# 669. Trim a Binary Search Tree

Given a binary search tree and the lowest and highest boundaries as `L` and `R`, trim the tree so that all its elements lies in `[L, R]` (R >= L). You might need to change the root of the tree, so the result should return the new root of the trimmed binary search tree.

**Example 1:**\\

```
Input: 
    1
   / \
  0   2

  L = 1
  R = 2

Output: 
    1
      \
       2
```

**Example 2:**\\

```
Input: 
    3
   / \
  0   4
   \
    2
   /
  1

  L = 1
  R = 3

Output: 
      3
     / 
   2   
  /
 1
```

```cpp
// Recursion
TreeNode* trimBST(TreeNode* root, int L, int R) { // time: O(n); space: O(h)
    if (!root) return nullptr;
    if (root->val >= L && root->val <= R) {
        root->left = trimBST(root->left, L, R);
        root->right = trimBST(root->right, L, R);
    } else if (root->val < L) {
        root = trimBST(root->right, L, R);
    } else if (root->val > R) {
        root = trimBST(root->left, L, R);
    }
    return root;
}
```

```cpp
// Iteration
TreeNode* trimBST(TreeNode* root, int L, int R) { // time: O(n); space: O(1)
    if (!root) return nullptr;
    while (root->val < L || root->val > R) {
        root = root->val < L ? root->right : root->left;
    }
    TreeNode* cur = root;
    while (cur) {
        while (cur->left && cur->left->val < L) {
            cur->left = cur->left->right;
        }
        cur = cur->left;
    }
    cur = root;
    while (cur) {
        while (cur->right && cur->right->val > R) {
            cur->right = cur->right->left;
        }
        cur = cur->right;
    }
    return root;
}
```
