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法律研究C++ 实现 AVL 树程序
AVL 树是一种自平衡二叉搜索树，其中所有节点的左右子树的高度差不能超过 1。
树旋转是一种不改变元素顺序的操作，它改变了 AVL 树的结构。它将一个节点向上移动，另一个节点向下移动。它用于改变树的形状，并通过将较小的子树向下移动，较大的子树向上移动来降低树的高度，从而提高许多树操作的性能。旋转的方向取决于树节点移动到的方向，也有人说它取决于哪个子节点取代了根节点的位置。这是一个用 C++ 实现 AVL 树的程序。
函数描述
height(avl *)：计算给定 AVL 树的高度。
difference(avl *)：计算给定树的子树高度差。
avl *rr_rotat(avl *)：右-右旋转是右旋转后接右旋转的组合。
avl *ll_rotat(avl *)：左-左旋转是左旋转后接左旋转的组合。
avl *lr_rotat(avl*)：左-右旋转是左旋转后接右旋转的组合。
avl *rl_rotat(avl *)：它是右旋转后接左旋转的组合。
avl * balance(avl *): 通过获取平衡因子来对树执行平衡操作
avl * insert(avl*, int)：执行插入操作。使用此函数在树中插入值。
show(avl*, int): 显示树的值。
inorder(avl *)：以中序方式遍历树。
preorder(avl *)：以先序方式遍历树。
postorder(avl*)：以后序方式遍历树。
示例代码
#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;
}输出
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
更新于： 2019-07-30
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