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;
     }
 }