Given an integer 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.

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1         3     3      2      1
 \       /     /      / \      \
  3     2     1      1   3      2
 /     /       \                 \
2     1         2                 3

Divide and Conquer

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/**
 * 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) {
        if (n <= 0) {
            return new LinkedList<TreeNode>();
        }
        return genTrees(1,n);
    }
        
    public List<TreeNode> genTrees (int start, int end){
        List<TreeNode> list = new ArrayList<TreeNode>();

        if(start>end) {
            list.add(null);
        }
        
        List<TreeNode> left,right;
        for (int i = start; i <= end; i++) {
            left = genTrees(start, i-1);
            right = genTrees(i+1,end);
            for (TreeNode lnode: left) {
                for (TreeNode rnode: right) {
                    TreeNode root = new TreeNode(i);
                    root.left = lnode;
                    root.right = rnode;
                    list.add(root);
                }
            }
        }
        return list;
    }
}

DP solution

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public static List<TreeNode> generateTrees(int n) {
    List<TreeNode>[] result = new List[n + 1];
    result[0] = new ArrayList<TreeNode>();
    if (n == 0) {
        return result[0];
    }

    result[0].add(null);
    for (int len = 1; len <= n; len++) {
        result[len] = new ArrayList<TreeNode>();
        for (int j = 0; j < len; j++) {
            for (TreeNode nodeL : result[j]) {
                for (TreeNode nodeR : result[len - j - 1]) {
                    TreeNode node = new TreeNode(j + 1);
                    node.left = nodeL;
                    node.right = clone(nodeR, j + 1);
                    result[len].add(node);
                }
            }
        }
    }
    return result[n];
}

private static TreeNode clone(TreeNode n, int offset) {
    if (n == null) {
        return null;
    }
    TreeNode node = new TreeNode(n.val + offset);
    node.left = clone(n.left, offset);
    node.right = clone(n.right, offset);
    return node;
}