它是一 棵空树或它的左右两个子树的高度差的绝对值不超过1，并且左右两个子树都是一棵平衡二叉（搜索）树。

 

二分：用有序数组中中间的数生成搜索二叉树的头节点，然后对数组的左右部分分别生成左右子树即可（重复过程）。

生成的二叉树中序遍历一定还是这个序列。

 

非常简单，不过多叙述：

public class SortedArrayToBalancedBST {public static class Node {public int value;public Node left;public Node right;public Node(int data) {this.value = data;}}public static Node generateTree(int[] sortArr) {if (sortArr == null) {return null;}return generate(sortArr, 0, sortArr.length - 1);}public static Node generate(int[] sortArr, int start, int end) {if (start > end) {return null;}int mid = (start + end) / 2;Node head = new Node(sortArr[mid]);head.left = generate(sortArr, start, mid - 1);head.right = generate(sortArr, mid + 1, end);return head;}// for test -- print treepublic static void printTree(Node head) {System.out.println("Binary Tree:");printInOrder(head, 0, "H", 17);System.out.println();}public static void printInOrder(Node head, int height, String to, int len) {if (head == null) {return;}printInOrder(head.right, height + 1, "v", len);String val = to + head.value + to;int lenM = val.length();int lenL = (len - lenM) / 2;int lenR = len - lenM - lenL;val = getSpace(lenL) + val + getSpace(lenR);System.out.println(getSpace(height * len) + val);printInOrder(head.left, height + 1, "^", len);}public static String getSpace(int num) {String space = " ";StringBuffer buf = new StringBuffer("");for (int i = 0; i < num; i++) {buf.append(space);}return buf.toString();}public static void main(String[] args) {int[] arr = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };printTree(generateTree(arr));}}