4.10. Binar daraxt balandligi
Binar daraxtning balandligi deb daraxt bosqichlari soniga aytiladi. Binar
daraxt balandligini aniqlash uchun uning har bir tuguni chap va o‟ng
qismdaraxtlari balandliklari solishtiriladi va maksimal qiymat balandlik deb
olinadi. Misol uchun quyidagi 4.9-rasmdagi daraxtning balandligi 2 ga teng.
4.9-rasm. Binar daraxt balandligi
Daraxt balandligini aniqlash dastur kodini keltiramiz.
int height(node *tree){
int h1,h2;
if (tree==NULL) return (-1);
else {
h1 = height(tree->left);
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h2 = height(tree->right);
if (h1>h2) return (1 + h1);
else return (1 + h2);
}
}
4.11. Binar daraxtni muvozanatlanganmi yoki yo‟qligini tekshirish
Daraxtning balandligini aniqlashni o‟rganganimizdan keyin uning muvoza-
natlanganligini tekshirish mumkin. Binar daraxtning muvozanatlanganligini
tekshirish uchun uning har bir tugunini har ikkala qismdaraxti balandliklarini
hisoblab, farqlarini tekshirib ko‟rish kerak. Agar farq 0 yoki 1 ga teng bo‟lsa, bu
muvozanatlangan daraxt hisoblanadi. Quyida binar daraxtni muvozanatlanganlikka
tekshirishning rekursiv funksiyasini qo‟llovchi dastur keltirilgan.
Dastur kodi
#include
#include
using namespace std;
class node{
public: int info;
node *left;
node *right;
};
int k=0,Flag=1;
int height(node *tree){
int h1,h2;
if (tree==NULL) return (-1);
else {
h1 = height(tree->left);
h2 = height(tree->right);
if (h1>h2) return (1 + h1);
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else return (1 + h2);
}
}
void vizual(node *tree,int l)
{ int i;
if(tree!=NULL) {
vizual(tree->right,l+1);
for (i=1; i<=l; i++) cout<<" ";
cout<info<
vizual(tree->left,l+1);
}
}
int AVLtree (node *tree){
int t;
if (tree!=NULL){
t = height (tree->left) - height (tree->right);
if ((t<-1) || (t>1)) { Flag = 0; return Flag; }
AVLtree (tree->left); AVLtree (tree->right);
}
}
int GetFlag(){return Flag;}
int main()
{ int n,key,s; node *tree=NULL,*next=NULL;
cout<<"n="; cin>>n; int arr[n];
for(int i=0; i
node *p=new node;
node *last=new node;
cin>>s;
p->info=s;
p->left=NULL;
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p->right=NULL;
if(i==0){tree=p; next=tree; continue; }
next=tree;
while(1)
{ last=next;
if(p->infoinfo)next=next->left;
else next=next->right;
if(next==NULL)break; }
if(p->infoinfo)last->left=p;
else last->right=p;}
cout<
cout<<"\nbinar daraxt:\n";
vizual(tree,0);
AVLtree(tree);
if(GetFlag()) cout<<"ha, muvozanatlangan daraxt"; else cout<<"yo’q,
muvozanatlanmagan daraxt";cout<
getch();
}
Dastur natijasi
4.12. Binar daraxtni vizuallashtirish
Binar
daraxtni
ko‟rikdan o‟tkazayotganda biz yuqorida har bir
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tugunni o‟ngida va chapida turgan tugunlarni so‟z bilan ifodaladik. Lekin bu usul
bir muncha noqulay. Daraxtni vizual ko‟rinishda ifodalash uni anglashning juda
qulay usuli hisoblanadi. Daraxtni vizuallashtirishning grafik ko‟rinishi va konsol
oynasida ifodalash kabi turlari mavjud. Shundan konsol oynasida daraxtni
vizuallashtirishni ko‟rib chiqamiz. Bunda sonlar daraxt shaklida joylashtiriladi.
Quyida bunday usulning dastur kodi keltirilgan.
void vizual(node *tree,int l)
{ int i;
if(tree!=NULL) {
vizual(tree->right,l+1);
for (i=1; i<=l; i++) cout<<" ";
cout<info<
vizual(tree->left,l+1);
}
}
Dastur kodi quyidagi 4.10 a-rasmdagi daraxtni konsol ekranida 4.10 b-rasm
ko‟rinishda ifodalaydi.
a. b.
4.10-rasm. a - binar daraxt; b - binar daraxtning ekranda namoyon bo‟lishi
Yuqorida keltirilgan bir nechta algoritmlarni qo‟llab bitta misol ko‟rib
chiqamiz.
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Misol: berilgan binar daraxtning balandligini aniqlang va muvozanatlang.
