[LeetCode-7] 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.

Here the difinition of height balanced is a binary tree in which the depth of the two subtrees of every node never differ by more than 1.

This means difference of max depth of left tree and right tree are less than or equal to 1. 

different with balanced is defined by all the node differs in depth less than or equal to 1.

java 

public boolean isBalanced(TreeNode root) {        if(root == null) return true;        if(Math.abs(getHeight(root.left)-getHeight(root.right))>1) return false;        return isBalanced(root.left) && isBalanced(root.right);    }public int getHeight(TreeNode root){if(root == null) return 0;int left = getHeight(root.left);int right = getHeight(root.right);return Math.max(left, right)+1;}

c++

int maxDepth(TreeNode *root) {    if(root == NULL)        return 0;    int left = maxDepth(root->left);    int right = maxDepth(root->right);    return max(left,right)+1;}bool isBalanced(TreeNode *root) {    if(root == NULL) return true;    if(abs(maxDepth(root->left)-maxDepth(root->right))>1) return false;    return isBalanced(root->left)&& isBalanced(root->right);}

From Cracking Coding Interview book, we could get another improved algorithm. 

On each node, we recursively get the heights of the left and right subtrees through the checkHeight method. If the subtree is balanced, then checkHeight will return the actual height of the subtree. If the substree is not balanced, then checkHeight will return -1. We will immediately break and return -1 from the current call.

public int checkHeight(TreeNode root){if(root==null) return 0;int leftHeight = checkHeight(root.left);if(leftHeight==-1) return -1;int rightHeight = checkHeight(root.right);if(leftHeight==-1) return -1;int heightOff = leftHeight-rightHeight;if(Math.abs(heightOff)>1)return -1;elsereturn Math.max(leftHeight, rightHeight)+1;}