[面试真题] LeetCode：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.

递归地计算每个节点的左右子树深度，看其是否平衡。由于节点被重复访问，效率较低。

Program Runtime: 68 milli secs

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
    
        
    int maxDepth(TreeNode *root){
        if(NULL == root){
            return 0;
        }
        int maxL = maxDepth(root->left);
        int maxR = maxDepth(root->right);
        return 1 + (maxL > maxR ? maxL : maxR);
    }
    
public:
    bool isBalanced(TreeNode *root) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if(NULL == root){
            return true;
        }
        int diff = maxDepth(root->left) - maxDepth(root->right);
        if((diff>1) || (diff<-1)){
            return false;
        }
         return isBalanced(root->left) && isBalanced(root->right);
    }
};

改进：使用后序遍历二叉树的节点，遍历时记录节点深度，同时也可以更快的判断出二叉树不平衡的情况。

可是奇怪的是执行时间反而变长了，不解。

Program Runtime: 84 milli secs

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
    bool isBalanced(TreeNode *root, int *depth){
        if(NULL == root){
            *depth = 0;
            return true;
        }
        int left, right;
        if(isBalanced(root->left, &left) && isBalanced(root->right, &right)){
            int diff = left - right;
            if((diff>1) || (diff<-1)){
                return false;
            }
            *depth = 1 + (left > right ? left : right);
            return true;
        }
    } 
    
public:
    bool isBalanced(TreeNode *root) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int depth = 0;
        return isBalanced(root, &depth);
    }
};