Dastur kodi
#include
#include
using namespace std;
class node{
public: int info;
node *left;
node *right;
};
int k=0;
int intrave(node *tree){
if (tree!=NULL){int a=NULL, b=NULL;
if (tree->left!=NULL){ a=tree->left->info; }
if (tree->right!=NULL){ b=tree->right->info; }
cout<info<<"--chapida=>"<"<
intrave(tree->left);
intrave(tree->right); }
return 0;
}
int height(node *tree){
int h1,h2;
if (tree==NULL) return (-1);
else {
h1 = height(tree->left);
h2 = height(tree->right);
if (h1>h2) return (1 + h1);
else return (1 + h2);
}
}
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int create_arr(node *tree,int *arr){
if(!tree) return 0;
else{
create_arr(tree->left,arr);
arr[k++]=tree->info;
create_arr(tree->right,arr);
}
}
node *new_tree(int *arr, int start, int end)
{
if(start>end) return NULL;
else {
int mid=(start+end)/2;
node *tree=new node;
tree->info=arr[mid];
tree->left=new_tree(arr,start,mid-1);
tree->right=new_tree(arr,mid+1,end);
return tree;
}
}
void vizual(node *tree,int l)
{ int i;
if(tree!=NULL) {
vizual(tree->right,l+1);
for (i=1; i<=l; i++) cout<<" ";
cout<info<
vizual(tree->left,l+1);
}
}
int main()
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{ int n,key,s; node *tree=NULL,*next=NULL;
cout<<"n="; cin>>n; int arr[n];
for(int i=0; i
node *p=new node;
node *last=new node;
cin>>s;
p->info=s;
p->left=NULL;
p->right=NULL;
if(i==0){tree=p; next=tree; continue; }
next=tree;
while(1)
{ last=next;
if(p->infoinfo)next=next->left;
else next=next->right;
if(next==NULL)break; }
if(p->infoinfo)last->left=p;
else last->right=p;}
cout<
intrave(tree);
cout<<"\nya'ni\n";
vizual(tree,0);
int h=height(tree);
cout<<"balandligi="<
create_arr(tree,arr);
for(int i=0;i
tree=new_tree(arr,0,k-1);
vizual(tree,0);
getch();
}
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Dastur natijasi
Ishni bajarishga namuna
Topshiriq variantlariga o‟xshash bitta misolning algoritmi va to‟liq dasturini
ko‟rib chiqaylik.
Misol: berilgan binar daraxtdan ko‟rsatilgan key kalitga mos tugunni
o‟chirish dasturini tuzing.
Algoritm
Asosiy dastur tanasi - int main()
1. i=0; n – daraxtga kiritiladigan elementlar sonini aniqlash. Daraxt ildizi
ko‟rsatkichi tree=NULL. Next yangi elementni joylashtiradigan shoxga o‟tishda
ishlatiladi va last next dan 1 qadam orqada yuradi.
2. Agar i bo‟lsa, daraxtga kiritiladigan navbatdagi elementga qiymat
kiritish va uni yangi p element info maydoniga yozish, left va right maydonlarga
NULL yozish. Aks holda 8-qadamga o‟tish.
3. Agar tree=NULL bo‟lsa, p ni
daraxt ildizi qilish, ya‟ni tree=p va
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next=last=p.
4. Agar p->info next->info dan kichik bo‟lsa, chap shoxga o‟tish kerak,
ya‟ni last=next va next=next->left, aks holda o‟ng shoxga o‟tamiz, ya‟ni last=next
va next=next->right.
5. Agar next=NULL bo‟lsa, 6-qadamga o‟tish, aks holda 4-qadamga o‟tish.
6. Agar p->infoinfo bo‟lsa, last->left=p, aks holda last->right=p.
7. i++, 2-qadamga o‟tish.
8. intrave(tree) funksiyasini ishlatish.
9. Key kalitga mos elementni daraxtdan o‟chiradigan del(tree,key)
funksiyasini ishlatish.
10. Natijaviy daraxtni ko‟rikdan o‟tkazish uchun intrave(tree) funksiyasini
ishlatish va algoritmni yakunlash.
intrave(tree) funksiyasining ishlash algoritmi
1. Agar funksiyaning kirishiga berilgan tugun NULL bo‟lmasa, 2-qadamga
o‟tish, aks holda funksiya chaqirilgan joyga qaytib borish.
2. Agar tugunning chap shoxi tuguni NULL bo‟lmasa, uning info maydonini
yangi butun toifali a ga o‟zlashtirish, aks holda a=0.
3. Agar tugunning o‟ng shoxi tuguni NULL bo‟lmasa, uning info maydonini
yangi butun toifali b ga o‟zlashtirish, aks holda b=0.
4. Ekranga tugunning info maydoni qiymatini, tugunning chapidagi a va
o‟ngidagi b ni chiqaramiz.
5. Endi shu intrave() funksiyasining kirishiga joriy tugunning chap shoxi
tugunini berib chaqiramiz, ya‟ni yuqoridagi 4 ta amalni joriy tugunning chap
shoxidagi tugun ustida bajaramiz.
6. Endi shu intrave() funksiyasining kirishiga joriy tugunning o‟ng shoxi
tugunini berib chaqiramiz, ya‟ni yuqoridagi 4 ta amalni joriy tugunning o‟ng
shoxidagi tugun ustida bajaramiz.
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