Unique Binary Search Trees II 解答

Question

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 

Solution

Key to the solution is to divide the problem into two sub-problems. Unlike "Unique Binary Search Trees", this problem is NP-hard.

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<TreeNode> generateTrees(int n) {
        return generateTreesHelper(1, n); 
    }
    private List<TreeNode> generateTreesHelper(int start, int end) {
        List<TreeNode> result = new ArrayList<TreeNode>();
        if (start > end) {
            result.add(null);
            return result;
        }
        for (int i = start; i <= end; i++) {
            List<TreeNode> lefts = generateTreesHelper(start, i - 1);
            List<TreeNode> rights = generateTreesHelper(i + 1, end);
            for (TreeNode left : lefts) {
                for (TreeNode right : rights) {
                    TreeNode tmp = new TreeNode(i);
                    tmp.left = left;
                    tmp.right = right;
                    result.add(tmp);
                }
            }
        }
        return result;
    }
}