95. Unique Binary Search Trees II

题目

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

Example:

Input: 3
Output:
[
  [1,null,3,2],
  [3,2,null,1],
  [3,1,null,null,2],
  [2,1,3],
  [1,null,2,null,3]
]
Explanation:
The above output corresponds to the 5 unique BST's shown below:

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

题目大意

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。

解题思路

• 输出 1n 元素组成的 BST 所有解。这一题递归求解即可。外层循环遍历 1n 所有结点，作为根结点，内层双层递归分别求出左子树和右子树。

代码

package leetcode

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func generateTrees(n int) []*TreeNode {
	if n == 0 {
		return []*TreeNode{}
	}
	return generateBSTree(1, n)
}

func generateBSTree(start, end int) []*TreeNode {
	tree := []*TreeNode{}
	if start > end {
		tree = append(tree, nil)
		return tree
	}
	for i := start; i <= end; i++ {
		left := generateBSTree(start, i-1)
		right := generateBSTree(i+1, end)
		for _, l := range left {
			for _, r := range right {
				root := &TreeNode{Val: i, Left: l, Right: r}
				tree = append(tree, root)
			}
		}
	}
	return tree
}

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