LeetCode

题目：

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

思路：

仍和Unique Binary Search Trees的思路一样，确定左右树。

package bst;

import java.util.ArrayList;
import java.util.List;

class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode(int x) { val = x; }
}

public class UniqueBinarySearchTreesII {

    public List<TreeNode> generateTrees(int n) {
        List<TreeNode> res = new ArrayList<TreeNode>();
        if (n <= 0) return res;
        return generateTrees(1, n);
    }
    
    private List<TreeNode> generateTrees(int left, int right) {
        List<TreeNode> roots = new ArrayList<TreeNode>();
        if (left > right || left <= 0 || right <= 0) {
            roots.add(null);
        } else if (left == right) {
            TreeNode root = new TreeNode(left);
            roots.add(root);
        } else {
            for (int i = left; i <= right; ++i) {
                List<TreeNode> leftTree = generateTrees(left, i - 1);
                List<TreeNode> rightTree = generateTrees(i + 1, right);
                for (int j = 0; j < leftTree.size(); ++j) {
                    for (int k = 0; k < rightTree.size(); ++k) {
                        TreeNode root = new TreeNode(i);
                        root.left = leftTree.get(j);
                        root.right = rightTree.get(k);
                        roots.add(root);
                    }
                }
            }
        }
        
        return roots;        
    }
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        UniqueBinarySearchTreesII u = new UniqueBinarySearchTreesII();
        u.generateTrees(3);
    }

}