leetcode 95. Unique Binary Search Trees II | Java最短代码实现

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

confused what "{1,#,2,3}" means? > read more on how binary tree is serialized on OJ.

OJ's Binary Tree Serialization:

The serialization of a binary tree follows a level order traversal, where '#' signifies a path terminator where no node exists below.

Here's an example:

   1  / \ 2   3    /   4    \     5

The above binary tree is serialized as "{1,2,3,#,#,4,#,#,5}".

【抛砖】

这是卡特兰数的一种应用，采用动态规划：

1.从start到end，逐个取出一个rootVal作为根节点（n阶原问题）

2.以根rootVal为界划分为左右子树，并指向左右子树（n-1阶子问题）

3.反复递归：

    public List<TreeNode> generateTrees(int n) {        if (n <= 0) return new ArrayList<TreeNode>();        return generateSubTree(1, n);    }    public ArrayList<TreeNode> generateSubTree(int start, int end) {        ArrayList<TreeNode> result = new ArrayList<TreeNode>();        if (start > end) {            result.add(null);            return result;        }        for (int rootVal = start; rootVal <= end; rootVal++)            for (TreeNode leftSubTreeRoot : generateSubTree(start, rootVal - 1))                for (TreeNode rightSubTreeRoot : generateSubTree(rootVal + 1, end)) {                    TreeNode root = new TreeNode(rootVal);                    root.left = leftSubTreeRoot;                    root.right = rightSubTreeRoot;                    result.add(root);                }        return result;    }

9 / 9 test cases passed. Runtime: 4 ms  Your runtime beats 5.97% of javasubmissions.

欢迎优化！