用于检查给定的二叉树是否为AVL树的C ++程序
AVL树是一种自平衡二叉搜索树，其中左子树和右子树的高度之差对于所有节点都不能超过一个。
这是一个C++程序，用于检查给定的二叉树是否为AVL树。
算法
Beginfunction AVL() returns true if the given tree is AVL otherwise false.
if(root == NULL)
return 1
leftheight = height(root->left)
rightheight = height(root->right)
if(abs(leftheight-rightheight) <= 1 && AVL(root->left) && AVL(root->right))
return 1
return 0
End示例
#include <bits/stdc++.h>
using namespace std;
class nod { //node declaration
public:
int data;
nod* l;
nod* r;
};
nod* newNod(int d) { //creation of new node
nod* Nod = new nod();
Nod->data = d;
Nod->l = NULL;
Nod->r = NULL;
return(Nod);
}
int max(int x, int y) { //return maximum between two values
return (x >= y)? x: y;
}
int height(nod* node) { //get the height means the number of nodes along the longest path from the root
node down to the farthest leaf node of the tree.
if(node == NULL)
return 0;
return 1 + max(height(node->l), height(node->r));
}
bool AVL(nod *root) {
int lh;
int rh;
if(root == NULL)
return 1;
lh = height(root->l); // left height
rh = height(root->r); // right height
if(abs(lh-rh) <= 1 && AVL(root->l) && AVL(root->r)) return 1;
return 0;
}
int main() {
//将树的节点作为输入
nod *root = newNod(7);
root->l = newNod(6);
root->r = newNod(12);
root->l->l = newNod(4);
root->l->r = newNod(5);
root->r->r = newNod(13);
if(AVL(root))
cout << "The Tree is AVL Tree"<<endl;
else
cout << "The Tree is not AVL Tree "<<endl;
nod *root1 = newNod(7);
root1->l = newNod(6);
root1->r = newNod(12);
root1->l->l = newNod(4);
root1->l->r = newNod(5);
root1->r->r = newNod(13);
root1->r->r->r = newNod(26);
if(AVL(root1))
cout << "The Tree is AVL Tree"<<endl;
else
cout << "The Tree is not AVL Tree "<<endl;
return 0;
}输出结果
The Tree is AVL Tree The Tree is not AVL Tree