【Leetcode】Unique Binary Search Tree II (DP)

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

这道题和一唯一的不同在于要求返回所有的树，所以需要知道几个特性

1. [1,2,3,4,...i-1,i,i+1...n]这样的数组中，以i为根节点，[1~i-1]为左子树，[i+1~n]为右子树所构造出来的BST具有唯一性

2. 每一个数建立左节点一定在左子树里找，建立右节点一定在右子树里找，就不会出错

代码如下

public ArrayList<TreeNode> generateTrees(int n) {return helper(1, n);}private ArrayList<TreeNode> helper(int left, int right) {ArrayList<TreeNode> result = new ArrayList<TreeNode>();if (left > right) {result.add(null);return result;}for (int i = left; i <= right; i++) {ArrayList<TreeNode> leftSub = helper(left, i - 1);ArrayList<TreeNode> rightSub = helper(i + 1, right);for (int j = 0; j < leftSub.size(); j++) {for (int k = 0; k < rightSub.size(); k++) {TreeNode root = new TreeNode(i);root.left = leftSub.get(j);root.right = rightSub.get(k);result.add(root);}}}return result;}