题目地址

https://leetcode-cn.com/problems/unique-binary-search-trees-ii/

题目描述

给定一个整数 n，生成所有由 1 ... n 为节点所组成的二叉搜索树。

示例:

输入: 3
输出:
[
  [1,null,3,2],
  [3,2,null,1],
  [3,1,null,null,2],
  [2,1,3],
  [1,null,2,null,3]
]
解释:
以上的输出对应以下 5 种不同结构的二叉搜索树：

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

题解

递归解法

定义递归函数 public List<TreeNode> build(int left, int right)，用来描述通过 [left, right] 构建的所有二叉搜索树。

class Solution {
    public List<TreeNode> generateTrees(int n) {
        return build(1, n);
    }

    public List<TreeNode> build(int left, int right) {
        if (left == right) {
            return Arrays.asList(new TreeNode(left));
        }
        if (left > right) {
            List<TreeNode> roots = new ArrayList<>();
            roots.add(null);
            return roots;
        }

        List<TreeNode> roots = new ArrayList<>();

        for (int i = left; i <= right; ++ i) {
            // [left, i - 1] 作为 left 子树
            List<TreeNode> leftTree = build(left, i - 1);

            // [i+1, right] 作为 right 子树
            List<TreeNode> rightTree = build(i+1, right);

            for (int leftIndex = 0; leftIndex < leftTree.size(); ++ leftIndex) {
                for (int rightIndex = 0; rightIndex < rightTree.size(); ++ rightIndex) {
                    // i 作为 root 节点
                    TreeNode root = new TreeNode(i);

                    root.left = leftTree.get(leftIndex);
                    root.right = rightTree.get(rightIndex);

                    roots.add(root);
                }
            }
        }
        
        return roots;
    }
}