938. Range Sum of BST

Problem Statement

link: LeetCode.cn LeetCode

Given the root node of a binary search tree and two integers low and high, return the sum of values of all nodes with a value in the inclusive range [low, high].

Example:

Input: root = [10,5,15,3,7,null,18], low = 7, high = 15 Output: 32

Input: root = [10,5,15,3,7,13,18,1,null,6], low = 6, high = 10 Output: 23

Constraints:

The number of nodes in the tree is in the range [1, 2 * 10^4]. 1 <= Node.val <= 10^5 1 <= low <= high <= 10^5 All Node.val are unique.

Solution Approach

The algorithm traverses the binary search tree (BST) using either depth-first search (DFS) or breadth-first search (BFS) to accumulate the sum of node values that fall within the given range [low, high], efficiently skipping branches that do not contribute to the result.

Algorithm

1. Range Filtering: The algorithm efficiently skips subtrees that are outside the given range [low, high], avoiding unnecessary computation by checking node values before traversing their children.
2. Traversal Methods: Both depth-first search (DFS) and breadth-first search (BFS) approaches are utilized to visit nodes within the specified range, accumulating the sum of valid node values.
3. Early Stopping: The algorithm leverages BST properties, such as left and right subtrees’ value constraints, to stop traversing paths that cannot contain values within the range, improving performance.

Complexity

time complexity: O(n) space complexity: O(h)

Implement

    #     10 #     /\ #    5  15 #    /\  \ #  3   7  18 class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right
class Solution:
    def rangeSumBST(self, root: TreeNode, low: int, high: int) -> int:
        if not root:
            return 0
        if root.val > high:
            return self.rangeSumBST(root.left, low, high)
        if root.val < low:
            return self.rangeSumBST(root.right, low, high)
        return root.val + self.rangeSumBST(root.left, low, high) + self.rangeSumBST(root.right, low, high)

class Solution:
    def rangeSumBST(self, root: TreeNode, low: int, high: int) -> int:
        total = 0
        q = collections.deque([root])
        while q:
            node = q.popleft()
            if not node:
                continue
            if node.val > high:
                q.append(node.left)
            elif node.val < low:
                q.append(node.right)
            else:
                total += node.val
                q.append(node.left)
                q.append(node.right)

        return total

    
    

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