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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++）

/*
 * Created by Chimomo
 */

#include <iostream>

#define NULL 0

using namespace std;

template<class T>
struct BTNode {
    T data;
    BTNode<T> *lChild, *rChild;

    BTNode();

    explicit 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 << "Failed 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;
    }
}

int 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;
    }

    return 0;
}

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

*/