Range Sum of BST - Problem
Range Sum of BST
You're given the root node of a Binary Search Tree (BST) and two integers
A Binary Search Tree has a special property: for any node, all values in the left subtree are smaller, and all values in the right subtree are larger. This property allows us to optimize our search and skip entire branches that are guaranteed to be outside our target range.
Goal: Calculate the sum of all nodes with values between
Example: If we have a BST with nodes [10, 5, 15, 3, 7, null, 18] and range [7, 15], we should sum up nodes with values 7, 10, and 15, giving us 32.
You're given the root node of a Binary Search Tree (BST) and two integers
low and high. Your task is to find the sum of all node values that fall within the inclusive range [low, high].A Binary Search Tree has a special property: for any node, all values in the left subtree are smaller, and all values in the right subtree are larger. This property allows us to optimize our search and skip entire branches that are guaranteed to be outside our target range.
Goal: Calculate the sum of all nodes with values between
low and high (inclusive).Example: If we have a BST with nodes [10, 5, 15, 3, 7, null, 18] and range [7, 15], we should sum up nodes with values 7, 10, and 15, giving us 32.
Input & Output
example_1.py — Basic BST Range Sum
$
Input:
root = [10,5,15,3,7,null,18], low = 7, high = 15
›
Output:
32
💡 Note:
Nodes 7, 10, and 15 are in the range [7, 15]. Sum = 7 + 10 + 15 = 32
example_2.py — Larger Range
$
Input:
root = [10,5,15,3,7,13,18,1,null,6], low = 6, high = 10
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Output:
23
💡 Note:
Nodes 6, 7, and 10 are in the range [6, 10]. Sum = 6 + 7 + 10 = 23
example_3.py — Single Node
$
Input:
root = [5], low = 3, high = 7
›
Output:
5
💡 Note:
Only one node with value 5, which is in range [3, 7], so sum = 5
Visualization
Tap to expand
Understanding the Visualization
1
Start at Root
Begin at the root section and check if current shelf's book price is in our target range
2
Make Smart Decisions
If current book is too expensive, ignore all shelves to the right (they'll be even more expensive)
3
Prune Branches
If current book is too cheap, ignore all shelves to the left (they'll be even cheaper)
4
Sum Valid Books
Only visit and sum books that could potentially be in our price range
Key Takeaway
🎯 Key Insight: BST property allows us to eliminate entire subtrees, making the search much more efficient than checking every single node!
Time & Space Complexity
Time Complexity
O(n)
We visit every node in the tree exactly once, where n is the total number of nodes
✓ Linear Growth
Space Complexity
O(h)
Recursion stack space, where h is the height of the tree (O(log n) for balanced BST, O(n) for skewed tree)
✓ Linear Space
Constraints
- The number of nodes in the tree is in the range [1, 2 × 104]
- 1 ≤ Node.val ≤ 105
- 1 ≤ low ≤ high ≤ 105
- All Node.val are unique (guaranteed BST property)
💡
Explanation
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