110. Balanced Binary Tree

最新推荐文章于 2022-07-18 20:53:17 发布

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最新推荐文章于 2022-07-18 20:53:17 发布

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本文通过深度优先搜索（DFS）递归方法，分析并实现了一个算法来判断给定的二叉树是否为平衡树。平衡树定义为每个节点的左右子树高度之差不超过1。该算法同时计算树的高度，使用高度-1表示树不平衡。

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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.

分析：判断一颗二叉树是否是平衡的，dfs递归求解，递归的过程中顺便求得树的高度

唯一的trick:不用生成新的data structure来保存“boolean isBalanced, int height”，直接用height = -1表示不平衡就行。

/**
 * Definition for binary tree
 * struct TreeNode {
 * int val;
 * TreeNode *left;
 * TreeNode *right;
 * TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    bool isBalanced(TreeNode *root) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        if(root == NULL)return true;
        if(height(root) == -1)return false;
        else return true;
    }
    //若root是平衡树，那么返回树的高度，否则返回-1
    int height(TreeNode *root)
    {
        if(root->left == NULL && root->right == NULL)return 1;
        int leftHeight = 0, rightHeight = 0;
        if(root->left)
            leftHeight = height(root->left);
        if(leftHeight == -1)return -1;
        if(root->right)
            rightHeight = height(root->right);
        if(rightHeight == -1)return -1;
        if(abs(leftHeight-rightHeight) > 1)return -1;
        return 1+max(leftHeight, rightHeight);
    }
};

15年9月14

----------------------

注意，用height=-1标记树是非平衡的。

class Solution {
private:
    int height(TreeNode* root) {
        if (!root) {
            return 0;
        }
        int leftTreeHeight = height(root->left);
        if (leftTreeHeight==-1) {
            return -1;
        }
        int rightTreeHeight = height(root->right);
        if (rightTreeHeight==-1) {
            return -1;
        } else if (abs(leftTreeHeight-rightTreeHeight)>=2) {
            return -1;
        } else {
            return max(leftTreeHeight, rightTreeHeight)+1;
        }
    }
public:
    bool isBalanced(TreeNode* root) {
        int h = height(root);
        if (h==-1) {
            return false;
        } else {
            return true;
        }
    }
};