返回与给定先序遍历 preorder 相匹配的二叉搜索树(binary search tree)的根结点。
(回想一下,二叉搜索树是二叉树的一种,其每个节点都满足以下规则,对于 node.left 的任何后代,值总 < node.val,而 node.right 的任何后代,值总 > node.val。此外,先序遍历首先显示节点的值,然后遍历 node.left,接着遍历 node.right。)
示例:
输入:[8,5,1,7,10,12]
输出:[8,5,10,1,7,null,12]
提示:
1 <= preorder.length <= 100
先序 preorder 中的值是不同的。
思路
二叉搜索树的中序遍历是一个不下降序列,将数组排序,即将问题转化为根据先序遍历和中序遍历构造二叉树
/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
class Solution {
public TreeNode bstFromPreorder(int[] preorder) {
if (preorder == null || preorder.length == 0) {
return null;
}
int[] temp = Arrays.copyOf(preorder, preorder.length);
Arrays.sort(temp);
int[] inorder = temp;
TreeNode root = buildMyTree(preorder, 0, preorder.length-1, inorder, 0, inorder.length-1);
return root;
}
public TreeNode buildMyTree(int[] preorder,
int preStart,
int preEnd,
int[] inorder,
int inStart,
int inEnd) {
if (inStart > inEnd) {
return null;
}
int value = preorder[preStart];
int position = findPosition(inorder, inStart, inEnd, value);
TreeNode root = new TreeNode(value);
root.left = buildMyTree(preorder, preStart+1, preStart+position-inStart, inorder, inStart, position-1);
root.right = buildMyTree(preorder, preStart+position-inStart+1, preEnd, inorder, position+1, inEnd);
return root;
}
public int findPosition(int[] array, int start, int end, int key) {
for (int i = start; i <= end; i++) {
if (array[i] == key) {
return i;
}
}
return -1;
}
}