在二叉搜索树上执行右旋转的 C++ 程序

2023-06-20 10:55:03 200

二叉搜索树是一种排序二叉树，其中所有节点都具有以下两个属性-

节点的右子树的键大于其父节点的键。

节点的左子树的键小于或等于其父节点的键。

每个节点不应有超过两个子节点。

树旋转是一种改变结构而不干扰二叉树上元素顺序的操作。它在树中向上移动一个节点，向下移动一个节点。它用于改变树的形状，并通过向下移动较小的子树和向上移动较大的子树来降低其高度，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的一侧，而其他人则说这取决于哪个孩子占据了根的位置。这是一个在二叉搜索树上执行左旋转的C++程序。

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
#include
#include
#include
#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 << "输入您的选择： ";
      cin >> c;
      switch (c) {
         case 1:
            cout << "输入要插入的值： ";
            cin >> i;
            r= avl.insert(r, i);
         break;
         case 2:
            if (r == NULL) {
               cout << "Tree is Empty" << endl;
               continue;
            }
            cout << "平衡AVL树：" << endl;
            avl.show(r, 1);
            cout<输出结果1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 13
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 10
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 15
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 5
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 11
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 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
输入您的选择： 1
输入要插入的值： 8
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 16
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 3
中序遍历：
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
输入您的选择： 4
预序遍历：
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
输入您的选择： 5
后序遍历：
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
输入您的选择： 1
输入要插入的值： 14
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 3
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 7
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 9
1.Insert Element into the tree
2.show Balanced AVL Tree
3.InOrder traversal
4.PreOrder traversal
5.PostOrder traversal
6.Exit
输入您的选择： 1
输入要插入的值： 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
输入您的选择： 6

在二叉搜索树上执行右旋转的 C++ 程序

算法

示例

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