-variable">*b1</span>, <span class="hljs-variable">*b2</span>, <span class="hljs-variable">*b3</span>; CreateBTNode(b1,<span class="hljs-string">"B(D,E(H(J,K(L,M(,N)))))"</span>); CreateBTNode(b2,<span class="hljs-string">"A(B(D(,G)),C(E,F))"</span>); CreateBTNode(b3,<span class="hljs-string">"u(v(w(,x)),y(z,p))"</span>); <span class="hljs-keyword">if</span>(Like(b1, b2)) <span class="hljs-keyword">printf</span>(<span class="hljs-string">"b1和b2相似\n"</span>); <span class="hljs-keyword">else</span> <span class="hljs-keyword">printf</span>(<span class="hljs-string">"b1和b2不相似\n"</span>); <span class="hljs-keyword">if</span>(Like(b2, b3)) <span class="hljs-keyword">printf</span>(<span class="hljs-string">"b2和b3相似\n"</span>); <span class="hljs-keyword">else</span> <span class="hljs-keyword">printf</span>(<span class="hljs-string">"b2和b3不相似\n"</span>); DestroyBTNode(b1); DestroyBTNode(b2); DestroyBTNode(b3); <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; }</code>
運行結果: