LeetCode - Unique Binary Search Trees II

1 minute read

Problem description

description

Given an integer n, generate all structurally unique BST’s (binary search trees) that store values 1 … n.

Example:

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Input: 3
Output:
[
  [1,null,3,2],
  [3,2,null,1],
  [3,1,null,null,2],
  [2,1,3],
  [1,null,2,null,3]
]
Explanation:
The above output corresponds to the 5 unique BST's shown below:

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

Analysis

The first thought is to use the inorder traversal to get a result. And this can only get part result of the solution.

And the solution from LeetCode is using divide and conquer.

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class Solution {
  public LinkedList<TreeNode> generate_trees(int start, int end) {
    LinkedList<TreeNode> all_trees = new LinkedList<TreeNode>();
    if (start > end) {
      all_trees.add(null);
      return all_trees;
    }

    // pick up a root
    for (int i = start; i <= end; i++) {
      // all possible left subtrees if i is choosen to be a root
      LinkedList<TreeNode> left_trees = generate_trees(start, i - 1);

      // all possible right subtrees if i is choosen to be a root
      LinkedList<TreeNode> right_trees = generate_trees(i + 1, end);

      // connect left and right trees to the root i
      for (TreeNode l : left_trees) {
        for (TreeNode r : right_trees) {
          TreeNode current_tree = new TreeNode(i);
          current_tree.left = l;
          current_tree.right = r;
          all_trees.add(current_tree);
        }
      }
    }
    return all_trees;
  }

  public List<TreeNode> generateTrees(int n) {
    if (n == 0) {
      return new LinkedList<TreeNode>();
    }
    return generate_trees(1, n);
  }
}

What to improve

  • think if this method can solve the question.