## 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


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## Solution

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#### Approach #1: Recursion [Accepted]

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Intuition

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Let trim(node) be the desired answer for the subtree at that node. We can construct the answer recursively.

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Algorithm

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When , we know that the trimmed binary tree must occur to the left of the node. Similarly, when , the trimmed binary tree occurs to the right of the node. Otherwise, we will trim both sides of the tree.

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Complexity Analysis

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Time Complexity: , where is the total number of nodes in the given tree. We visit each node at most once.

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Space Complexity: . Even though we don\'t explicitly use any additional memory, the call stack of our recursion could be as large as the number of nodes in the worst case.

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Analysis written by: @awice

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