数据结构 - 平衡二叉树

平衡二叉树的定义

平衡二叉树（Balanced Binary Tree）是具有以下性质的二叉树：它是一棵空树或它的左右两个子树的高度差的绝对值不超过1，并且左右两个子树都是一棵平衡二叉树。

判断一棵二叉树是否平衡（C++）

#include <iostream>

#define NULL 0

using namespace std;

template<class T>
struct BTNode
{
T data;
BTNode<T> *lChild, *rChild;
BTNode();
BTNode(const T &val, BTNode<T> *childL = NULL, BTNode<T> *childR = NULL)
{
data = val;
lChild = childL;
rChild = childR;
}

BTNode<T>* CopyTree()
{
BTNode<T> *nl, *nr, *nn;
if(&data == NULL)
{
return NULL;
}

nl = lChild->CopyTree();
nr = rChild->CopyTree();
nn = new BTNode<T>(data, nl, nr);

return nn;
}
};

template<class T>
BTNode<T>::BTNode()
{
lChild = rChild = NULL;
}

template<class T>
class BinaryTree
{
public:
BTNode<T> *root;
BinaryTree();
~BinaryTree();
void DestroyTree();
BTNode<T>* MakeTree(const T &element, BTNode<T> *l, BTNode<T> *r)
{
root = new BTNode<T> (element, l, r);
if(root == NULL)
{
cout << "Failure for applying storage address, system will close the process." << endl;
exit(1);
}

return root;
}

private:
void Destroy(BTNode<T> *&r);
};

template<class T>
BinaryTree<T>::BinaryTree()
{
root = NULL;
}

template<class T>
BinaryTree<T>::~BinaryTree()
{
DestroyTree();
}

template<class T>
void BinaryTree<T>::DestroyTree()
{
Destroy(root);
}

template<class T>
void BinaryTree<T>::Destroy(BTNode<T> *&r)
{
if(r != NULL)
{
Destroy(r->lChild);
Destroy(r->rChild);
delete r;
r = NULL;
}
}

template<class T>
int isBalanced(BTNode<T> *r)
{
if(!r)
{
return 0;
}

int left = isBalanced(r->lChild);
int right = isBalanced(r->rChild);
if((left >= 0) && (right >= 0) && ((left - right) <= 1) && ((left - right) >= -1))
{
return (left < right) ? (right + 1) : (left + 1);
}
else
{
return -1;
}
}

void main()
{
BTNode<char> *b, *c, *d, *e, *f, *g;
BinaryTree<char> a;

b = a.MakeTree('F', NULL, NULL);
c = a.MakeTree('E', NULL, NULL);
d = a.MakeTree('D', b, NULL);
e = a.MakeTree('C', NULL, NULL);
f = a.MakeTree('B', d, c);
g = a.MakeTree('A', f, e);

if(isBalanced(a.root) >= 0)
{
cout << "This IS a balanced binary tree." << endl;
}
else
{
cout << "This is NOT a balanced binary tree." << endl;
}
}

// Output:
/*
This is NOT a balanced binary tree.
*/