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法律研究C++程式實現二叉搜尋樹的右旋轉
二叉搜尋樹是一種排序的二叉樹，其中所有節點都具有以下兩個屬性：
節點的右子樹的鍵值大於其父節點的鍵值。
節點的左子樹的鍵值小於或等於其父節點的鍵值。
每個節點最多隻能有兩個子節點。
樹旋轉是一種改變結構而不干擾二叉樹上元素順序的操作。它將一個節點向上移動到樹中，並將另一個節點向下移動。它用於改變樹的形狀，並透過將較小的子樹向下移動，將較大的子樹向上移動來降低其高度，從而提高許多樹操作的效能。旋轉的方向取決於樹節點移動到的側面，或者有人說它取決於哪個子節點取代了根節點的位置。這是一個C++程式，用於在二叉搜尋樹上執行左旋轉。
演算法
Begin Create a structure avl to declare variables data d, a left pointer l and a right pointer r. Declare a class avl_tree to declare following functions: height() - To calculate height of the tree by max function. Difference() - To calculate height difference of the tree. rr_rotat() - For right-right rotation of the tree. ll_rotat() - For left-left rotation of the tree. lr_rotat() - For left-right rotation of the tree. rl_rotat() - For right-left rotation of the tree. balance() - Balance the tree by getting balance factor. Put the difference in bal_factor. If bal_factor>1 balance the left subtree. If bal_factor<-1 balance the right subtree. insert() - To insert the elements in the tree. show() - To print the tree. inorder() - To print inorder traversal of the tree. preorder() - To print preorder traversal of the tree. postorder() - To print postorder traversal of the tree. In main(), perform switch operation and call the functions as per choice. End.
示例
#include<iostream>
#include<cstdio>
#include<sstream>
#include<algorithm>
#define pow2(n) (1 << (n))
using namespace std;
struct avl {
int d;
struct avl *l;
struct avl *r;
}*r;
class avl_tree {
public:
int height(avl *);
int difference(avl *);
avl *rr_rotat(avl *);
avl *ll_rotat(avl *);
avl *lr_rotat(avl*);
avl *rl_rotat(avl *);
avl * balance(avl *);
avl * insert(avl*, int);
void show(avl*, int);
void inorder(avl *);
void preorder(avl *);
void postorder(avl*);
avl_tree() {
r = NULL;
}
};
int avl_tree::height(avl *t) {
int h = 0;
if (t != NULL) {
int l_height = height(t->l);
int r_height = height(t->r);
int max_height = max(l_height, r_height);
h = max_height + 1;
}
return h;
}
int avl_tree::difference(avl *t) {
int l_height = height(t->l);
int r_height = height(t->r);
int b_factor = l_height - r_height;
return b_factor;
}
avl *avl_tree::rr_rotat(avl *parent) {
avl *t;
t = parent->r;
parent->r = t->l;
t->l = parent;
cout<<"Right-Right Rotation";
return t;
}
avl *avl_tree::ll_rotat(avl *parent) {
avl *t;
t = parent->l;
parent->l = t->r;
t->r = parent;
cout<<"Left-Left Rotation";
return t;
}
avl *avl_tree::lr_rotat(avl *parent) {
avl *t;
t = parent->l;
parent->l = rr_rotat(t);
cout<<"Left-Right Rotation";
return ll_rotat(parent);
}
avl *avl_tree::rl_rotat(avl *parent) {
avl *t;
t= parent->r;
parent->r = ll_rotat(t);
cout<<"Right-Left Rotation";
return rr_rotat(parent);
}
avl *avl_tree::balance(avl *t) {
int bal_factor = difference(t);
if (bal_factor > 1) {
if (difference(t->l) > 0)
t = ll_rotat(t);
else
t = lr_rotat(t);
}
else if (bal_factor < -1) {
if (difference(t->r) > 0)
t= rl_rotat(t);
else
t = rr_rotat(t);
}
return t;
}
avl *avl_tree::insert(avl *r, int v) {
if (r == NULL) {
r= new avl;
r->d = v;
r->l = NULL;
r->r= NULL;
return r;
}
else if (v< r->d) {
r->l= insert(r->l, v);
r = balance(r);
}
else if (v >= r->d) {
r->r= insert(r->r, v);
r = balance(r);
}
return r;
}
void avl_tree::show(avl *p, int l) {
int i;
if (p != NULL) {
show(p->r, l+ 1);
cout<<" ";
if (p == r)
cout << "Root -> ";
for (i = 0; i < l&& p != r; i++)
cout << " ";
cout << p->d;
show(p->l, l + 1);
}
}
void avl_tree::inorder(avl *t) {
if (t == NULL)
return;
inorder(t->l);
cout << t->d << " ";
inorder(t->r);
}
void avl_tree::preorder(avl *t) {
if (t == NULL)
return;
cout << t->d << " ";
preorder(t->l);
preorder(t->r);
}
void avl_tree::postorder(avl *t) {
if (t == NULL)
return;
postorder(t ->l);
postorder(t ->r);
cout << t->d << " ";
}
int main() {
int c, i;
avl_tree avl;
while (1) {
cout << "1.Insert Element into the tree" << endl;
cout << "2.show Balanced AVL Tree" << endl;
cout << "3.InOrder traversal" << endl;
cout << "4.PreOrder traversal" << endl;
cout << "5.PostOrder traversal" << endl;
cout << "6.Exit" << endl;
cout << "Enter your Choice: ";
cin >> c;
switch (c) {
case 1:
cout << "Enter value to be inserted: ";
cin >> i;
r= avl.insert(r, i);
break;
case 2:
if (r == NULL) {
cout << "Tree is Empty" << endl;
continue;
}
cout << "Balanced AVL Tree:" << endl;
avl.show(r, 1);
cout<<endl;
break;
case 3:
cout << "Inorder Traversal:" << endl;
avl.inorder(r);
cout << endl;
break;
case 4:
cout << "Preorder Traversal:" << endl;
avl.preorder(r);
cout << endl;
break;
case 5:
cout << "Postorder Traversal:" << endl;
avl.postorder(r);
cout << endl;
break;
case 6:
exit(1);
break;
default:
cout << "Wrong Choice" << endl;
}
}
return 0;
}輸出
1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 13 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 10 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 15 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 5 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 11 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 4 Left-Left Rotation1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 8 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 16 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 3 Inorder Traversal: 4 5 8 10 11 13 15 16 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 4 Preorder Traversal: 10 5 4 8 13 11 15 16 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 5 Postorder Traversal: 4 8 5 11 16 15 13 10 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 14 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 3 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 7 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 9 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 52 Right-Right Rotation 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 6
更新於: 2019年7月30日
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