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Given an array where elements are sorted in ascending order, convert it to a height balanced BST.
题意:给一个升序排好的数组,构造一棵二叉查找树或者叫二叉搜索树BST,要求这颗树是平衡的
BST:二叉查找树,左子树所有节点都小于根节点。右子树所有节点都大于根节点,递归定义
堆(大根堆和小根堆)对应的二叉树:根节点大于所有节点(大根堆),递归定义
解题思路:
1.选数组中间元素插入到BST中。递归实现
2.如果value大于root插入右子树,value小于root插入左子树。递归实现
1 /** 2 * Definition for binary tree 3 * public class TreeNode { 4 * int val; 5 * TreeNode left; 6 * TreeNode right; 7 * TreeNode(int x) { val = x; } 8 * } 9 */ 10 public class Solution { 11 public TreeNode root ; 12 13 public TreeNode sortedArrayToBST(int[] num) { 14 if(num.length == 0) 15 return root; 16 if(1 == num.length){ 17 return new TreeNode(num[0]); 18 } 19 int middle = num.length / 2; 20 root = new TreeNode(num[middle]); 21 22 createBST(num, 0, middle - 1); 23 createBST(num, middle + 1, num.length - 1); 24 return root; 25 } 26 27 /** 28 * 根据num数组,创建一棵二叉查找树 29 * @param num 30 * @param start 31 * @param end 32 */ 33 private void createBST(int num[], int start, int end){ 34 int middle = 0; 35 if(start <= end && start >= 0 && end <num.length){ 36 middle = (start + end) / 2; 37 38 insertNode(root, num[middle]); 39 40 createBST(num, start, middle - 1); 41 createBST(num, middle + 1, end); 42 } 43 } 44 45 /** 46 * 向root所指的BST二叉查找树中插入value 47 * @param root 48 * @param value 49 */ 50 private void insertNode(TreeNode root, int value){ 51 if(value > root.val){ //比根节点大,在右子树插入 52 if(root.right == null){ 53 root.right = new TreeNode(value); 54 }else{ 55 root = root.right; 56 insertNode(root, value); 57 } 58 } 59 else{ 60 if(root.left == null){ 61 root.left = new TreeNode(value); 62 }else{ 63 root = root.left; 64 insertNode(root, value); //比根节点小的插入左子树 65 } 66 } 67 } 68 69 // /** 70 // * 先序遍历 71 // * @param root 72 // */ 73 // public void preTravel(TreeNode root){ 74 // if(root != null){ 75 // System.out.print(root.val + " "); 76 // preTravel(root.left); 77 // preTravel(root.right); 78 // } 79 // } 80 }
涉及到树的,很多都会用到递归实现,DFS,先序遍历等遍历...
Convert Sorted Array to Binary Search Tree
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原文地址:http://www.cnblogs.com/luckygxf/p/4189087.html