Description

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 left and right subtrees of every node differ in height by no 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.

Solution

根据题意，每个子节点不同分支的高度差不能大于1，很自然的想要搜索遍历所有的节点。

解法一 自顶向下的递归

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */

func isBalanced(root *TreeNode) bool {
    if root == nil {
        return true
    }
    return abs(findLength(root.Left) -findLength(root.Right)) <= 1 && isBalanced(root.Left) && isBalanced(root.Right)
}


func findLength(root *TreeNode) int {
    if root == nil {
        return 0
    }
    return max(findLength(root.Left), findLength(root.Right)) + 1
}


func max(x, y int) int {
    if x > y {
        return x
    }
    return y
}

func abs(x int) int {
    if x < 0 {
        return -1 * x
    }
    return x
}

解法二 自底向上的递归

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

func height(root *TreeNode) int {
    if root == nil {
        return 0
    }
    leftHeight := height(root.Left)
    rightHeight := height(root.Right)
    if leftHeight == -1 || rightHeight == -1 || abs(leftHeight - rightHeight) > 1 {
        return -1
    }
    return max(leftHeight, rightHeight) + 1
}

func max(x, y int) int {
    if x > y {
        return x
    }
    return y
}

func abs(x int) int {
    if x < 0 {
        return x * -1
    }
    return x
}