110. Balanced Binary Tree

• Difficulty: Easy

• Topics: Tree, Depth-first Search

• Similar Questions:

  • Maximum Depth of Binary Tree

Problem:

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.

Example 1:

Given the following tree [3,9,20,null,null,15,7]:

    3
   / \
  9  20
    /  \
   15   7

Return true.

Example 2:

Given the following tree [1,2,2,3,3,null,null,4,4]:

       1
      / \
     2   2
    / \
   3   3
  / \
 4   4

Return false.

Solutions:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    bool isBalanced(TreeNode* root) {
        int height;
        return isBalanced(root, height);
    }

    bool isBalanced(TreeNode* root, int& height) {
        if (root == nullptr) {
            height = 0;
            return true;
        }

        int leftHeight;
        int rightHeight;

        if (isBalanced(root->left, leftHeight) && isBalanced(root->right, rightHeight) && abs(leftHeight - rightHeight) <= 1) {
            height = 1 + max(leftHeight, rightHeight);
            return true;
        } else {
            return false;
        }

    }
};