力扣110. 平衡二叉树

方法1：自顶向下，会重复计算

定义一个求树的深度的函数

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
private:
 int maxdep(TreeNode* root)
 {
     if(root==NULL)
        return 0;
    return max(maxdep(root->left),maxdep(root->right))+1;
 }
public:
    bool isBalanced(TreeNode* root) {
        if(root==NULL)
            return true;
        return abs(maxdep(root->left)-maxdep(root->right))<=1 && isBalanced(root->left) && isBalanced(root->right);
    }
};

方法2：自底向上

class Solution {
public:
    int height(TreeNode* root) {
        if (root == NULL) {
            return 0;
        }
        int leftHeight = height(root->left);
        int rightHeight = height(root->right);
        if (leftHeight == -1 || rightHeight == -1 || abs(leftHeight - rightHeight) > 1) {
            return -1;
        } else {
            return max(leftHeight, rightHeight) + 1;
        }
    }

    bool isBalanced(TreeNode* root) {
        return height(root) >= 0;
    }
};

 再加一点小优化：当左子树不平衡时，不用再计算右子树了

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int height(TreeNode* root) {
        if (root == NULL) {
            return 0;
        }
        int leftHeight;
        int rightHeight;
        if ( (leftHeight = height(root->left))== -1 ||  (rightHeight = height(root->right))== -1 || abs(leftHeight - rightHeight) > 1) {
            return -1;
        } else {
            return max(leftHeight, rightHeight) + 1;
        }
    }
    bool isBalanced(TreeNode* root) {
        return height(root) >= 0;
    }
};