Leetcode: Unique Binary Search Trees II

最新推荐文章于 2025-08-08 11:49:43 发布

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本文提供了一种使用递归方法生成所有结构独特的BST（二叉搜索树），并详细解释了如何利用递归来获取所有可能的根节点、左右节点，并将返回的根节点用于后续递归中。

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Given n, generate all structurally unique BST's (binary search trees) that store values 1...n.

For example,
Given n = 3, your program should return all 5 unique BST's shown below.

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

Use recursion to get all possible roots, right nodes and left nodes. The returned roots are used as left or right nodes in next recursion.

/**
 * Definition for binary tree
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; left = null; right = null; }
 * }
 */
public class Solution {
    public ArrayList<TreeNode> generateTrees(int n) {
        return generate(1, n);
    }
    
    private ArrayList<TreeNode> generate(int start, int end) {
        ArrayList<TreeNode> res = new ArrayList<TreeNode>();
        
        if (start > end) {
            res.add(null);
            return res;
        }
        
        for (int i = start; i <= end; i++) {
            ArrayList<TreeNode> left = generate(start, i - 1);
            ArrayList<TreeNode> right = generate(i + 1, end);
            for (TreeNode l : left) {
                for (TreeNode r : right) {
                    TreeNode root = new TreeNode(i);
                    root.left = l;
                    root.right = r;
                    res.add(root);
                }
            }
        }
        
        return res;
    }
}