Balanced Binary Tree

Given a binary tree, determine if it is height-balanced.

For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1.

思路：首先我们先熟悉平衡二叉树的定义，平衡二叉树或为空树,或为如下性质的二叉排序树:（1）左右子树深度之差的绝对值不超过1;（2）左右子树仍然为平衡二叉树.

      平衡因子BF=左子树深度－右子树深度.

平衡二叉树每个结点的平衡因子只能是1，0，-1。若其绝对值超过1，则该二叉排序树就是不平衡的。

这道题主要就是计算左右子树各个深度，然后判断左右子树深度之差的绝对值不超过1.使用递归

/**

 * Definition for binary tree

 * struct TreeNode {

 *     int val;

 *     TreeNode *left;

 *     TreeNode *right;

 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}

 * };

 */

class Solution {

public:

    int DepthBalanced(TreeNode *root)

    {

        int pLeft,pRight;

        if(root==NULL)

            return 0;

        if(root->left==NULL)

            return DepthBalanced(root->right)+1;

        else if(root->right==NULL)

            return DepthBalanced(root->left)+1;

        else

        {

            pLeft=DepthBalanced(root->left);

            pRight=DepthBalanced(root->right);

            return (pLeft>pRight)?(pLeft+1):(pRight+1);

        }

    }

    bool isBalanced(TreeNode *root) {

        int pLeft,pRight;

        if(root==NULL)

            return true;

        pLeft=DepthBalanced(root->left);

        pRight=DepthBalanced(root->right);

        if(pLeft-pRight>=-1 && pLeft-pRight<=1)

            return isBalanced(root->left) && isBalanced(root->right);

        return false;

    }

};

 另一种解法：原理差不多，把判断拿到另一个函数中去判断了。

/**

 * Definition for binary tree

 * struct TreeNode {

 *     int val;

 *     TreeNode *left;

 *     TreeNode *right;

 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}

 * };

 */

class Solution {

public:

    int check(TreeNode *root,bool &value)

    {

        if(root==NULL)

        {

            return 0;

        }

        int pLeft=check(root->left,value);

        int pRight=check(root->right,value);

        int depth=(pLeft>pRight)?(pLeft+1):(pRight+1);

        if(pLeft-pRight<-1 || pLeft-pRight>1)

            value=false;

        return depth;

    }

    bool isBalanced(TreeNode *root) {

        bool value=true;

        check(root,value);

        return value;

    }

};