Given the root node of a binary search tree, return the sum of values of all nodes with value between L and R (inclusive).
The binary search tree is guaranteed to have unique values.
Example 1:
Input: root = [10,5,15,3,7,null,18], L = 7, R = 15
Output: 32
Example 2:
Input: root = [10,5,15,3,7,13,18,1,null,6], L = 6, R = 10
Output: 23
Note:
The number of nodes in the tree is at most 10000.
The final answer is guaranteed to be less than 2^31.
Solution:
Generally for a tree problem, we can think of either using a recursive traversal, or bfs.
We choose to use recursion here.
Knowing the property of BST and given a root node.
1. The exit condition is that when root is null, we return 0.
2. If root.val < L, we know all nodes in its left subtree are smaller than L. So we do not need to count that. We only consider its right subtree.
3. If root.val > R, we know all nodes in its right subtree are larger than R. So we do not need to count that. We only consider its left subtree.
4. If root.val is between L and R, we need to count this value. And we need to count both its left and right subtrees recursively.
The time complexity is O(n), assume n is the total number of nodes, since each node will be traversed only once.
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