95. Unique Binary Search Trees II #

Problem #

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

Problem Summary #

Given an integer n, generate all binary search trees composed of nodes with values from 1 … n.

Solution Approach #

• Output all solutions of BSTs composed of elements 1~n. This problem can be solved recursively. The outer loop traverses all nodes from 1~n as the root node, and the inner double recursion obtains the left subtree and right subtree respectively.

Code #

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
}